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Samuel Horváth

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28 papers

2 author rows

ICML Conference 2025 Conference Paper

Aequa: Fair Model Rewards in Collaborative Learning via Slimmable Networks

Nurbek Tastan
Samuel Horváth
Karthik Nandakumar

Collaborative learning enables multiple participants to learn a single global model by exchanging focused updates instead of sharing data. One of the core challenges in collaborative learning is ensuring that participants are rewarded fairly for their contributions, which entails two key sub-problems: contribution assessment and reward allocation. This work focuses on fair reward allocation, where the participants are incentivized through model rewards - differentiated final models whose performance is commensurate with the contribution. In this work, we leverage the concept of slimmable neural networks to collaboratively learn a shared global model whose performance degrades gracefully with a reduction in model width. We also propose a post-training fair allocation algorithm that determines the model width for each participant based on their contributions. We theoretically study the convergence of our proposed approach and empirically validate it using extensive experiments on different datasets and architectures. We also extend our approach to enable training-time model reward allocation.

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ICML Conference 2025 Conference Paper

Clipping Improves Adam-Norm and AdaGrad-Norm when the Noise Is Heavy-Tailed

Savelii Chezhegov
Yaroslav Klyukin
Andrei Semenov
Aleksandr Beznosikov
Alexander V. Gasnikov
Samuel Horváth
Martin Takác 0001
Eduard Gorbunov

Methods with adaptive stepsizes, such as AdaGrad and Adam, are essential for training modern Deep Learning models, especially Large Language Models. Typically, the noise in the stochastic gradients is heavy-tailed for the later ones. Gradient clipping provably helps to achieve good high-probability convergence for such noises. However, despite the similarity between AdaGrad/Adam and Clip-SGD, the current understanding of the high-probability convergence of AdaGrad/Adam-type methods is limited in this case. In this work, we prove that AdaGrad/Adam (and their delayed version) can have provably bad high-probability convergence if the noise is heavy-tailed. We also show that gradient clipping fixes this issue, i. e. , we derive new high-probability convergence bounds with polylogarithmic dependence on the confidence level for AdaGrad-Norm and Adam-Norm with clipping and with/without delay for smooth convex/non-convex stochastic optimization with heavy-tailed noise. We extend our results to the case of AdaGrad/Adam with delayed stepsizes. Our empirical evaluations highlight the superiority of clipped versions of AdaGrad/Adam in handling the heavy-tailed noise.

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TMLR Journal 2025 Journal Article

CYCle: Choosing Your Collaborators Wisely to Enhance Collaborative Fairness in Decentralized Learning

Nurbek Tastan
Samuel Horváth
Karthik Nandakumar

Collaborative learning (CL) enables multiple participants to jointly train machine learning (ML) models on decentralized data sources without raw data sharing. While the primary goal of CL is to maximize the expected accuracy gain for each participant, it is also important to ensure that the gains are fairly distributed: no client should be negatively impacted, and gains should reflect contributions. Most existing CL methods require central coordination and focus only on gain maximization, overlooking fairness. In this work, we first show that the existing measure of collaborative fairness based on the correlation between accuracy values without and with collaboration has drawbacks because it does not account for negative collaboration gain. We argue that maximizing mean collaboration gain (MCG) while simultaneously minimizing the collaboration gain spread (CGS) is a fairer alternative. Next, we propose the CYCle protocol that enables individual participants in a private decentralized learning (PDL) framework to achieve this objective through a novel reputation scoring method based on gradient alignment between the local cross-entropy and distillation losses. We further extend the CYCle protocol to operate on top of gossip-based decentralized algorithms such as Gossip-SGD. We also theoretically show that CYCle performs better than standard FedAvg in a two-client mean estimation setting under high heterogeneity. Empirical experiments demonstrate the effectiveness of the CYCle protocol to ensure positive and fair collaboration gains for all participants, even in cases where the data distributions of participants are highly skewed. The code can be found at https://github.com/tnurbek/cycle.

