Author name cluster

Alejandro Ribeiro

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57 papers

2 author rows

ICML Conference 2025 Conference Paper

A Manifold Perspective on the Statistical Generalization of Graph Neural Networks

Zhiyang Wang
Juan Cerviño
Alejandro Ribeiro

Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still lacking. Previous GNN generalization bounds ignore the underlying graph structures, often leading to bounds that increase with the number of nodes – a behavior contrary to the one experienced in practice. In this paper, we take a manifold perspective to establish the statistical generalization theory of GNNs on graphs sampled from a manifold in the spectral domain. As demonstrated empirically, we prove that the generalization bounds of GNNs decrease linearly with the size of the graphs in the logarithmic scale, and increase linearly with the spectral continuity constants of the filter functions. Notably, our theory explains both node-level and graph-level tasks. Our result has two implications: i) guaranteeing the generalization of GNNs to unseen data over manifolds; ii) providing insights into the practical design of GNNs, i. e. , restrictions on the discriminability of GNNs are necessary to obtain a better generalization performance. We demonstrate our generalization bounds of GNNs using synthetic and multiple real-world datasets.

NeurIPS Conference 2025 Conference Paper

Alignment of Large Language Models with Constrained Learning

Botong Zhang
Shuo Li
Ignacio Hounie
Osbert Bastani
Dongsheng Ding
Alejandro Ribeiro

We study the problem of computing an optimal large language model (LLM) policy for the constrained alignment problem, where the goal is to maximize a primary reward objective while satisfying constraints on secondary utilities. Despite the popularity of Lagrangian-based LLM policy search in constrained alignment, iterative primal-dual methods often fail to converge, and non-iterative dual-based methods do not achieve optimality in the LLM parameter space. To address these challenges, we employ Lagrangian duality to develop an iterative dual-based alignment method that alternates between updating the LLM policy via Lagrangian maximization and updating the dual variable via dual descent. In theory, we characterize the primal-dual gap between the primal value in the distribution space and the dual value in the LLM parameter space. We further quantify the optimality gap of the learned LLM policies at near-optimal dual variables with respect to both the objective and the constraint functions. These results prove that dual-based alignment methods can find an optimal constrained LLM policy, up to an LLM parametrization gap. We demonstrate the effectiveness and merits of our approach through extensive experiments conducted on the PKU-SafeRLHF and Anthropic HH-RLHF datasets.

NeurIPS Conference 2025 Conference Paper

Composition and Alignment of Diffusion Models using Constrained Learning

Shervin Khalafi
Ignacio Hounie
Dongsheng Ding
Alejandro Ribeiro

Diffusion models have become prevalent in generative modeling due to their ability to sample from complex distributions. To improve the quality of generated samples and their compliance with user requirements, two commonly used methods are: (i) Alignment, which involves finetuning a diffusion model to align it with a reward; and (ii) Composition, which combines several pretrained diffusion models together, each emphasizing a desirable attribute in the generated outputs. However, trade-offs often arise when optimizing for multiple rewards or combining multiple models, as they can often represent competing properties. Existing methods cannot guarantee that the resulting model faithfully generates samples with all the desired properties. To address this gap, we propose a constrained optimization framework that unifies alignment and composition of diffusion models by enforcing that the aligned model satisfies reward constraints and/or remains close to each pretrained model. We provide a theoretical characterization of the solutions to the constrained alignment and composition problems and develop a Lagrangian-based primal-dual training algorithm to approximate these solutions. Empirically, we demonstrate our proposed approach in image generation, applying it to alignment and composition, and show that our aligned or composed model satisfies constraints effectively. Our implementation can be found at: https: //github. com/shervinkhalafi/constrained comp align.

ICRA Conference 2025 Conference Paper

Constrained Learning for Decentralized Multi-Objective Coverage Control

Juan Cerviño
Saurav Agarwal
Vijay Kumar 0001
Alejandro Ribeiro

The multi-objective coverage control problem requires a robot swarm to collaboratively provide sensor coverage to multiple heterogeneous importance density fields (IDFs) simultaneously. We pose this as an optimization problem with constraints and study two different formulations: (1) Fair coverage, where we minimize the maximum coverage cost for any field, promoting equitable resource distribution among all fields; and (2) Constrained coverage, where each field must be covered below a certain cost threshold, ensuring that critical areas receive adequate coverage according to predefined importance levels. We study the decentralized setting where robots have limited communication and local sensing capabilities, making the system more realistic, scalable, and robust. Given the complexity, we propose a novel decentralized constrained learning approach that combines primal-dual optimization with a Learnable Perception-Action-Communication (LPAC) neural network architecture. We show that the Lagrangian of the dual problem can be reformulated as a linear combination of the IDFs, enabling the LPAC policy to serve as a primal solver. We empirically demonstrate that the proposed method (i) significantly outperforms state-of-the-art decentralized controllers by 30% on average in terms of coverage cost, (ii) transfers well to larger environments with more robots, and (iii) is scalable in the number of IDFs and robots in the swarm.

AAAI Conference 2025 Conference Paper

Deterministic Policy Gradient Primal-Dual Methods for Continuous-Space Constrained MDPs

Sergio Rozada
Dongsheng Ding
Antonio G. Marques
Alejandro Ribeiro

We study the problem of computing deterministic optimal policies for constrained Markov decision processes (MDPs) with continuous state and action spaces, which are widely encountered in constrained dynamical systems. Designing deterministic policy gradient methods in continuous state and action spaces is particularly challenging due to the lack of enumerable state-action pairs and the adoption of deterministic policies, hindering the application of existing policy gradient methods for constrained MDPs. To this end, we develop a deterministic policy gradient primal-dual method to find an optimal deterministic policy with non-asymptotic convergence. Specifically, we leverage regularization of the Lagrangian of the constrained MDP to propose a deterministic policy gradient primal-dual (D-PGPD) algorithm that updates the deterministic policy via a quadratic-regularized gradient ascent step and the dual variable via a quadratic-regularized gradient descent step. We prove that the primal-dual iterates of D-PGPD converge at a sub-linear rate to an optimal regularized primal-dual pair. We instantiate D-PGPD with function approximation and prove that the primal-dual iterates of D-PGPD converge at a sub-linear rate to an optimal regularized primal-dual pair, up to a function approximation error. Furthermore, we demonstrate the effectiveness of our method in two continuous control problems: robot navigation and fluid control. To the best of our knowledge, this appears to be the first work that proposes a deterministic policy search method for continuous-space constrained MDPs.

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AAAI Conference 2025 Conference Paper

Generalization of Graph Neural Networks Is Robust to Model Mismatch

Zhiyang Wang
Juan Cerviño
Alejandro Ribeiro

Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. However, the current analysis of GNN generalization relies on the assumption that training and testing data are independent and identically distributed (i.i.d). This imposes limitations on the cases where a model mismatch exists when generating testing data. In this paper, we examine GNNs that operate on geometric graphs generated from manifold models, explicitly focusing on scenarios where there is a mismatch between manifold models generating training and testing data. Our analysis reveals the robustness of the GNN generalization in the presence of such model mismatch. This indicates that GNNs trained on graphs generated from a manifold can still generalize well to unseen nodes and graphs generated from a mismatched manifold. We attribute this mismatch to both node feature perturbations and edge perturbations within the generated graph. Our findings indicate that the generalization gap decreases as the number of nodes grows in the training graph while increasing with larger manifold dimension as well as larger mismatch. Importantly, we observe a trade-off between the generalization of GNNs and the capability to discriminate high-frequency components when facing a model mismatch. The most important practical consequence of this analysis is to shed light on the filter design of generalizable GNNs robust to model mismatch. We verify our theoretical findings with experiments on multiple real-world datasets.

