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Rustem Islamov

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11 papers

2 author rows

ICLR Conference 2025 Conference Paper

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise

Enea Monzio Compagnoni
Tianlin Liu
Rustem Islamov
Frank Norbert Proske
Antonio Orvieto
Aurélien Lucchi

Despite the vast empirical evidence supporting the efficacy of adaptive optimization methods in deep learning, their theoretical understanding is far from complete. This work introduces novel SDEs for commonly used adaptive optimizers: SignSGD, RMSprop(W), and Adam(W). These SDEs offer a quantitatively accurate description of these optimizers and help illuminate an intricate relationship between adaptivity, gradient noise, and curvature. Our novel analysis of SignSGD highlights a noteworthy and precise contrast to SGD in terms of convergence speed, stationary distribution, and robustness to heavy-tail noise. We extend this analysis to AdamW and RMSpropW, for which we observe that the role of noise is much more complex. Crucially, we support our theoretical analysis with experimental evidence by verifying our insights: this includes numerically integrating our SDEs using Euler-Maruyama discretization on various neural network architectures such as MLPs, CNNs, ResNets, and Transformers. Our SDEs accurately track the behavior of the respective optimizers, especially when compared to previous SDEs derived for Adam and RMSprop. We believe our approach can provide valuable insights into best training practices and novel scaling rules.

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NeurIPS Conference 2025 Conference Paper

Enhancing Optimizer Stability: Momentum Adaptation of The NGN Step-size

Rustem Islamov
Niccolò Ajroldi
Antonio Orvieto
Aurelien Lucchi

Modern optimization algorithms that incorporate momentum and adaptive step-size offer improved performance in numerous challenging deep learning tasks. However, their effectiveness is often highly sensitive to the choice of hyperparameters, especially the step-size. Tuning these parameters is often difficult, resource-intensive, and time-consuming. Therefore, recent efforts have been directed toward enhancing the stability of optimizers across a wide range of hyperparameter choices [Schaipp et al. , 2024]. In this paper, we introduce an algorithm that matches the performance of state-of-the-art optimizers while improving stability to the choice of the step-size hyperparameter through a novel adaptation of the ${\sf NGN}$ step-size method [Orvieto and Xiao, 2024]. Specifically, we propose a momentum-based version ${\sf NGN}$-${\sf M}$ that attains the standard convergence rate of $\mathcal{O}(1/\sqrt{K})$ under less restrictive assumptions, without the need for interpolation condition or assumptions of bounded stochastic gradients or iterates, in contrast to previous approaches. Additionally, we empirically demonstrate that the combination of the ${\sf NGN}$ step-size with momentum results in enhanced robustness to the choice of the step-size hyperparameter while delivering performance that is comparable to or surpasses other state-of-the-art optimizers.

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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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ICML Conference 2025 Conference Paper

Safe-EF: Error Feedback for Non-smooth Constrained Optimization

Rustem Islamov
Yarden As
Ilyas Fatkhullin

Federated learning faces severe communication bottlenecks due to the high dimensionality of model updates. Communication compression with contractive compressors (e. g. , Top-$K$) is often preferable in practice but can degrade performance without proper handling. Error feedback (EF) mitigates such issues but has been largely restricted for smooth, unconstrained problems, limiting its real-world applicability where non-smooth objectives and safety constraints are critical. We advance our understanding of EF in the canonical non-smooth convex setting by establishing new lower complexity bounds for first-order algorithms with contractive compression. Next, we propose Safe-EF, a novel algorithm that matches our lower bound (up to a constant) while enforcing safety constraints essential for practical applications. Extending our approach to the stochastic setting, we bridge the gap between theory and practical implementation. Extensive experiments in a reinforcement learning setup, simulating distributed humanoid robot training, validate the effectiveness of Safe-EF in ensuring safety and reducing communication complexity.