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ICML Conference 2025 Conference Paper

FRUGAL: Memory-Efficient Optimization by Reducing State Overhead for Scalable Training

Philip Zmushko
Aleksandr Beznosikov
Martin Takác 0001
Samuel Horváth

With the increase in the number of parameters in large language models, the training process increasingly demands larger volumes of GPU memory. A significant portion of this memory is typically consumed by the optimizer state. To overcome this challenge, recent approaches such as low-rank adaptation (LoRA), low-rank gradient projection (GaLore), and blockwise optimization (BAdam) have been proposed. However, in all these algorithms, the effective rank of the weight updates remains low-rank, which can lead to a substantial loss of information from the gradient. This loss can be critically important, especially during the pre-training stage. In this paper, we introduce FRUGAL ( F ull- R ank U pdates with G r A dient sp L itting), a new memory-efficient optimization framework. FRUGAL leverages gradient splitting to perform low-dimensional updates using advanced algorithms (such as Adam), while updates along the remaining directions are executed via state-free methods like SGD or signSGD. Our framework can be integrated with various low-rank update selection techniques, including GaLore and BAdam. We provide theoretical convergence guarantees for our framework when using SGDM for low-dimensional updates and SGD for state-free updates. Additionally, our method consistently outperforms concurrent approaches, achieving state-of-the-art results in pre-training and fine-tuning tasks while balancing memory efficiency and performance metrics.

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ICLR Conference 2025 Conference Paper

Methods for Convex (L0, L1)-Smooth Optimization: Clipping, Acceleration, and Adaptivity

Eduard Gorbunov
Nazarii Tupitsa
Sayantan Choudhury
Alen Aliev
Peter Richtárik
Samuel Horváth
Martin Takác 0001

Due to the non-smoothness of optimization problems in Machine Learning, generalized smoothness assumptions have been gaining a lot of attention in recent years. One of the most popular assumptions of this type is $(L_0,L_1)$-smoothness (Zhang et al., 2020). In this paper, we focus on the class of (strongly) convex $(L_0,L_1)$-smooth functions and derive new convergence guarantees for several existing methods. In particular, we derive improved convergence rates for Gradient Descent with (Smoothed) Gradient Clipping and for Gradient Descent with Polyak Stepsizes. In contrast to the existing results, our rates do not rely on the standard smoothness assumption and do not suffer from the exponential dependency on the initial distance to the solution. We also extend these results to the stochastic case under the over-parameterization assumption, propose a new accelerated method for convex $(L_0,L_1)$-smooth optimization, and derive new convergence rates for Adaptive Gradient Descent (Malitsky and Mishchenko, 2020).

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ICLR Conference 2025 Conference Paper

Methods with Local Steps and Random Reshuffling for Generally Smooth Non-Convex Federated Optimization

Yury Demidovich
Petr Ostroukhov
Grigory Malinovsky
Samuel Horváth
Martin Takác 0001
Peter Richtárik
Eduard Gorbunov

Non-convex Machine Learning problems typically do not adhere to the standard smoothness assumption. Based on empirical findings, Zhang et al. (2020b) proposed a more realistic generalized $(L_0,L_1)$-smoothness assumption, though it remains largely unexplored. Many existing algorithms designed for standard smooth problems need to be revised. However, in the context of Federated Learning, only a few works address this problem but rely on additional limiting assumptions. In this paper, we address this gap in the literature: we propose and analyze new methods with local steps, partial participation of clients, and Random Reshuffling without extra restrictive assumptions beyond generalized smoothness. The proposed methods are based on the proper interplay between clients' and server's stepsizes and gradient clipping. Furthermore, we perform the first analysis of these methods under the Polyak-Łojasiewicz condition. Our theory is consistent with the known results for standard smooth problems, and our experimental results support the theoretical insights.

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TMLR Journal 2025 Journal Article

Partially Personalized Federated Learning: Breaking the Curse of Data Heterogeneity

Konstantin Mishchenko
Rustem Islamov
Eduard Gorbunov
Samuel Horváth

We consider a partially personalized formulation of Federated Learning (FL) that strikes a balance between the flexibility of personalization and cooperativeness of global training. In our framework, we split the variables into global parameters, which are shared across all clients, and individual local parameters, which are kept private. We prove that under the right split of parameters, it is possible to find global parameters that allow each client to fit their data perfectly, and refer to the obtained problem as overpersonalized. For instance, the shared global parameters can be used to learn good data representations, whereas the personalized layers are fine-tuned for a specific client. Moreover, we present a simple algorithm for the partially personalized formulation that offers significant benefits to all clients. In particular, it breaks the curse of data heterogeneity in several settings, such as training with local steps, asynchronous training, and Byzantine-robust training.