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ICML Conference 2025 Conference Paper

GIVE: Structured Reasoning of Large Language Models with Knowledge Graph Inspired Veracity Extrapolation

Jiashu He
Mingyu Derek Ma
Jinxuan Fan
Dan Roth 0001
Wei Wang 0010
Alejandro Ribeiro

Existing approaches based on context prompting or reinforcement learning (RL) to improve the reasoning capacities of large language models (LLMs) depend on the LLMs’ internal knowledge to produce reliable Chain-Of-Thought (CoT). However, no matter the size of LLMs, certain problems cannot be resolved in a single forward pass. Meanwhile, agent-based reasoning systems require access to a comprehensive nonparametric knowledge base, which is often costly or not feasible for use in scientific and niche domains. We present Graph Inspired Veracity Extrapolation (GIVE), a novel reasoning method that merges parametric and non-parametric memories to improve accurate reasoning with minimal external input. GIVE guides the LLM agent to select the most pertinent expert data ($\textbf{observe}$), engage in query-specific associative thinking ($\textbf{reflect}$), and then synthesize this information to produce the final output ($\textbf{speak}$). Extensive experiments demonstrated the following benefits of our framework: (1) GIVE increases the performance of LLMs across various sizes. (2) In some scenarios, GIVE allows smaller LLMs to surpass larger, more sophisticated ones in scientific tasks ($\textbf{GPT3. 5T + GIVE > GPT4}$). (3) GIVE is effective on scientific and open-domain assessments. (4) GIVE is a training-free method that enables LLMs to tackle new problems that extend beyond their training data (up to $\textbf{43. 5}$% $\rightarrow$ $\textbf{88. 2}$% accuracy improvement). (5) GIVE allows LLM agents to reason using both restricted (very small) and noisy (very large) knowledge sources, accommodating knowledge graphs (KG) ranging from $\textbf{135}$ to more than $\textbf{840k}$ nodes. (6) The reasoning process involved in GIVE is fully interpretable. Our code is available at https: //github. com/Jason-Tree/GIVE

ICLR Conference 2025 Conference Paper

Learning Efficient Positional Encodings with Graph Neural Networks

Charilaos I. Kanatsoulis
Evelyn Choi
Stefanie Jegelka
Jure Leskovec
Alejandro Ribeiro

Positional encodings (PEs) are essential for effective graph representation learning because they provide position awareness in inherently position-agnostic transformer architectures and increase the expressive capacity of Graph Neural Networks (GNNs). However, designing powerful and efficient PEs for graphs poses significant challenges due to the absence of canonical node ordering and the scale of the graph. In this work, we identify four key properties that graph PEs should satisfy: stability, expressive power, scalability, and genericness. We find that existing eigenvector-based PE methods often fall short of jointly satisfying these criteria. To address this gap, we introduce PEARL, a novel framework of learnable PEs for graphs. Our primary insight is that message-passing GNNs function as nonlinear mappings of eigenvectors, enabling the design of GNN architectures for generating powerful and efficient PEs. A crucial challenge lies in initializing node features in a manner that is both expressive and permutation equivariant. We tackle this by initializing GNNs with random node inputs or standard basis vectors, thereby unlocking the expressive power of message-passing operations, while employing statistical pooling functions to maintain permutation equivariance. Our analysis demonstrates that PEARL approximates equivariant functions of eigenvectors with linear complexity, while rigorously establishing its stability and high expressive power. Experimental evaluations show that PEARL outperforms lightweight versions of eigenvector-based PEs and achieves comparable performance to full eigenvector-based PEs, but with one or two orders of magnitude lower complexity. Our code is available at https://github.com/ehejin/Pearl-PE.

ICLR Conference 2025 Conference Paper

LoRanPAC: Low-rank Random Features and Pre-trained Models for Bridging Theory and Practice in Continual Learning

Liangzu Peng
Juan Elenter
Joshua Agterberg
Alejandro Ribeiro
René Vidal

The goal of continual learning (CL) is to train a model that can solve multiple tasks presented sequentially. Recent CL approaches have achieved strong performance by leveraging large pre-trained models that generalize well to downstream tasks. However, such methods lack theoretical guarantees, making them prone to unexpected failures. Conversely, principled CL approaches often fail to achieve competitive performance. In this work, we aim to bridge this gap between theory and practice by designing a simple CL method that is theoretically sound and highly performant. Specifically, we lift pre-trained features into a higher dimensional space and formulate an over-parametrized minimum-norm least-squares problem. We find that the lifted features are highly ill-conditioned, potentially leading to large training errors (numerical instability) and increased generalization errors. We address these challenges by continually truncating the singular value decomposition of the lifted features. Our approach, termed LoRanPAC, is stable with respect to the choice of hyperparameters, can handle hundreds of tasks, and outperforms state-of-the-art CL methods on multiple datasets. Importantly, our method satisfies a recurrence relation throughout its continual learning process, which allows us to prove it maintains small training and test errors by appropriately truncating a fraction of SVD factors. This results in a stable continual learning method with strong empirical performance and theoretical guarantees. Code available: \url{https://github.com/liangzu/loranpac}.

NeurIPS Conference 2024 Conference Paper

Constrained Diffusion Models via Dual Training

Shervin Khalafi
Dongsheng Ding
Alejandro Ribeiro

Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes are prone to generating samples that reflect biases in a training dataset. To address this issue, we develop constrained diffusion models by imposing diffusion constraints based on desired distributions that are informed by requirements. Specifically, we cast the training of diffusion models under requirements as a constrained distribution optimization problem that aims to reduce the distribution difference between original and generated data while obeying constraints on the distribution of generated data. We show that our constrained diffusion models generate new data from a mixture data distribution that achieves the optimal trade-off among objective and constraints. To train constrained diffusion models, we develop a dual training algorithm and characterize the optimality of the trained constrained diffusion model. We empirically demonstrate the effectiveness of our constrained models in two constrained generation tasks: (i) we consider a dataset with one or more underrepresented classes where we train the model with constraints to ensure fairly sampling from all classes during inference; (ii) we fine-tune a pre-trained diffusion model to sample from a new dataset while avoiding overfitting.

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ICLR Conference 2024 Conference Paper

Counting Graph Substructures with Graph Neural Networks

Charilaos I. Kanatsoulis
Alejandro Ribeiro

Graph Neural Networks (GNNs) are powerful representation learning tools that have achieved remarkable performance in various downstream tasks. However, there are still open questions regarding their ability to count and list substructures, which play a crucial role in biological and social networks. In this work, we fill this gap and characterize the representation {and generalization} power of GNNs in terms of their ability to produce powerful representations that count substructures. In particular, we study the message-passing operations of GNNs with random node input in a novel fashion, and show how they can produce equivariant representations that are associated with high-order statistical moments. Using these representations, we prove that GNNs can learn how to count cycles, {cliques}, quasi-cliques, and the number of connected components in a graph. We also provide new insights into the generalization capacity of GNNs. Our analysis is constructive and enables the design of a generic GNN architecture that shows remarkable performance in four distinct tasks: cycle detection, cycle counting, graph classification, and molecular property prediction.

