Author name cluster

Justin Romberg

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

12 papers

2 author rows

AAMAS Conference 2024 Conference Paper

Confidence-Based Curriculum Learning for Multi-Agent Path Finding

Thomy Phan
Joseph Driscoll
Justin Romberg
Sven Koenig

A wide range of real-world applications can be formulated as Multi- Agent Path Finding (MAPF) problem, where the goal is to find collision-free paths for multiple agents with individual start and goal locations. State-of-the-art MAPF solvers are mainly centralized and depend on global information, which limits their scalability and flexibility regarding changes or new maps that would require expensive replanning. Multi-agent reinforcement learning (MARL) offers an alternative way by learning decentralized policies that can generalize over a variety of maps. While there exist some prior works that attempt to connect both areas, the proposed techniques are heavily engineered and very complex due to the integration of many mechanisms that limit generality and are expensive to use. We argue that much simpler and general approaches are needed to bring the areas of MARL and MAPF closer together with significantly lower costs. In this paper, we propose Confidence-based Auto-Curriculum for Team Update Stability (CACTUS) as a lightweight MARL approach to MAPF. CACTUS defines a simple reverse curriculum scheme, where the goal of each agent is randomly placed within an allocation radius around the agent’s start location. The allocation radius increases gradually as all agents improve, which is assessed by a confidence-based measure. We evaluate CACTUS in various maps of different sizes, obstacle densities, and numbers of agents. Our experiments demonstrate better performance and generalization capabilities than state-of-the-art MARL approaches with less than 600, 000 trainable parameters, which is less than 5% of the neural network size of current MARL approaches to MAPF.

PDF

NeurIPS Conference 2024 Conference Paper

Precise asymptotics of reweighted least-squares algorithms for linear diagonal networks

Chiraag Kaushik
Justin Romberg
Vidya Muthukumar

The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each step. Varieties of this algorithm have been shown to achieve favorable empirical performance and theoretical guarantees for sparse recovery and $\ell_p$-norm minimization. Recently, some preliminary connections have also been made between IRLS and certain types of non-convex linear neural network architectures that are observed to exploit low-dimensional structure in high-dimensional linear models. In this work, we provide a unified asymptotic analysis for a family of algorithms that encompasses IRLS, the recently proposed lin-RFM algorithm (which was motivated by feature learning in neural networks), and the alternating minimization algorithm on linear diagonal neural networks. Our analysis operates in a "batched" setting with i. i. d. Gaussian covariates and shows that, with appropriately chosen reweighting policy, the algorithm can achieve favorable performance in only a handful of iterations. We also extend our results to the case of group-sparse recovery and show that leveraging this structure in the reweighting scheme provably improves test error compared to coordinate-wise reweighting.

PDF Details DOI

NeurIPS Conference 2023 Conference Paper

Connected Superlevel Set in (Deep) Reinforcement Learning and its Application to Minimax Theorems

Sihan Zeng
Thinh Doan
Justin Romberg

The aim of this paper is to improve the understanding of the optimization landscape for policy optimization problems in reinforcement learning. Specifically, we show that the superlevel set of the objective function with respect to the policy parameter is always a connected set both in the tabular setting and under policies represented by a class of neural networks. In addition, we show that the optimization objective as a function of the policy parameter and reward satisfies a stronger “equiconnectedness” property. To our best knowledge, these are novel and previously unknown discoveries. We present an application of the connectedness of these superlevel sets to the derivation of minimax theorems for robust reinforcement learning. We show that any minimax optimization program which is convex on one side and is equiconnected on the other side observes the minimax equality (i. e. has a Nash equilibrium). We find that this exact structure is exhibited by an interesting class of robust reinforcement learning problems under an adversarial reward attack, and the validity of its minimax equality immediately follows. This is the first time such a result is established in the literature.

PDF Details

NeurIPS Conference 2023 Conference Paper

PETAL: Physics Emulation Through Averaged Linearizations for Solving Inverse Problems

Jihui Jin
Etienne Ollivier
Richard Touret
Matthew McKinley
Karim Sabra
Justin Romberg

Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear forward model can be computationally expensive, as it often involves computing and inverting a linearization at a series of estimates. Rather than inverting the physics-based model, we instead train a surrogate forward model (emulator) and leverage modern auto-grad libraries to solve for the input within a classical optimization framework. Current methods to train emulators are done in a black box supervised machine learning fashion and fail to take advantage of any existing knowledge of the forward model. In this article, we propose a simple learned weighted average model that embeds linearizations of the forward model around various reference points into the model itself, explicitly incorporating known physics. Grounding the learned model with physics based linearizations improves the forward modeling accuracy and provides richer physics based gradient information during the inversion process leading to more accurate signal recovery. We demonstrate the efficacy on an ocean acoustic tomography (OAT) example that aims to recover ocean sound speed profile (SSP) variations from acoustic observations (e. g. eigenray arrival times) within simulation of ocean dynamics in the Gulf of Mexico.