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ECAI Conference 2025 Conference Paper

Quantize Once, Train Fast: Allreduce-Compatible Compression with Provable Guarantees

Jihao Xin
Marco Canini
Peter Richtárik
Samuel Horváth

Distributed training enables large-scale deep learning, but suffers from high communication overhead, especially as models and datasets grow. Gradient compression, particularly quantization, is a promising approach to mitigate this bottleneck. However, existing quantization schemes are often incompatible with Allreduce, the dominant communication primitive in distributed deep learning, and many prior solutions rely on heuristics without theoretical guarantees. We introduce Global-QSGD, an Allreduce-compatible gradient quantization method that leverages global norm scaling to reduce communication overhead while preserving accuracy. Global-QSGD is backed by rigorous theoretical analysis, extending standard unbiased compressor frameworks to establish formal convergence guarantees. Additionally, we develop a performance model to evaluate its impact across different hardware configurations. Extensive experiments on NVLink, PCIe, and large-scale cloud environments show that Global-QSGD accelerates distributed training by up to 3. 51× over baseline quantization methods, making it a practical and efficient solution for large-scale deep learning workloads.

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NeurIPS Conference 2024 Conference Paper

Byzantine Robustness and Partial Participation Can Be Achieved at Once: Just Clip Gradient Differences

Grigory Malinovsky
Peter Richtárik
Samuel Horváth
Eduard Gorbunov

Distributed learning has emerged as a leading paradigm for training large machine learning models. However, in real-world scenarios, participants may be unreliable or malicious, posing a significant challenge to the integrity and accuracy of the trained models. Byzantine fault tolerance mechanisms have been proposed to address these issues, but they often assume full participation from all clients, which is not always practical due to the unavailability of some clients or communication constraints. In our work, we propose the first distributed method with client sampling and provable tolerance to Byzantine workers. The key idea behind the developed method is the use of gradient clipping to control stochastic gradient differences in recursive variance reduction. This allows us to bound the potential harm caused by Byzantine workers, even during iterations when all sampled clients are Byzantine. Furthermore, we incorporate communication compression into the method to enhance communication efficiency. Under general assumptions, we prove convergence rates for the proposed method that match the existing state-of-the-art (SOTA) theoretical results. We also propose a heuristic on how to adjust any Byzantine-robust method to a partial participation scenario via clipping.

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IJCAI Conference 2024 Conference Paper

Dirichlet-based Uncertainty Quantification for Personalized Federated Learning with Improved Posterior Networks

Nikita Kotelevskii
Samuel Horváth
Karthik Nandakumar
Martin Takac
Maxim Panov

In modern federated learning, one of the main challenges is to account for inherent heterogeneity and the diverse nature of data distributions for different clients. This problem is often addressed by introducing personalization of the models towards the data distribution of the particular client. However, a personalized model might be unreliable when applied to the data that is not typical for this client. Eventually, it may perform worse for these data than the non-personalized global model trained in a federated way on the data from all the clients. This paper presents a new approach to federated learning that allows selecting a model from global and personalized ones that would perform better for a particular input point. It is achieved through a careful modeling of predictive uncertainties that helps to detect local and global in- and out-of-distribution data and use this information to select the model that is confident in a prediction. The comprehensive experimental evaluation on the popular real-world image datasets shows the superior performance of the model in the presence of out-of-distribution data while performing on par with state-of-the-art personalized federated learning algorithms in the standard scenarios.