ICML Conference 2024 Conference Paper

Loss Shaping Constraints for Long-Term Time Series Forecasting

Ignacio Hounie
Javier Porras-Valenzuela
Alejandro Ribeiro

Several applications in time series forecasting require predicting multiple steps ahead. Despite the vast amount of literature in the topic, both classical and recent deep learning based approaches have mostly focused on minimising performance averaged over the predicted window. We observe that this can lead to disparate distributions of errors across forecasting steps, especially for recent transformer architectures trained on popular forecasting benchmarks. That is, optimising performance on average can lead to undesirably large errors at specific time-steps. In this work, we present a Constrained Learning approach for long-term time series forecasting that aims to find the best model in terms of average performance that respects a user-defined upper bound on the loss at each time-step. We call our approach loss shaping constraints because it imposes constraints on the loss at each time step, and leverage recent duality results to show that despite its non-convexity, the resulting problem has a bounded duality gap. We propose a practical primal-dual algorithm to tackle it, and demonstrate that the proposed approach exhibits competitive average performance in time series forecasting benchmarks, while shaping the distribution of errors across the predicted window.

ICLR Conference 2024 Conference Paper

Near-Optimal Solutions of Constrained Learning Problems

Juan Elenter
Luiz F. O. Chamon
Alejandro Ribeiro

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

ICML Conference 2024 Conference Paper

Neural Tangent Kernels Motivate Cross-Covariance Graphs in Neural Networks

Shervin Khalafi
Saurabh Sihag
Alejandro Ribeiro

Neural tangent kernels (NTKs) provide a theoretical regime to analyze the learning and generalization behavior of over-parametrized neural networks. For a supervised learning task, the association between the eigenvectors of the NTK and given data (a concept referred to as alignment in this paper) can govern the rate of convergence of gradient descent, as well as generalization to unseen data. Building upon this concept and leveraging the structure of NTKs for graph neural networks (GNNs), we theoretically investigate NTKs and alignment, where our analysis reveals that optimizing the alignment translates to optimizing the graph representation or the graph shift operator (GSO) in a GNN. Our results further establish theoretical guarantees on the optimality of the alignment for a two-layer GNN and these guarantees are characterized by the graph shift operator being a function of the cross-covariance between the input and the output data. The theoretical insights drawn from the analysis of NTKs are validated by our experiments focused on a multi-variate time series prediction task for a publicly available dataset. Specifically, they demonstrate that GNN-based learning models that operate on the cross-covariance matrix indeed outperform those that operate on the covariance matrix estimated from only the input data.

ICRA Conference 2024 Conference Paper

Opportunistic Communication in Robot Teams

Daniel Mox
Kashish Garg
Alejandro Ribeiro
Vijay Kumar 0001

In this paper we present a new approach to Mobile Infrastructure on Demand (MID) where a dedicated team of robots creates and sustains a wireless network that satisfies the communication requirements of a different team of task-oriented robots seeking to coordinate their actions in the absence of existing communication infrastructure. Different from previous works, our approach forgoes heuristics for network performance such as algebraic-connectivity or network flow optimizations and instead positions communication support robots to directly maximize the probability of packet delivery by the underlying opportunistic routing protocol. Our system is task agnostic and practical to implement and operate on robots equipped with off-the-shelf WiFi radios. We demonstrate this through a set of experiments showing our MID system maintaining the delivery of critical mission data in a situational awareness setting and enabling foraging robots to effectively coordinate their actions during multi-robot exploration.

ICML Conference 2023 Conference Paper

Automatic Data Augmentation via Invariance-Constrained Learning

Ignacio Hounie
Luiz F. O. Chamon
Alejandro Ribeiro

Underlying data structures, such as symmetries or invariance to transformations, are often exploited to improve the solution of learning tasks. However, embedding these properties in models or learning algorithms can be challenging and computationally intensive. Data augmentation, on the other hand, induces these symmetries during training by applying multiple transformations to the input data. Despite its ubiquity, its effectiveness depends on the choices of which transformations to apply, when to do so, and how often. In fact, there is both empirical and theoretical evidence that the indiscriminate use of data augmentation can introduce biases that outweigh its benefits. This work tackles these issues by automatically adapting the data augmentation while solving the learning task. To do so, it formulates data augmentation as an invariance constrained learning problem and leverages Monte Carlo Markov Chain (MCMC) sampling to solve it. The result is an algorithm that not only does away with a priori searches for augmentation distributions, but also dynamically controls if and when data augmentation is applied. We validate empirically our theoretical developments in automatic data augmentation benchmarks for CIFAR and ImageNet-100 datasets. Furthermore, our experiments show how this approach can be used to gather insights on the actual symmetries underlying a learning task.

NeurIPS Conference 2023 Conference Paper

Explainable Brain Age Prediction using coVariance Neural Networks

Saurabh Sihag
Gonzalo Mateos
Corey McMillan
Alejandro Ribeiro

In computational neuroscience, there has been an increased interest in developing machine learning algorithms that leverage brain imaging data to provide estimates of "brain age" for an individual. Importantly, the discordance between brain age and chronological age (referred to as "brain age gap") can capture accelerated aging due to adverse health conditions and therefore, can reflect increased vulnerability towards neurological disease or cognitive impairments. However, widespread adoption of brain age for clinical decision support has been hindered due to lack of transparency and methodological justifications in most existing brain age prediction algorithms. In this paper, we leverage coVariance neural networks (VNN) to propose an explanation-driven and anatomically interpretable framework for brain age prediction using cortical thickness features. Specifically, our brain age prediction framework extends beyond the coarse metric of brain age gap in Alzheimer’s disease (AD) and we make two important observations: (i) VNNs can assign anatomical interpretability to elevated brain age gap in AD by identifying contributing brain regions, (ii) the interpretability offered by VNNs is contingent on their ability to exploit specific eigenvectors of the anatomical covariance matrix. Together, these observations facilitate an explainable and anatomically interpretable perspective to the task of brain age prediction.

NeurIPS Conference 2023 Conference Paper

Last-Iterate Convergent Policy Gradient Primal-Dual Methods for Constrained MDPs

Dongsheng Ding
Chen-Yu Wei
Kaiqing Zhang
Alejandro Ribeiro

We study the problem of computing an optimal policy of an infinite-horizon discounted constrained Markov decision process (constrained MDP). Despite the popularity of Lagrangian-based policy search methods used in practice, the oscillation of policy iterates in these methods has not been fully understood, bringing out issues such as violation of constraints and sensitivity to hyper-parameters. To fill this gap, we employ the Lagrangian method to cast a constrained MDP into a constrained saddle-point problem in which max/min players correspond to primal/dual variables, respectively, and develop two single-time-scale policy-based primal-dual algorithms with non-asymptotic convergence of their policy iterates to an optimal constrained policy. Specifically, we first propose a regularized policy gradient primal-dual (RPG-PD) method that updates the policy using an entropy-regularized policy gradient, and the dual variable via a quadratic-regularized gradient ascent, simultaneously. We prove that the policy primal-dual iterates of RPG-PD converge to a regularized saddle point with a sublinear rate, while the policy iterates converge sublinearly to an optimal constrained policy. We further instantiate RPG-PD in large state or action spaces by including function approximation in policy parametrization, and establish similar sublinear last-iterate policy convergence. Second, we propose an optimistic policy gradient primal-dual (OPG-PD) method that employs the optimistic gradient method to update primal/dual variables, simultaneously. We prove that the policy primal-dual iterates of OPG-PD converge to a saddle point that contains an optimal constrained policy, with a linear rate. To the best of our knowledge, this work appears to be the first non-asymptotic policy last-iterate convergence result for single-time-scale algorithms in constrained MDPs. We further validate the merits and the effectiveness of our methods in computational experiments.