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ICLR Conference 2025 Conference Paper

Towards Faster Decentralized Stochastic Optimization with Communication Compression

Rustem Islamov
Yuan Gao 0025
Sebastian U. Stich

Communication efficiency has garnered significant attention as it is considered the main bottleneck for large-scale decentralized Machine Learning applications in distributed and federated settings. In this regime, clients are restricted to transmitting small amounts of compressed information to their neighbors over a communication graph. Numerous endeavors have been made to address this challenging problem by developing algorithms with compressed communication for decentralized non-convex optimization problems. Despite considerable efforts, current theoretical understandings of the problem are still very limited, and existing algorithms all suffer from various limitations. In particular, these algorithms typically rely on strong, and often infeasible assumptions such as bounded data heterogeneity or require large batch access while failing to achieve linear speedup with the number of clients. In this paper, we introduce MoTEF, a novel approach that integrates communication compression with $\textbf{Mo}$mentum $\textbf{T}$racking and $\textbf{E}$rror $\textbf{F}$eedback. MoTEF is the first algorithm to achieve an asymptotic rate matching that of distributed SGD under arbitrary data heterogeneity, hence resolving a long-standing theoretical obstacle in decentralized optimization with compressed communication. We provide numerical experiments to validate our theoretical findings and confirm the practical superiority of MoTEF.

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ICLR Conference 2024 Conference Paper

EControl: Fast Distributed Optimization with Compression and Error Control

Yuan Gao 0025
Rustem Islamov
Sebastian U. Stich

Modern distributed training relies heavily on communication compression to reduce the communication overhead. In this work, we study algorithms employing a popular class of contractive compressors in order to reduce communication overhead. However, the naive implementation often leads to unstable convergence or even exponential divergence due to the compression bias. Error Compensation (EC) is an extremely popular mechanism to mitigate the aforementioned issues during the training of models enhanced by contractive compression operators. Compared to the effectiveness of EC in the data homogeneous regime, the understanding of the practicality and theoretical foundations of EC in the data heterogeneous regime is limited. Existing convergence analyses typically rely on strong assumptions such as bounded gradients, bounded data heterogeneity, or large batch accesses, which are often infeasible in modern Machine Learning Applications. We resolve the majority of current issues by proposing EControl, a novel mechanism that can regulate error compensation by controlling the strength of the feedback signal. We prove fast convergence for EControl in standard strongly convex, general convex, and nonconvex settings without any additional assumptions on the problem or data heterogeneity. We conduct extensive numerical evaluations to illustrate the efficacy of our method and support our theoretical findings.

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NeurIPS Conference 2024 Conference Paper

Loss Landscape Characterization of Neural Networks without Over-Parametrization

Rustem Islamov
Niccoló Ajroldi
Antonio Orvieto
Aurelien Lucchi

Modern machine learning heavily depends on the effectiveness of optimization techniques. While deep learning models have achieved remarkable empirical results in training, their theoretical underpinnings remain somewhat elusive. Ensuring the convergence of optimization methods requires imposing specific structures on the objective function which often do not hold in practice. One prominent example is the widely recognized Polyak-Lojasiewicz (PL) inequality, which has garnered considerable attention in recent years. However, validating such assumptions for deep neural networks entails substantial and often impractical levels of over-parametrization. In order to address this limitation, we propose a novel class of functions that can characterize the loss landscape of modern deep models without requiring extensive over-parametrization and can also include saddle points. Crucially, we prove that gradient-based optimizers possess theoretical guarantees of convergence under this assumption. Finally, we validate the soundness of our assumption through both theoretical analysis and empirical experimentation across a diverse range of deep learning models.

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TMLR Journal 2023 Journal Article

Adaptive Compression for Communication-Efficient Distributed Training

Maksim Makarenko
Elnur Gasanov
Abdurakhmon Sadiev
Rustem Islamov
Peter Richtárik

We propose Adaptive Compressed Gradient Descent (AdaCGD) -- a novel optimization algorithm for communication-efficient training of supervised machine learning models with adaptive compression level. Our approach is inspired by the recently proposed three point compressor (3PC) framework of Richtarik et al. (2022), which includes error feedback (EF21), lazily aggregated gradient (LAG), and their combination as special cases, and offers the current state-of-the-art rates for these methods under weak assumptions. While the above mechanisms offer a fixed compression level or adapt between two extreme compression levels, we propose a much finer adaptation. In particular, we allow users to choose between selected contractive compression mechanisms, such as Top-$K$ sparsification with a user-defined selection of sparsification levels $K$, or quantization with a user-defined selection of quantization levels, or their combination. AdaCGD chooses the appropriate compressor and compression level adaptively during the optimization process. Besides i) proposing a theoretically-grounded multi-adaptive communication compression mechanism, we further ii) extend the 3PC framework to bidirectional compression, i.e., allow the server to compress as well, and iii) provide sharp convergence bounds in the strongly convex, convex, and nonconvex settings. The convex regime results are new even for several key special cases of our general mechanism, including 3PC and EF21. In all regimes, our rates are superior compared to all existing adaptive compression methods.