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ICML Conference 2024 Conference Paper

High-Probability Convergence for Composite and Distributed Stochastic Minimization and Variational Inequalities with Heavy-Tailed Noise

Eduard Gorbunov
Abdurakhmon Sadiev
Marina Danilova
Samuel Horváth
Gauthier Gidel
Pavel E. Dvurechensky
Alexander V. Gasnikov
Peter Richtárik

High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to derive good high-probability guarantees when the noise is heavy-tailed. However, if implemented naively, clipping can spoil the convergence of the popular methods for composite and distributed optimization (Prox-SGD/Parallel SGD) even in the absence of any noise. Due to this reason, many works on high-probability analysis consider only unconstrained non-distributed problems, and the existing results for composite/distributed problems do not include some important special cases (like strongly convex problems) and are not optimal. To address this issue, we propose new stochastic methods for composite and distributed optimization based on the clipping of stochastic gradient differences and prove tight high-probability convergence results (including nearly optimal ones) for the new methods. In addition, we also develop new methods for composite and distributed variational inequalities and analyze the high-probability convergence of these methods.

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ICML Conference 2024 Conference Paper

Maestro: Uncovering Low-Rank Structures via Trainable Decomposition

Samuel Horváth
Stefanos Laskaridis
Shashank Rajput
Hongyi Wang 0001

Deep Neural Networks (DNNs) have been a large driver for AI breakthroughs in recent years, ranging from self-driving cars to intelligent assistants. However, these models have been getting increasingly large as they become more accurate and safe. This means that their training becomes increasingly costly and time-consuming, and typically yields a single model to fit all targets. To mitigate this, various techniques have been proposed in the literature, including pruning, sparsification or quantization of the model weights and updates. While achieving high compression rates, they often incur significant computational overheads at training or lead to non-negligible accuracy penalty. Alternatively, factorization methods have been leveraged for low-rank compression of DNNs. Similarly, such techniques (e. g. , SVD) frequently rely on heavy iterative decompositions of layers and are potentially sub-optimal for non-linear models, such as DNNs. We take a further step in designing efficient low-rank models and propose Maestro, a framework for trainable low-rank layers. Instead of iteratively applying a priori decompositions, the low-rank structure is baked into the training process through LoD, a low-rank ordered decomposition. Not only is this the first time importance ordering via sampling is applied on the decomposed DNN structure, but it also allows selecting ranks at a layer granularity. Our theoretical analysis demonstrates that LoD recovers the SVD decomposition of linear mapping on uniformly distributed data and PCA for linear autoencoders. Applied to DNNs, Maestro enables the extraction of lower footprint models that preserve performance. Simultaneously, it enables the graceful tradeoff between accuracy-latency for deployment to even more constrained devices, without retraining.

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TMLR Journal 2024 Journal Article

PaDPaF: Partial Disentanglement with Partially-Federated GANs

Abdulla Jasem Almansoori
Samuel Horváth
Martin Takáč

Federated learning has become a popular machine learning paradigm with many potential real-life applications, including recommendation systems, the Internet of Things (IoT), healthcare, and self-driving cars. Though most current applications focus on classification-based tasks, learning personalized generative models remains largely unexplored, and their benefits in the heterogeneous setting still need to be better understood. This work proposes a novel architecture combining global client-agnostic and local client-specific generative models. We show that using standard techniques for training federated models, our proposed model achieves privacy and personalization by implicitly disentangling the globally-consistent representation (i.e. content) from the client-dependent variations (i.e. style). Using such decomposition, personalized models can generate locally unseen labels while preserving the given style of the client and can predict the labels for all clients with high accuracy by training a simple linear classifier on the global content features. Furthermore, disentanglement enables other essential applications, such as data anonymization, by sharing only the content. Extensive experimental evaluation corroborates our findings, and we also discuss a theoretical motivation for the proposed approach.

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IJCAI Conference 2024 Conference Paper