ICML Conference 2023 Conference Paper

Learning Globally Smooth Functions on Manifolds

Juan Cerviño
Luiz F. O. Chamon
Benjamin D. Haeffele
René Vidal
Alejandro Ribeiro

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives. Our code is available at https: //github. com/JuanCervino/smoothbench.

TMLR Journal 2023 Journal Article

Learning Graph Structure from Convolutional Mixtures

Max Wasserman
Saurabh Sihag
Gonzalo Mateos
Alejandro Ribeiro

Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved, noisy, or dynamic, the problem of inferring graph structure from data becomes relevant. In this paper, we postulate a graph convolutional relationship between the observed and latent graphs, and formulate the graph structure learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods or iterative optimization solutions, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN). GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive as well as node permutation equivariant. We corroborate GDN's superior graph learning performance and its generalization to larger graphs using synthetic data in supervised settings. Moreover, we demonstrate the robustness and representation power of GDNs on real world neuroimaging and social network datasets.

NeurIPS Conference 2023 Conference Paper

Resilient Constrained Learning

Ignacio Hounie
Alejandro Ribeiro
Luiz F. O. Chamon

When deploying machine learning solutions, they must satisfy multiple requirements beyond accuracy, such as fairness, robustness, or safety. These requirements are imposed during training either implicitly, using penalties, or explicitly, using constrained optimization methods based on Lagrangian duality. Either way, specifying requirements is hindered by the presence of compromises and limited prior knowledge about the data. Furthermore, their impact on performance can often only be evaluated by actually solving the learning problem. This paper presents a constrained learning approach that adapts the requirements while simultaneously solving the learning task. To do so, it relaxes the learning constraints in a way that contemplates how much they affect the task at hand by balancing the performance gains obtained from the relaxation against a user-defined cost of that relaxation. We call this approach resilient constrained learning after the term used to describe ecological systems that adapt to disruptions by modifying their operation. We show conditions under which this balance can be achieved and introduce a practical algorithm to compute it, for which we derive approximation and generalization guarantees. We showcase the advantages of this resilient learning method in image classification tasks involving multiple potential invariances and in federated learning under distribution shift.

IROS Conference 2023 Conference Paper

Robust Localization of Aerial Vehicles via Active Control of Identical Ground Vehicles

Igor Spasojevic
Xu Liu 0007
Ankit Prabhu
Alejandro Ribeiro
George J. Pappas
Vijay Kumar 0001

This paper addresses the problem of active collaborative localization in heterogeneous robot teams with unknown data association. It involves positioning a small number of identical unmanned ground vehicles (UGVs) at desired positions so that an unmanned aerial vehicle (UAV) can, through unlabelled measurements of UGVs, uniquely determine its global pose. We model the problem as a sequential two player game, in which the first player positions the UGVs and the second identifies the two distinct hypothetical poses of the UAV at which the sets of measurements to the UGVs differ by as little as possible. We solve the underlying problem from the vantage point of the first player for a subclass of measurement models using a mixture of local optimization and exhaustive search procedures. Real-world experiments with a team of UAV and UGVs show that our method can achieve centimeter-level global localization accuracy. We also show that our method consistently outperforms random positioning of UGVs by a large margin, with as much as a 90% reduction in position and angular estimation error. Our method can tolerate a significant amount of random as well as non-stochastic measurement noise. This indicates its potential for reliable state estimation on board size, weight, and power (SWaP) constrained UAVs. This work enables robust localization in perceptually-challenged GPS-denied environments, thus paving the road for large-scale multi-robot navigation and mapping.

NeurIPS Conference 2022 Conference Paper

A Lagrangian Duality Approach to Active Learning

Juan Elenter
Navid Naderializadeh
Alejandro Ribeiro

We consider the pool-based active learning problem, where only a subset of the training data is labeled, and the goal is to query a batch of unlabeled samples to be labeled so as to maximally improve model performance. We formulate the problem using constrained learning, where a set of constraints bounds the performance of the model on labeled samples. Considering a primal-dual approach, we optimize the primal variables, corresponding to the model parameters, as well as the dual variables, corresponding to the constraints. As each dual variable indicates how significantly the perturbation of the respective constraint affects the optimal value of the objective function, we use it as a proxy of the informativeness of the corresponding training sample. Our approach, which we refer to as Active Learning via Lagrangian dualitY, or ALLY, leverages this fact to select a diverse set of unlabeled samples with the highest estimated dual variables as our query set. We demonstrate the benefits of our approach in a variety of classification and regression tasks and discuss its limitations depending on the capacity of the model used and the degree of redundancy in the dataset. We also examine the impact of the distribution shift induced by active sampling and show that ALLY can be used in a generative mode to create novel, maximally-informative samples.

ICLR Conference 2022 Conference Paper

An Agnostic Approach to Federated Learning with Class Imbalance

Zebang Shen
Juan Cerviño
Seyed Hamed Hassani
Alejandro Ribeiro

Federated Learning (FL) has emerged as the tool of choice for training deep models over heterogeneous and decentralized datasets. As a reflection of the experiences from different clients, severe class imbalance issues are observed in real-world FL problems. Moreover, there exists a drastic mismatch between the imbalances from the local and global perspectives, i.e. a local majority class can be the minority of the population. Additionally, the privacy requirement of FL poses an extra challenge, as one should handle class imbalance without identifying the minority class. In this paper we propose a novel agnostic constrained learning formulation to tackle the class imbalance problem in FL, without requiring further information beyond the standard FL objective. A meta algorithm, CLIMB, is designed to solve the target optimization problem, with its convergence property analyzed under certain oracle assumptions. Through an extensive empirical study over various data heterogeneity and class imbalance configurations, we showcase that CLIMB considerably improves the performance in the minority class without compromising the overall accuracy of the classifier, which significantly outperforms previous arts. In fact, we observe the greatest performance boost in the most difficult scenario where every client only holds data from one class. The code can be found here https://github.com/shenzebang/Federated-Learning-Pytorch.

NeurIPS Conference 2022 Conference Paper

coVariance Neural Networks

Saurabh Sihag
Gonzalo Mateos
Corey McMillan
Alejandro Ribeiro

Graph neural networks (GNN) are an effective framework that exploit inter-relationships within graph-structured data for learning. Principal component analysis (PCA) involves the projection of data on the eigenspace of the covariance matrix and draws similarities with the graph convolutional filters in GNNs. Motivated by this observation, we study a GNN architecture, called coVariance neural network (VNN), that operates on sample covariance matrices as graphs. We theoretically establish the stability of VNNs to perturbations in the covariance matrix, thus, implying an advantage over standard PCA-based data analysis approaches that are prone to instability due to principal components associated with close eigenvalues. Our experiments on real-world datasets validate our theoretical results and show that VNN performance is indeed more stable than PCA-based statistical approaches. Moreover, our experiments on multi-resolution datasets also demonstrate that VNNs are amenable to transferability of performance over covariance matrices of different dimensions; a feature that is infeasible for PCA-based approaches.