PDF Details

NeurIPS Conference 2022 Conference Paper

Regularized Gradient Descent Ascent for Two-Player Zero-Sum Markov Games

Sihan Zeng
Thinh Doan
Justin Romberg

We study the problem of finding the Nash equilibrium in a two-player zero-sum Markov game. Due to its formulation as a minimax optimization program, a natural approach to solve the problem is to perform gradient descent/ascent with respect to each player in an alternating fashion. However, due to the non-convexity/non-concavity of the underlying objective function, theoretical understandings of this method are limited. In our paper, we consider solving an entropy-regularized variant of the Markov game. The regularization introduces structures into the optimization landscape that make the solutions more identifiable and allow the problem to be solved more efficiently. Our main contribution is to show that under proper choices of the regularization parameter, the gradient descent ascent algorithm converges to the Nash equilibrium of the original unregularized problem. We explicitly characterize the finite-time performance of the last iterate of our algorithm, which vastly improves over the existing convergence bound of the gradient descent ascent algorithm without regularization. Finally, we complement the analysis with numerical simulations that illustrate the accelerated convergence of the algorithm.

PDF Details

UAI Conference 2021 Conference Paper

A decentralized policy gradient approach to multi-task reinforcement learning

Sihan Zeng
Malik Aqeel Anwar
Thinh T. Doan 0001
Arijit Raychowdhury
Justin Romberg

We develop a mathematical framework for solving multi-task reinforcement learning (MTRL) problems based on a type of policy gradient method. The goal in MTRL is to learn a common policy that operates effectively in different environments; these environments have similar (or overlapping) state spaces, but have different rewards and dynamics. We highlight two fundamental challenges in MTRL that are not present in its single task counterpart, and illustrate them with simple examples. We then develop a decentralized entropyregularized policy gradient method for solving the MTRL problem, and study its finite-time convergence rate. We demonstrate the effectiveness of the proposed method using a series of numerical experiments. These experiments range from small-scale "GridWorld" problems that readily demonstrate the trade-offs involved in multi-task learning to large-scale problems, where common policies are learned to navigate an airborne drone in multiple (simulated) environments.

Details

JMLR Journal 2020 Journal Article

Convex Programming for Estimation in Nonlinear Recurrent Models

Sohail Bahmani
Justin Romberg

We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide a sample complexity for this estimator in the case of stable dynamics, where the nonlinear recursion has a certain contraction property, and under certain regularity conditions on the input distribution. We evaluate the performance of the estimator by simulation on synthetic data. These numerical experiments also suggest the extent at which the imposed theoretical assumptions may be relaxed. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

PDF Details

NeurIPS Conference 2020 Conference Paper

Sample complexity and effective dimension for regression on manifolds

Andrew McRae
Justin Romberg
Mark Davenport

We consider the theory of regression on a manifold using reproducing kernel Hilbert space methods. Manifold models arise in a wide variety of modern machine learning problems, and our goal is to help understand the effectiveness of various implicit and explicit dimensionality-reduction methods that exploit manifold structure. Our first key contribution is to establish a novel nonasymptotic version of the Weyl law from differential geometry. From this we are able to show that certain spaces of smooth functions on a manifold are effectively finite-dimensional, with a complexity that scales according to the manifold dimension rather than any ambient data dimension. Finally, we show that given (potentially noisy) function values taken uniformly at random over a manifold, a kernel regression estimator (derived from the spectral decomposition of the manifold) yields minimax-optimal error bounds that are controlled by the effective dimension.