Redefining Contributions: Shapley-Driven Federated Learning

Nurbek Tastan
Samar Fares
Toluwani Aremu
Samuel Horváth
Karthik Nandakumar

Federated learning (FL) has emerged as a pivotal approach in machine learning, enabling multiple participants to collaboratively train a global model without sharing raw data. While FL finds applications in various domains such as healthcare and finance, it is challenging to ensure global model convergence when participants do not contribute equally and/or honestly. To overcome this challenge, principled mechanisms are required to evaluate the contributions made by individual participants in the FL setting. Existing solutions for contribution assessment rely on general accuracy evaluation, often failing to capture nuanced dynamics and class-specific influences. This paper proposes a novel contribution assessment method called ShapFed for fine-grained evaluation of participant contributions in FL. Our approach uses Shapley values from cooperative game theory to provide a granular understanding of class-specific influences. Based on ShapFed, we introduce a weighted aggregation method called ShapFed-WA, which outperforms conventional federated averaging, especially in class-imbalanced scenarios. Personalizing participant updates based on their contributions further enhances collaborative fairness by delivering differentiated models commensurate with the participant contributions. Experiments on CIFAR-10, Chest X-Ray, and Fed-ISIC2019 datasets demonstrate the effectiveness of our approach in improving utility, efficiency, and fairness in FL systems. The code can be found at \href{https: //github. com/tnurbek/shapfed}{https: //github. com/tnurbek/shapfed}.

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NeurIPS Conference 2024 Conference Paper

Remove that Square Root: A New Efficient Scale-Invariant Version of AdaGrad

Sayantan Choudhury
Nazarii Tupitsa
Nicolas Loizou
Samuel Horváth
Martin Takáč
Eduard Gorbunov

Adaptive methods are extremely popular in machine learning as they make learning rate tuning less expensive. This paper introduces a novel optimization algorithm named KATE, which presents a scale-invariant adaptation of the well-known AdaGrad algorithm. We prove the scale-invariance of KATE for the case of Generalized Linear Models. Moreover, for general smooth non-convex problems, we establish a convergence rate of $O((\log T)/\sqrt{T})$ for KATE, matching the best-known ones for AdaGrad and Adam. We also compare KATE to other state-of-the-art adaptive algorithms Adam and AdaGrad in numerical experiments with different problems, including complex machine learning tasks like image classification and text classification on real data. The results indicate that KATE consistently outperforms AdaGrad and matches/surpasses the performance of Adam in all considered scenarios.

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NeurIPS Conference 2023 Conference Paper

Accelerated Zeroth-order Method for Non-Smooth Stochastic Convex Optimization Problem with Infinite Variance

Nikita Kornilov
Ohad Shamir
Aleksandr Lobanov
Darina Dvinskikh
Alexander Gasnikov
Innokentiy Shibaev
Eduard Gorbunov
Samuel Horváth

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the batched accelerated gradient method, was proposed in (Gasnikov et. al. , 2022). This optimality is defined in terms of iteration and oracle complexity, as well as the maximal admissible level of adversarial noise. However, the assumption of finite variance is burdensome and it might not hold in many practical scenarios. To address this, we demonstrate how to adapt a refined clipped version of the accelerated gradient (Stochastic Similar Triangles) method from (Sadiev et al. , 2023) for a two-point zero-order oracle. This adaptation entails extending the batching technique to accommodate infinite variance — a non-trivial task that stands as a distinct contribution of this paper.

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NeurIPS Conference 2023 Conference Paper

Byzantine-Tolerant Methods for Distributed Variational Inequalities

Nazarii Tupitsa
Abdulla Jasem Almansoori
Yanlin Wu
Martin Takac
Karthik Nandakumar
Samuel Horváth
Eduard Gorbunov

Robustness to Byzantine attacks is a necessity for various distributed training scenarios. When the training reduces to the process of solving a minimization problem, Byzantine robustness is relatively well-understood. However, other problem formulations, such as min-max problems or, more generally, variational inequalities, arise in many modern machine learning and, in particular, distributed learning tasks. These problems significantly differ from the standard minimization ones and, therefore, require separate consideration. Nevertheless, only one work [Abidi et al. , 2022] addresses this important question in the context of Byzantine robustness. Our work makes a further step in this direction by providing several (provably) Byzantine-robust methods for distributed variational inequality, thoroughly studying their theoretical convergence, removing the limitations of the previous work, and providing numerical comparisons supporting the theoretical findings.

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ICML Conference 2023 Conference Paper

Convergence of Proximal Point and Extragradient-Based Methods Beyond Monotonicity: the Case of Negative Comonotonicity

Eduard Gorbunov
Adrien B. Taylor
Samuel Horváth
Gauthier Gidel

Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works (Diakonikolas et al. , 2021; Lee & Kim, 2021; Pethick et al. , 2022; Bohm, 2022) aiming at going beyond monotonicity by considering the weaker negative comonotonicity assumption. In this work, we provide tight complexity analyses for the Proximal Point (PP), Extragradient (EG), and Optimistic Gradient (OG) methods in this setup, closing several questions on their working guarantees beyond monotonicity. In particular, we derive the first non-asymptotic convergence rates for PP under negative comonotonicity and star-negative comonotonicity and show their tightness via constructing worst-case examples; we also relax the assumptions for the last-iterate convergence guarantees for EG and OG and prove the tightness of the existing best-iterate guarantees for EG and OG via constructing counter-examples.