ICRA Conference 2022 Conference Paper

Coverage Control in Multi-Robot Systems via Graph Neural Networks

Walker Gosrich
Siddharth Mayya
Rebecca Li
James Paulos
Mark Yim
Alejandro Ribeiro
Vijay Kumar 0001

This paper develops a decentralized approach to mobile sensor coverage by a multi-robot system. We consider a scenario where a team of robots with limited sensing range must position itself to effectively detect events of interest in a region characterized by areas of varying importance. Towards this end, we develop a decentralized control policy for the robots-realized via a Graph Neural Network-which uses inter-robot communication to leverage non-local information for control decisions. By explicitly sharing information between multi-hop neighbors, the decentralized controller achieves a higher quality of coverage when compared to classical approaches that do not communicate and leverage only local information available to each robot. Simulated experiments demonstrate the efficacy of multi-hop communication for multi-robot coverage and evaluate the scalability and transferability of the learning-based controllers.

ICLR Conference 2022 Conference Paper

Space-Time Graph Neural Networks

Samar Hadou
Charilaos I. Kanatsoulis
Alejandro Ribeiro

We introduce space-time graph neural network (ST-GNN), a novel GNN architecture, tailored to jointly process the underlying space-time topology of time-varying network data. The cornerstone of our proposed architecture is the composition of time and graph convolutional filters followed by pointwise nonlinear activation functions. We introduce a generic definition of convolution operators that mimic the diffusion process of signals over its underlying support. On top of this definition, we propose space-time graph convolutions that are built upon a composition of time and graph shift operators. We prove that ST-GNNs with multivariate integral Lipschitz filters are stable to small perturbations in the underlying graphs as well as small perturbations in the time domain caused by time warping. Our analysis shows that small variations in the network topology and time evolution of a system does not significantly affect the performance of ST-GNNs. Numerical experiments with decentralized control systems showcase the effectiveness and stability of the proposed ST-GNNs.

NeurIPS Conference 2021 Conference Paper

Adversarial Robustness with Semi-Infinite Constrained Learning

Alexander Robey
Luiz Chamon
George J. Pappas
Hamed Hassani
Alejandro Ribeiro

Despite strong performance in numerous applications, the fragility of deep learning to input perturbations has raised serious questions about its use in safety-critical domains. While adversarial training can mitigate this issue in practice, state-of-the-art methods are increasingly application-dependent, heuristic in nature, and suffer from fundamental trade-offs between nominal performance and robustness. Moreover, the problem of finding worst-case perturbations is non-convex and underparameterized, both of which engender a non-favorable optimization landscape. Thus, there is a gap between the theory and practice of robust learning, particularly with respect to when and why adversarial training works. In this paper, we take a constrained learning approach to address these questions and to provide a theoretical foundation for robust learning. In particular, we leverage semi-infinite optimization and non-convex duality theory to show that adversarial training is equivalent to a statistical problem over perturbation distributions. Notably, we show that a myriad of previous robust training techniques can be recovered for particular, sub-optimal choices of these distributions. Using these insights, we then propose a hybrid Langevin Markov Chain Monte Carlo approach for which several common algorithms (e. g. , PGD) are special cases. Finally, we show that our approach can mitigate the trade-off between nominal and robust performance, yielding state-of-the-art results on MNIST and CIFAR-10. Our code is available at: https: //github. com/arobey1/advbench.

IROS Conference 2021 Conference Paper

Learning Connectivity for Data Distribution in Robot Teams

Ekaterina I. Tolstaya
Landon Butler
Daniel Mox
James Paulos
Vijay Kumar 0001
Alejandro Ribeiro

Many algorithms for control of multi-robot teams operate under the assumption that low-latency, global state information necessary to coordinate agent actions can readily be disseminated among the team. However, in harsh environments with no existing communication infrastructure, robots must form ad-hoc networks, forcing the team to operate in a distributed fashion. To overcome this challenge, we propose a task-agnostic, decentralized, low-latency method for data distribution in ad-hoc networks using Graph Neural Networks (GNN). Our approach enables multi-agent algorithms based on global state information to function by ensuring it is available at each robot. To do this, agents glean information about the topology of the network from packet transmissions and feed it to a GNN running locally which instructs the agent when and where to transmit the latest state information. We train the distributed GNN communication policies via reinforcement learning using the average Age of Information as the reward function and show that it improves training stability compared to task-specific reward functions. Our approach performs favorably compared to industry-standard methods for data distribution such as random flooding and round robin. We also show that the trained policies generalize to larger teams of both static and mobile agents.

IROS Conference 2021 Conference Paper

Multi-Robot Coverage and Exploration using Spatial Graph Neural Networks

Ekaterina I. Tolstaya
James Paulos
Vijay Kumar 0001
Alejandro Ribeiro

The multi-robot coverage problem is an essential building block for systems that perform tasks like inspection, exploration, or search and rescue. We discretize the coverage problem to induce a spatial graph of locations and represent robots as nodes in the graph. Then, we train a Graph Neural Network controller that leverages the spatial equivariance of the task to imitate an expert open-loop routing solution. This approach generalizes well to much larger maps and larger teams that are intractable for the expert. In particular, the model generalizes effectively to a simulation of ten quadrotors and dozens of buildings in an urban setting. We also demonstrate the GNN controller can surpass planning-based approaches in an exploration task.

JMLR Journal 2020 Journal Article

A Class of Parallel Doubly Stochastic Algorithms for Large-Scale Learning

Aryan Mokhtari
Alec Koppel
Martin Takac
Alejandro Ribeiro

We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We call the algorithm random parallel because it utilizes multiple parallel processors to operate on a randomly chosen subset of blocks of the feature vector. RAPSA is doubly stochastic since each processor utilizes a random set of functions to compute the stochastic gradient associated with a randomly chosen sets of variable coordinates. Algorithms that are parallel in either of these dimensions exist, but RAPSA is the first attempt at a methodology that is parallel in both the selection of blocks and the selection of elements of the training set. In RAPSA, processors utilize the randomly chosen functions to compute the stochastic gradient component associated with a randomly chosen block. The technical contribution of this paper is to show that this minimally coordinated algorithm converges to the optimal classifier when the training objective is strongly convex. Moreover, we present an accelerated version of RAPSA (ARAPSA) that incorporates the objective function curvature information by premultiplying the descent direction by a Hessian approximation matrix. We further extend the results for asynchronous settings and show that if the processors perform their updates without any coordination the algorithms are still convergent to the optimal argument. RAPSA and its extensions are then numerically evaluated on a linear estimation problem and a binary image classification task using the MNIST handwritten digit dataset. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

IROS Conference 2020 Conference Paper

Graph Neural Networks for Decentralized Multi-Robot Path Planning

Qingbiao Li
Fernando Gama
Alejandro Ribeiro
Amanda Prorok

Effective communication is key to successful, decentralized, multi-robot path planning. Yet, it is far from obvious what information is crucial to the task at hand, and how and when it must be shared among robots. To side-step these issues and move beyond hand-crafted heuristics, we propose a combined model that automatically synthesizes local communication and decision-making policies for robots navigating in constrained workspaces. Our architecture is composed of a convolutional neural network (CNN) that extracts adequate features from local observations, and a graph neural network (GNN) that communicates these features among robots. We train the model to imitate an expert algorithm, and use the resulting model online in decentralized planning involving only local communication and local observations. We evaluate our method in simulations by navigating teams of robots to their destinations in 2D cluttered workspaces. We measure the success rates and sum of costs over the planned paths. The results show a performance close to that of our expert algorithm, demonstrating the validity of our approach. In particular, we show our model's capability to generalize to previously unseen cases (involving larger environments and larger robot teams).