PDF Details

NeurIPS Conference 2019 Conference Paper

Decentralized sketching of low rank matrices

Rakshith Sharma Srinivasa
Kiryung Lee
Marius Junge
Justin Romberg

We address a low-rank matrix recovery problem where each column of a rank-r matrix X of size (d1, d2) is compressed beyond the point of recovery to size L with L << d1. Leveraging the joint structure between the columns, we propose a method to recover the matrix to within an epsilon relative error in the Frobenius norm from a total of O(r(d 1 + d 2)\log^6(d 1 + d 2)/\epsilon^2) observations. This guarantee holds uniformly for all incoherent matrices of rank r. In our method, we propose to use a novel matrix norm called the mixed-norm along with the maximum l2 norm of the columns to design a novel convex relaxation for low-rank recovery that is tailored to our observation model. We also show that our proposed mixed-norm, the standard nuclear norm, and the max-norm are particular instances of convex regularization of low-rankness via tensor norms. Finally, we provide a scalable ADMM algorithm for the mixed-norm based method and demonstrate its empirical performance via large-scale simulations.

PDF Details

ICML Conference 2019 Conference Paper

Finite-Time Analysis of Distributed TD(0) with Linear Function Approximation on Multi-Agent Reinforcement Learning

Thinh T. Doan 0001
Siva Theja Maguluri
Justin Romberg

We study the policy evaluation problem in multi-agent reinforcement learning. In this problem, a group of agents works cooperatively to evaluate the value function for the global discounted accumulative reward problem, which is composed of local rewards observed by the agents. Over a series of time steps, the agents act, get rewarded, update their local estimate of the value function, then communicate with their neighbors. The local update at each agent can be interpreted as a distributed consensus-based variant of the popular temporal difference learning algorithm TD(0). While distributed reinforcement learning algorithms have been presented in the literature, almost nothing is known about their convergence rate. Our main contribution is providing a finite-time analysis for the convergence of the distributed TD(0) algorithm. We do this when the communication network between the agents is time-varying in general. We obtain an explicit upper bound on the rate of convergence of this algorithm as a function of the network topology and the discount factor. Our results mirror what we would expect from using distributed stochastic gradient descent for solving convex optimization problems.

Details

NeurIPS Conference 2017 Conference Paper

Net-Trim: Convex Pruning of Deep Neural Networks with Performance Guarantee

Alireza Aghasi
Afshin Abdi
Nam Nguyen
Justin Romberg

We introduce and analyze a new technique for model reduction for deep neural networks. While large networks are theoretically capable of learning arbitrarily complex models, overfitting and model redundancy negatively affects the prediction accuracy and model variance. Our Net-Trim algorithm prunes (sparsifies) a trained network layer-wise, removing connections at each layer by solving a convex optimization program. This program seeks a sparse set of weights at each layer that keeps the layer inputs and outputs consistent with the originally trained model. The algorithms and associated analysis are applicable to neural networks operating with the rectified linear unit (ReLU) as the nonlinear activation. We present both parallel and cascade versions of the algorithm. While the latter can achieve slightly simpler models with the same generalization performance, the former can be computed in a distributed manner. In both cases, Net-Trim significantly reduces the number of connections in the network, while also providing enough regularization to slightly reduce the generalization error. We also provide a mathematical analysis of the consistency between the initial network and the retrained model. To analyze the model sample complexity, we derive the general sufficient conditions for the recovery of a sparse transform matrix. For a single layer taking independent Gaussian random vectors of length $N$ as inputs, we show that if the network response can be described using a maximum number of $s$ non-zero weights per node, these weights can be learned from $\mathcal{O}(s\log N)$ samples.

PDF Details

NeurIPS Conference 2015 Conference Paper

Efficient Compressive Phase Retrieval with Constrained Sensing Vectors

Sohail Bahmani
Justin Romberg

We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on constrained sensing vectors and a two-stage reconstruction method that consists of two standard convex programs that are solved sequentially. In recent years, various methods are proposed for compressive phase retrieval, but they have suboptimal sample complexity or lack robustness guarantees. The main obstacle has been that there is no straightforward convex relaxations for the type of structure in the target. Given a set of underdetermined measurements, there is a standard framework for recovering a sparse matrix, and a standard framework for recovering a low-rank matrix. However, a general, efficient method for recovering a jointly sparse and low-rank matrix has remained elusive. Deviating from the models with generic measurements, in this paper we show that if the sensing vectors are chosen at random from an incoherent subspace, then the low-rank and sparse structures of the target signal can be effectively decoupled. We show that a recovery algorithm that consists of a low-rank recovery stage followed by a sparse recovery stage will produce an accurate estimate of the target when the number of measurements is $\mathsf{O}(k\, \log\frac{d}{k})$, where $k$ and $d$ denote the sparsity level and the dimension of the input signal. We also evaluate the algorithm through numerical simulation.

PDF Details