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NeurIPS Conference 2023 Conference Paper

Handling Data Heterogeneity via Architectural Design for Federated Visual Recognition

Sara Pieri
Jose Restom
Samuel Horváth
Hisham Cholakkal

Federated Learning (FL) is a promising research paradigm that enables the collaborative training of machine learning models among various parties without the need for sensitive information exchange. Nonetheless, retaining data in individual clients introduces fundamental challenges to achieving performance on par with centrally trained models. Our study provides an extensive review of federated learning applied to visual recognition. It underscores the critical role of thoughtful architectural design choices in achieving optimal performance, a factor often neglected in the FL literature. Many existing FL solutions are tested on shallow or simple networks, which may not accurately reflect real-world applications. This practice restricts the transferability of research findings to large-scale visual recognition models. Through an in-depth analysis of diverse cutting-edge architectures such as convolutional neural networks, transformers, and MLP-mixers, we experimentally demonstrate that architectural choices can substantially enhance FL systems' performance, particularly when handling heterogeneous data. We study visual recognition models from five different architectural families on four challenging FL datasets. We also re-investigate the inferior performance convolution-based architectures in the FL setting and analyze the influence of normalization layers on the FL performance. Our findings emphasize the importance of architectural design for computer vision tasks in practical scenarios, effectively narrowing the performance gap between federated and centralized learning.

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ICML Conference 2023 Conference Paper

High-Probability Bounds for Stochastic Optimization and Variational Inequalities: the Case of Unbounded Variance

Abdurakhmon Sadiev
Marina Danilova
Eduard Gorbunov
Samuel Horváth
Gauthier Gidel
Pavel E. Dvurechensky
Alexander V. Gasnikov
Peter Richtárik

During the recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity bounds are more accurate and less studied than in-expectation ones. However, SOTA high-probability non-asymptotic convergence results are derived under strong assumptions such as boundedness of the gradient noise variance or of the objective’s gradient itself. In this paper, we propose several algorithms with high-probability convergence results under less restrictive assumptions. In particular, we derive new high-probability convergence results under the assumption that the gradient/operator noise has bounded central $\alpha$-th moment for $\alpha \in (1, 2]$ in the following setups: (i) smooth non-convex / Polyak-Lojasiewicz / convex / strongly convex / quasi-strongly convex minimization problems, (ii) Lipschitz / star-cocoercive and monotone / quasi-strongly monotone variational inequalities. These results justify the usage of the considered methods for solving problems that do not fit standard functional classes studied in stochastic optimization.

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JMLR Journal 2023 Journal Article

On Biased Compression for Distributed Learning

Aleksandr Beznosikov
Samuel Horváth
Peter Richtárik
Mher Safaryan

In the last few years, various communication compression techniques have emerged as an indispensable tool helping to alleviate the communication bottleneck in distributed learning. However, despite the fact biased compressors often show superior performance in practice when compared to the much more studied and understood unbiased compressors, very little is known about them. In this work we study three classes of biased compression operators, two of which are new, and their performance when applied to (stochastic) gradient descent and distributed (stochastic) gradient descent. We show for the first time that biased compressors can lead to linear convergence rates both in the single node and distributed settings. We prove that distributed compressed SGD method, employed with error feedback mechanism, enjoys the ergodic rate $O\left( \delta L \exp[-\frac{\mu K}{\delta L}] + \frac{(C + \delta D)}{K\mu}\right)$, where $\delta\ge1$ is a compression parameter which grows when more compression is applied, $L$ and $\mu$ are the smoothness and strong convexity constants, $C$ captures stochastic gradient noise ($C=0$ if full gradients are computed on each node) and $D$ captures the variance of the gradients at the optimum ($D=0$ for over-parameterized models). Further, via a theoretical study of several synthetic and empirical distributions of communicated gradients, we shed light on why and by how much biased compressors outperform their unbiased variants. Finally, we propose several new biased compressors with promising theoretical guarantees and practical performance. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