NeurIPS Conference 2020 Conference Paper

Graphon Neural Networks and the Transferability of Graph Neural Networks

Luana Ruiz
Luiz Chamon
Alejandro Ribeiro

Graph neural networks (GNNs) rely on graph convolutions to extract local features from network data. These graph convolutions combine information from adjacent nodes using coefficients that are shared across all nodes. Since these coefficients are shared and do not depend on the graph, one can envision using the same coefficients to define a GNN on another graph. This motivates analyzing the transferability of GNNs across graphs. In this paper we introduce graphon NNs as limit objects of GNNs and prove a bound on the difference between the output of a GNN and its limit graphon-NN. This bound vanishes with growing number of nodes if the graph convolutional filters are bandlimited in the graph spectral domain. This result establishes a tradeoff between discriminability and transferability of GNNs.

ICRA Conference 2020 Conference Paper

Mobile Wireless Network Infrastructure on Demand

Daniel Mox
Miguel Calvo-Fullana
Mikhail Gerasimenko
Jonathan Fink
Vijay Kumar 0001
Alejandro Ribeiro

In this work, we introduce Mobile Wireless Infrastructure on Demand: a framework for providing wireless connectivity to multi-robot teams via autonomously reconfiguring ad-hoc networks. In many cases, previous multi-agent systems either assumed the availability of existing communication infrastructure or were required to create a network in addition to completing their objective. Instead our system explicitly assumes the responsibility of creating and sustaining a wireless network capable of satisfying end-to-end communication requirements of a team of agents, called the task team, performing an arbitrary objective. To accomplish this goal, we propose a joint optimization framework that alternates between finding optimal network routes to support data flows between the task agents and improving the performance of the network by repositioning a collection of mobile relay nodes referred to as the network team. We demonstrate our approach with simulations and experiments wherein wireless connectivity is provided to patrolling task agents.

NeurIPS Conference 2020 Conference Paper

Probably Approximately Correct Constrained Learning

Luiz Chamon
Alejandro Ribeiro

As learning solutions reach critical applications in social, industrial, and medical domains, the need to curtail their behavior has become paramount. There is now ample evidence that without explicit tailoring, learning can lead to biased, unsafe, and prejudiced solutions. To tackle these problems, we develop a generalization theory of constrained learning based on the probably approximately correct (PAC) learning framework. In particular, we show that imposing requirements does not make a learning problem harder in the sense that any PAC learnable class is also PAC constrained learnable using a constrained counterpart of the empirical risk minimization (ERM) rule. For typical parametrized models, however, this learner involves solving a constrained non-convex optimization program for which even obtaining a feasible solution is challenging. To overcome this issue, we prove that under mild conditions the empirical dual problem of constrained learning is also a PAC constrained learner that now leads to a practical constrained learning algorithm based solely on solving unconstrained problems. We analyze the generalization properties of this solution and use it to illustrate how constrained learning can address problems in fair and robust classification.

NeurIPS Conference 2020 Conference Paper

Sinkhorn Barycenter via Functional Gradient Descent

Zebang Shen
Zhenfu Wang
Alejandro Ribeiro
Hamed Hassani

In this paper, we consider the problem of computing the barycenter of a set of probability distributions under the Sinkhorn divergence. This problem has recently found applications across various domains, including graphics, learning, and vision, as it provides a meaningful mechanism to aggregate knowledge. Unlike previous approaches which directly operate in the space of probability measures, we recast the Sinkhorn barycenter problem as an instance of unconstrained functional optimization and develop a novel functional gradient descent method named \texttt{Sinkhorn Descent} (\texttt{SD}). We prove that \texttt{SD} converges to a stationary point at a sublinear rate, and under reasonable assumptions, we further show that it asymptotically finds a global minimizer of the Sinkhorn barycenter problem. Moreover, by providing a mean-field analysis, we show that \texttt{SD} preserves the {weak convergence} of empirical measures. Importantly, the computational complexity of \texttt{SD} scales linearly in the dimension $d$ and we demonstrate its scalability by solving a $100$-dimensional Sinkhorn barycenter problem.

NeurIPS Conference 2020 Conference Paper

Sinkhorn Natural Gradient for Generative Models

Zebang Shen
Zhenfu Wang
Alejandro Ribeiro
Hamed Hassani

We consider the problem of minimizing a functional over a parametric family of probability measures, where the parameterization is characterized via a push-forward structure. An important application of this problem is in training generative adversarial networks. In this regard, we propose a novel Sinkhorn Natural Gradient (SiNG) algorithm which acts as a steepest descent method on the probability space endowed with the Sinkhorn divergence. We show that the Sinkhorn information matrix (SIM), a key component of SiNG, has an explicit expression and can be evaluated accurately in complexity that scales logarithmically with respect to the desired accuracy. This is in sharp contrast to existing natural gradient methods that can only be carried out approximately. Moreover, in practical applications when only Monte-Carlo type integration is available, we design an empirical estimator for SIM and provide the stability analysis. In our experiments, we quantitatively compare SiNG with state-of-the-art SGD-type solvers on generative tasks to demonstrate its efficiency and efficacy of our method.

ICRA Conference 2020 Conference Paper

Sufficiently Accurate Model Learning

Clark Zhang
Arbaaz Khan
Santiago Paternain
Alejandro Ribeiro

Modeling how a robot interacts with the environment around it is an important prerequisite for designing control and planning algorithms. In fact, the performance of controllers and planners is highly dependent on the quality of the model. One popular approach is to learn data driven models in order to compensate for inaccurate physical measurements and to adapt to systems that evolve over time. In this paper, we investigate a method to regularize model learning techniques to provide better error characteristics for traditional control and planning algorithms. This work proposes learning "Sufficiently Accurate" models of dynamics using a primal-dual method that can explicitly enforce constraints on the error in pre-defined parts of the state-space. The result of this method is that the error characteristics of the learned model is more predictable and can be better utilized by planning and control algorithms. The characteristics of Sufficiently Accurate models are analyzed through experiments on a simulated ball paddle system.

NeurIPS Conference 2019 Conference Paper

Constrained Reinforcement Learning Has Zero Duality Gap

Santiago Paternain
Luiz Chamon
Miguel Calvo-Fullana
Alejandro Ribeiro

Autonomous agents must often deal with conflicting requirements, such as completing tasks using the least amount of time/energy, learning multiple tasks, or dealing with multiple opponents. In the context of reinforcement learning~(RL), these problems are addressed by (i)~designing a reward function that simultaneously describes all requirements or (ii)~combining modular value functions that encode them individually. Though effective, these methods have critical downsides. Designing good reward functions that balance different objectives is challenging, especially as the number of objectives grows. Moreover, implicit interference between goals may lead to performance plateaus as they compete for resources, particularly when training on-policy. Similarly, selecting parameters to combine value functions is at least as hard as designing an all-encompassing reward, given that the effect of their values on the overall policy is not straightforward. The later is generally addressed by formulating the conflicting requirements as a constrained RL problem and solved using Primal-Dual methods. These algorithms are in general not guaranteed to converge to the optimal solution since the problem is not convex. This work provides theoretical support to these approaches by establishing that despite its non-convexity, this problem has zero duality gap, i. e. , it can be solved exactly in the dual domain, where it becomes convex. Finally, we show this result basically holds if the policy is described by a good parametrization~(e. g. , neural networks) and we connect this result with primal-dual algorithms present in the literature and we establish the convergence to the optimal solution.