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ICLR Conference 2023 Conference Paper

Variance Reduction is an Antidote to Byzantines: Better Rates, Weaker Assumptions and Communication Compression as a Cherry on the Top

Eduard Gorbunov
Samuel Horváth
Peter Richtárik
Gauthier Gidel

Byzantine-robustness has been gaining a lot of attention due to the growth of the interest in collaborative and federated learning. However, many fruitful directions, such as the usage of variance reduction for achieving robustness and communication compression for reducing communication costs, remain weakly explored in the field. This work addresses this gap and proposes Byz-VR-MARINA -- a new Byzantine-tolerant method with variance reduction and compression. A key message of our paper is that variance reduction is key to fighting Byzantine workers more effectively. At the same time, communication compression is a bonus that makes the process more communication efficient. We derive theoretical convergence guarantees for Byz-VR-MARINA outperforming previous state-of-the-art for general non-convex and Polyak-Lojasiewicz loss functions. Unlike the concurrent Byzantine-robust methods with variance reduction and/or compression, our complexity results are tight and do not rely on restrictive assumptions such as boundedness of the gradients or limited compression. Moreover, we provide the first analysis of a Byzantine-tolerant method supporting non-uniform sampling of stochastic gradients. Numerical experiments corroborate our theoretical findings.

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TMLR Journal 2022 Journal Article

FedShuffle: Recipes for Better Use of Local Work in Federated Learning

Samuel Horváth
Maziar Sanjabi
Lin Xiao
Peter Richtárik
Michael Rabbat

The practice of applying several local updates before aggregation across clients has been empirically shown to be a successful approach to overcoming the communication bottleneck in Federated Learning (FL). Such methods are usually implemented by having clients perform one or more epochs of local training per round while randomly reshuffling their finite dataset in each epoch. Data imbalance, where clients have different numbers of local training samples, is ubiquitous in FL applications, resulting in different clients performing different numbers of local updates in each round. In this work, we propose a general recipe, FedShuffle, that better utilizes the local updates in FL, especially in this regime encompassing random reshuffling and heterogeneity. FedShuffle is the first local update method with theoretical convergence guarantees that incorporates random reshuffling, data imbalance, and client sampling — features that are essential in large-scale cross-device FL. We present a comprehensive theoretical analysis of FedShuffle and show, both theoretically and empirically, that it does not suffer from the objective function mismatch that is present in FL methods that assume homogeneous updates in heterogeneous FL setups, such as FedAvg (McMahan et al., 2017). In addition, by combining the ingredients above, FedShuffle improves upon FedNova (Wang et al., 2020), which was previously proposed to solve this mismatch. Similar to Mime (Karimireddy et al., 2020), we show that FedShuffle with momentum variance reduction (Cutkosky & Orabona, 2019) improves upon non-local methods under a Hessian similarity assumption.

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TMLR Journal 2022 Journal Article

Optimal Client Sampling for Federated Learning

Wenlin Chen
Samuel Horváth
Peter Richtárik

It is well understood that client-master communication can be a primary bottleneck in federated learning (FL). In this work, we address this issue with a novel client subsampling scheme, where we restrict the number of clients allowed to communicate their updates back to the master node. In each communication round, all participating clients compute their updates, but only the ones with "important" updates communicate back to the master. We show that importance can be measured using only the norm of the update and give a formula for optimal client participation. This formula minimizes the distance between the full update, where all clients participate, and our limited update, where the number of participating clients is restricted. In addition, we provide a simple algorithm that approximates the optimal formula for client participation, which allows for secure aggregation and stateless clients, and thus does not compromise client privacy. We show both theoretically and empirically that for Distributed SGD (DSGD) and Federated Averaging (FedAvg), the performance of our approach can be close to full participation and superior to the baseline where participating clients are sampled uniformly. Moreover, our approach is orthogonal to and compatible with existing methods for reducing communication overhead, such as local methods and communication compression methods.