ICML Conference 2019 Conference Paper

Hessian Aided Policy Gradient

Zebang Shen
Alejandro Ribeiro
Seyed Hamed Hassani
Hui Qian 0001
Chao Mi

Reducing the variance of estimators for policy gradient has long been the focus of reinforcement learning research. While classic algorithms like REINFORCE find an $\epsilon$-approximate first-order stationary point in $\OM({1}/{\epsilon^4})$ random trajectory simulations, no provable improvement on the complexity has been made so far. This paper presents a Hessian aided policy gradient method with the first improved sample complexity of $\OM({1}/{\epsilon^3})$. While our method exploits information from the policy Hessian, it can be implemented in linear time with respect to the parameter dimension and is hence applicable to sophisticated DNN parameterization. Simulations on standard tasks validate the efficiency of our method.

IROS Conference 2019 Conference Paper

Inverse Optimal Planning for Air Traffic Control

Ekaterina I. Tolstaya
Alejandro Ribeiro
Vijay Kumar 0001
Ashish Kapoor

We envision a system that concisely describes the rules of air traffic control, assists human operators and supports dense autonomous air traffic around commercial airports. We develop a method to learn the rules of air traffic control from real data as a cost function via maximum entropy inverse reinforcement learning. This cost function is used as a penalty for a search-based motion planning method that discretizes both the control and the state space. We illustrate the methodology by showing that our approach can learn to imitate the airport arrival routes and separation rules of dense commercial air traffic. The resulting trajectories are shown to be safe, feasible, and efficient.

IROS Conference 2019 Conference Paper

Learning Safe Unlabeled Multi-Robot Planning with Motion Constraints

Arbaaz Khan
Chi Zhang
Shuo Li
Jiayue Wu
Brent Schlotfeldt
Sarah Y. Tang
Alejandro Ribeiro
Osbert Bastani

In this paper, we present a learning approach to goal assignment and trajectory planning for unlabeled robots operating in 2D, obstacle-filled workspaces. More specifically, we tackle the unlabeled multi-robot motion planning problem with motion constraints as a multi-agent reinforcement learning problem with some sparse global reward. In contrast with previous works, which formulate an entirely new hand-crafted optimization cost or trajectory generation algorithm for a different robot dynamic model, our framework is a general approach that is applicable to arbitrary robot models. Further, by using the velocity obstacle, we devise a smooth projection that guarantees collision free trajectories for all robots with respect to their neighbors and obstacles. The efficacy of our algorithm is demonstrated through varied simulations. A video describing our method and results can be found here.

JMLR Journal 2019 Journal Article

Parsimonious Online Learning with Kernels via Sparse Projections in Function Space

Alec Koppel
Garrett Warnell
Ethan Stump
Alejandro Ribeiro

Despite their attractiveness, popular perception is that techniques for nonparametric function approximation do not scale to streaming data due to an intractable growth in the amount of storage they require. To solve this problem in a memory-affordable way, we propose an online technique based on functional stochastic gradient descent in tandem with supervised sparsification based on greedy function subspace projections. The method, called parsimonious online learning with kernels (POLK), provides a controllable tradeoff between its solution accuracy and the amount of memory it requires. We derive conditions under which the generated function sequence converges almost surely to the optimal function, and we establish that the memory requirement remains finite. We evaluate POLK for kernel multi-class logistic regression and kernel hinge-loss classification on three canonical data sets: a synthetic Gaussian mixture model, the MNIST hand-written digits, and the Brodatz texture database. On all three tasks, we observe a favorable trade-off of objective function evaluation, classification performance, and complexity of the nonparametric regressor extracted by the proposed method. [abs] [ pdf ][ bib ] &copy JMLR 2019. ( edit, beta )

NeurIPS Conference 2019 Conference Paper

Stability of Graph Scattering Transforms

Fernando Gama
Alejandro Ribeiro
Joan Bruna

Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to translations. This stability property dons the scattering transform with a robustness to small changes in the metric domain of the data. When considering network data, regular convolutions do not hold since the data domain presents an irregular structure given by the network topology. In this work, we extend scattering transforms to network data by using multi-resolution graph wavelets, whose computation can be obtained by means of graph convolutions. Furthermore, we prove that the resulting graph scattering transforms are stable to metric perturbations of the underlying network. This renders graph scattering transforms robust to changes on the network topology, making it particularly useful for cases of transfer learning, topology estimation or time-varying graphs.

IROS Conference 2018 Conference Paper

Composable Learning with Sparse Kernel Representations

Ekaterina I. Tolstaya
Ethan Stump
Alec Koppel
Alejandro Ribeiro

We present a reinforcement learning algorithm for learning sparse non-parametric controllers in a Reproducing Kernel Hilbert Space. We improve the sample complexity of this approach by imposing a structure of the state-action function through a normalized advantage function (NAF). This representation of the policy enables efficiently composing multiple learned models without additional training samples or interaction with the environment. We demonstrate the performance of this algorithm on learning obstacle-avoidance policies in multiple simulations of a robot equipped with a laser scanner while navigating in a 2D environment. We apply the composition operation to various policy combinations and test them to show that the composed policies retain the performance of their components. We also transfer the composed policy directly to a physical platform operating in an arena with obstacles in order to demonstrate a degree of generalization.

IROS Conference 2018 Conference Paper

Learning Sample-Efficient Target Reaching for Mobile Robots

Arbaaz Khan
Vijay Kumar 0001
Alejandro Ribeiro

In this paper, we propose a novel architecture and a self-supervised policy gradient algorithm, which employs unsupervised auxiliary tasks to enable a mobile robot to learn how to navigate to a given goal. The dependency on the global information is eliminated by providing only sparse range-finder measurements to the robot. The partially observable planning problem is addressed by splitting it into a hierarchical process. We use convolutional networks to plan locally, and a differentiable memory to provide information about past time steps in the trajectory. These modules, combined in our network architecture, produce globally consistent plans. The sparse reward problem is mitigated by our modified policy gradient algorithm. We model the robots uncertainty with unsupervised tasks to force exploration. The novel architecture we propose with the modified version of the policy gradient algorithm allows our robot to reach the goal in a sample efficient manner, which is orders of magnitude faster than the current state of the art policy gradient algorithm. Simulation and experimental results are provided to validate the proposed approach.

NeurIPS Conference 2017 Conference Paper

Approximate Supermodularity Bounds for Experimental Design

Luiz Chamon
Alejandro Ribeiro

This work provides performance guarantees for the greedy solution of experimental design problems. In particular, it focuses on A- and E-optimal designs, for which typical guarantees do not apply since the mean-square error and the maximum eigenvalue of the estimation error covariance matrix are not supermodular. To do so, it leverages the concept of approximate supermodularity to derive non-asymptotic worst-case suboptimality bounds for these greedy solutions. These bounds reveal that as the SNR of the experiments decreases, these cost functions behave increasingly as supermodular functions. As such, greedy A- and E-optimal designs approach (1-1/e)-optimality. These results reconcile the empirical success of greedy experimental design with the non-supermodularity of the A- and E-optimality criteria.

NeurIPS Conference 2017 Conference Paper

First-Order Adaptive Sample Size Methods to Reduce Complexity of Empirical Risk Minimization

Aryan Mokhtari
Alejandro Ribeiro

This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic methods. In contrast to traditional methods that attempt to solve the ERM problem corresponding to the full dataset directly, adaptive sample size schemes start with a small number of samples and solve the corresponding ERM problem to its statistical accuracy. The sample size is then grown geometrically -- e. g. , scaling by a factor of two -- and use the solution of the previous ERM as a warm start for the new ERM. Theoretical analyses show that the use of adaptive sample size methods reduces the overall computational cost of achieving the statistical accuracy of the whole dataset for a broad range of deterministic and stochastic first-order methods. The gains are specific to the choice of method. When particularized to, e. g. , accelerated gradient descent and stochastic variance reduce gradient, the computational cost advantage is a logarithm of the number of training samples. Numerical experiments on various datasets confirm theoretical claims and showcase the gains of using the proposed adaptive sample size scheme.