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ICLR Conference 2021 Conference Paper

A Better Alternative to Error Feedback for Communication-Efficient Distributed Learning

Samuel Horváth
Peter Richtárik

Modern large-scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computing systems. A key bottleneck of such systems is the communication overhead for exchanging information across the workers, such as stochastic gradients. Among the many techniques proposed to remedy this issue, one of the most successful is the framework of compressed communication with error feedback (EF). EF remains the only known technique that can deal with the error induced by contractive compressors which are not unbiased, such as Top-$K$ or PowerSGD. In this paper, we propose a new and theoretically and practically better alternative to EF for dealing with contractive compressors. In particular, we propose a construction which can transform any contractive compressor into an induced unbiased compressor. Following this transformation, existing methods able to work with unbiased compressors can be applied. We show that our approach leads to vast improvements over EF, including reduced memory requirements, better communication complexity guarantees and fewer assumptions. We further extend our results to federated learning with partial participation following an arbitrary distribution over the nodes and demonstrate the benefits thereof. We perform several numerical experiments which validate our theoretical findings.

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NeurIPS Conference 2021 Conference Paper

FjORD: Fair and Accurate Federated Learning under heterogeneous targets with Ordered Dropout

Samuel Horváth
Stefanos Laskaridis
Mario Almeida
Ilias Leontiadis
Stylianos Venieris
Nicholas Lane

Federated Learning (FL) has been gaining significant traction across different ML tasks, ranging from vision to keyboard predictions. In large-scale deployments, client heterogeneity is a fact and constitutes a primary problem for fairness, training performance and accuracy. Although significant efforts have been made into tackling statistical data heterogeneity, the diversity in the processing capabilities and network bandwidth of clients, termed system heterogeneity, has remained largely unexplored. Current solutions either disregard a large portion of available devices or set a uniform limit on the model's capacity, restricted by the least capable participants. In this work, we introduce Ordered Dropout, a mechanism that achieves an ordered, nested representation of knowledge in Neural Networks and enables the extraction of lower footprint submodels without the need for retraining. We further show that for linear maps our Ordered Dropout is equivalent to SVD. We employ this technique, along with a self-distillation methodology, in the realm of FL in a framework called FjORD. FjORD alleviates the problem of client system heterogeneity by tailoring the model width to the client's capabilities. Extensive evaluation on both CNNs and RNNs across diverse modalities shows that FjORD consistently leads to significant performance gains over state-of-the-art baselines while maintaining its nested structure.

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NeurIPS Conference 2020 Conference Paper

Lower Bounds and Optimal Algorithms for Personalized Federated Learning

Filip Hanzely
Slavomír Hanzely
Samuel Horváth
Peter Richtarik

In this work, we consider the optimization formulation of personalized federated learning recently introduced by Hanzely & Richtarik (2020) which was shown to give an alternative explanation to the workings of local SGD methods. Our first contribution is establishing the first lower bounds for this formulation, for both the communication complexity and the local oracle complexity. Our second contribution is the design of several optimal methods matching these lower bounds in almost all regimes. These are the first provably optimal methods for personalized federated learning. Our optimal methods include an accelerated variant of FedProx, and an accelerated variance-reduced version of FedAvg/Local SGD. We demonstrate the practical superiority of our methods through extensive numerical experiments.

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ICML Conference 2019 Conference Paper

Nonconvex Variance Reduced Optimization with Arbitrary Sampling

Samuel Horváth
Peter Richtárik

We provide the first importance sampling variants of variance reduced algorithms for empirical risk minimization with non-convex loss functions. In particular, we analyze non-convex versions of \texttt{SVRG}, \texttt{SAGA} and \texttt{SARAH}. Our methods have the capacity to speed up the training process by an order of magnitude compared to the state of the art on real datasets. Moreover, we also improve upon current mini-batch analysis of these methods by proposing importance sampling for minibatches in this setting. Surprisingly, our approach can in some regimes lead to superlinear speedup with respect to the minibatch size, which is not usually present in stochastic optimization. All the above results follow from a general analysis of the methods which works with arbitrary sampling, i. e. , fully general randomized strategy for the selection of subsets of examples to be sampled in each iteration. Finally, we also perform a novel importance sampling analysis of \texttt{SARAH} in the convex setting.

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