NeurIPS Conference 2016 Conference Paper

Adaptive Newton Method for Empirical Risk Minimization to Statistical Accuracy

Aryan Mokhtari
Hadi Daneshmand
Aurelien Lucchi
Thomas Hofmann
Alejandro Ribeiro

We consider empirical risk minimization for large-scale datasets. We introduce Ada Newton as an adaptive algorithm that uses Newton's method with adaptive sample sizes. The main idea of Ada Newton is to increase the size of the training set by a factor larger than one in a way that the minimization variable for the current training set is in the local neighborhood of the optimal argument of the next training set. This allows to exploit the quadratic convergence property of Newton's method and reach the statistical accuracy of each training set with only one iteration of Newton's method. We show theoretically that we can iteratively increase the sample size while applying single Newton iterations without line search and staying within the statistical accuracy of the regularized empirical risk. In particular, we can double the size of the training set in each iteration when the number of samples is sufficiently large. Numerical experiments on various datasets confirm the possibility of increasing the sample size by factor 2 at each iteration which implies that Ada Newton achieves the statistical accuracy of the full training set with about two passes over the dataset.

JMLR Journal 2016 Journal Article

DSA: Decentralized Double Stochastic Averaging Gradient Algorithm

Aryan Mokhtari
Alejandro Ribeiro

This paper considers optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for this setup is to solve large scale machine learning problems where elements of the training set are distributed to multiple computational elements. The decentralized double stochastic averaging gradient (DSA) algorithm is proposed as a solution alternative that relies on: (i) The use of local stochastic averaging gradients. (ii) Determination of descent steps as differences of consecutive stochastic averaging gradients. Strong convexity of local functions and Lipschitz continuity of local gradients is shown to guarantee linear convergence of the sequence generated by DSA in expectation. Local iterates are further shown to approach the optimal argument for almost all realizations. The expected linear convergence of DSA is in contrast to the sublinear rate characteristic of existing methods for decentralized stochastic optimization. Numerical experiments on a logistic regression problem illustrate reductions in convergence time and number of feature vectors processed until convergence relative to these other alternatives. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

ICRA Conference 2016 Conference Paper

Hybrid architecture for communication-aware multi-robot systems

James Stephan
Jonathan Fink
Vijay Kumar 0001
Alejandro Ribeiro

In this paper we propose a hybrid architecture that allows a team of mobile robots to self-organize into a multi-hop ad-hoc network and solve the joint mobility and communication problem in complex environments to complete a given task. The system consists of an outer global planning loop and an inner local loop responsible for motion and network routing, arranged in a two-stage feedback system. This system is able to leverage the benefits of previous systems, while avoiding their drawbacks. This results in a lightweight responsive system that is able to operate in complex environments with minimal global coordination while maintaining a minimum end-to-end data rate between robots. Two main benefits of our approach are demonstrated through experimentation superior performance over existing systems and dynamic adjustment to unexpected events. We conclude with a demonstration of the system operating in a realistic scenario, in which the team patrols a set of hallways.

IROS Conference 2016 Conference Paper

Online learning for characterizing unknown environments in ground robotic vehicle models

Alec Koppel
Jonathan Fink
Garrett Warnell
Ethan Stump
Alejandro Ribeiro

In pursuit of increasing the operational tempo of a ground robotics platform in unknown domains, we consider the problem of predicting the distribution of structural state-estimation error due to poorly-modeled platform dynamics as well as environmental effects. Such predictions are a critical component of any modern control approach that utilizes uncertainty information to provide robustness in control design. We use an online learning algorithm based on matrix factorization techniques to fit a statistical model of error that provides enough expressive power to enable prediction directly from motion control signals and low-level visual features. Moreover, we empirically demonstrate that this technique compares favorably to predictors that do not incorporate this information.

IROS Conference 2015 Conference Paper

D4L: Decentralized dynamic discriminative dictionary learning

Alec Koppel
Garrett Warnell
Ethan Stump
Alejandro Ribeiro

We consider discriminative dictionary learning in a distributed online setting, where a team of networked robots aims to jointly learn both a common basis of the feature space and a classifier over this basis from sequentially observed signals. We formulate this problem as a distributed stochastic program with a non-convex objective and present a block variant of the Arrow-Hurwicz saddle point algorithm to solve it. Only neighboring nodes in the communications network need to exchange information, and we penalize the discrepency between the individual feature basis and classifiers using Lagrange multipliers. The application we consider is for a team of robots to collaboratively recognize objects of interest in dynamic environments. As a preliminary performance benchmark, we consider the problem of learning a texture classifier across a network of robots moving around an urban setting where separate training examples are sequentially observed at each robot. Results are shown for both a standard texture dataset and a new dataset from an urban training facility, and we compare the performance of the standard centralized construction to the new distributed algorithm for the case when distinct samples from all classes are seen by the robots. These experiments yield comparable performance between the decentralized and the centralized cases, demonstrating the proposed method's practical utility.

JMLR Journal 2015 Journal Article

Global Convergence of Online Limited Memory BFGS

Aryan Mokhtari
Alejandro Ribeiro

Global convergence of an online (stochastic) limited memory version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi- Newton method for solving optimization problems with stochastic objectives that arise in large scale machine learning is established. Lower and upper bounds on the Hessian eigenvalues of the sample functions are shown to suffice to guarantee that the curvature approximation matrices have bounded determinants and traces, which, in turn, permits establishing convergence to optimal arguments with probability 1. Experimental evaluation on a search engine advertising problem showcase reductions in convergence time relative to stochastic gradient descent algorithms. [abs] [ pdf ][ bib ] &copy JMLR 2015. ( edit, beta )

ICML Conference 2014 Conference Paper

Hierarchical Quasi-Clustering Methods for Asymmetric Networks

Gunnar E. Carlsson
Facundo Mémoli
Alejandro Ribeiro
Santiago Segarra

This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States.

IROS Conference 2014 Conference Paper

Robust routing and Multi-Confirmation Transmission Protocol for connectivity management of mobile robotic teams

James Stephan
Jonathan Fink
Benjamin Charrow
Alejandro Ribeiro
Vijay Kumar 0001

Providing reliable end-to-end communication for teams of robots requires the integration of novel routing techniques, motion planning algorithms, and transport level communication protocols. In this paper we look at existing robust routing solutions that provide redundancy at the routing layer and develop the Multi-Confirmation Transmission Protocol (MCTP) to take advantage of that redundancy at the transport level. The resulting system that integrates robust routing and MCTP is evaluated in experiments performed in complex environments. The integrated system is observed to provide a robust architecture that allows for near lossless communication while operating in a complex environment with less traffic than standard confirmation protocols.

ICRA Conference 2012 Conference Paper

Motion planning for robust wireless networking

Jonathan Fink
Alejandro Ribeiro
Vijay Kumar 0001

We propose an architecture and algorithms for maintaining end-to-end network connectivity for autonomous teams of robots. By adopting stochastic models of point-to-point wireless communication and computing robust solutions to the network routing problem, we ensure reliable connectivity during robot movement in complex environments. We fully integrate the solution to network routing with the choice of node positions through the use of randomized motion planning techniques. Experiments demonstrate that our method succeeds in navigating a complex environment while ensuring that end-to-end communication rates meet or exceed prescribed values within a target failure tolerance.