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TMLR Journal 2023 Journal Article

Distributed Newton-Type Methods with Communication Compression and Bernoulli Aggregation

Rustem Islamov
Xun Qian
Slavomir Hanzely
Mher Safaryan
Peter Richtárik

Despite their high computation and communication costs, Newton-type methods remain an appealing option for distributed training due to their robustness against ill-conditioned convex problems. In this work, we study communication compression and aggregation mechanisms for curvature information in order to reduce these costs while preserving theoretically superior local convergence guarantees. We prove that the recently developed class of three point compressors (3PC) of [Richtarik et al., 2022] for gradient communication can be generalized to Hessian communication as well. This result opens up a wide variety of communication strategies, such as contractive compression and lazy aggregation, available to our disposal to compress prohibitively costly curvature information. Moreover, we discovered several new 3PC mechanisms, such as adaptive thresholding and Bernoulli aggregation, which require reduced communication and occasional Hessian computations. Furthermore, we extend and analyze our approach to bidirectional communication compression and partial device participation setups to cater to the practical considerations of applications in federated learning. For all our methods, we derive fast condition-number-independent local linear and/or superlinear convergence rates. Finally, with extensive numerical evaluations on convex optimization problems, we illustrate that our designed schemes achieve state-of-the-art communication complexity compared to several key baselines using second-order information.

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ICML Conference 2022 Conference Paper

FedNL: Making Newton-Type Methods Applicable to Federated Learning

Mher Safaryan
Rustem Islamov
Xun Qian
Peter Richtárik

Inspired by recent work of Islamov et al (2021), we propose a family of Federated Newton Learn (\algname{FedNL}) methods, which we believe is a marked step in the direction of making second-order methods applicable to FL. In contrast to the aforementioned work, \algname{FedNL} employs a different Hessian learning technique which i) enhances privacy as it does not rely on the training data to be revealed to the coordinating server, ii) makes it applicable beyond generalized linear models, and iii) provably works with general contractive compression operators for compressing the local Hessians, such as Top-$K$ or Rank-$R$, which are vastly superior in practice. Notably, we do not need to rely on error feedback for our methods to work with contractive compressors. Moreover, we develop \algname{FedNL-PP}, \algname{FedNL-CR} and \algname{FedNL-LS}, which are variants of \algname{FedNL} that support partial participation, and globalization via cubic regularization and line search, respectively, and \algname{FedNL-BC}, which is a variant that can further benefit from bidirectional compression of gradients and models, i. e. , smart uplink gradient and smart downlink model compression. We prove local convergence rates that are independent of the condition number, the number of training data points, and compression variance. Our communication efficient Hessian learning technique provably learns the Hessian at the optimum. Finally, we perform a variety of numerical experiments that show that our \algname{FedNL} methods have state-of-the-art communication complexity when compared to key baselines.

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ICML Conference 2021 Conference Paper

Distributed Second Order Methods with Fast Rates and Compressed Communication

Rustem Islamov
Xun Qian
Peter Richtárik

We develop several new communication-efficient second-order methods for distributed optimization. Our first method, NEWTON-STAR, is a variant of Newton’s method from which it inherits its fast local quadratic rate. However, unlike Newton’s method, NEWTON-STAR enjoys the same per iteration communication cost as gradient descent. While this method is impractical as it relies on the use of certain unknown parameters characterizing the Hessian of the objective function at the optimum, it serves as the starting point which enables us to design practical variants thereof with strong theoretical guarantees. In particular, we design a stochastic sparsification strategy for learning the unknown parameters in an iterative fashion in a communication efficient manner. Applying this strategy to NEWTON-STAR leads to our next method, NEWTON-LEARN, for which we prove local linear and superlinear rates independent of the condition number. When applicable, this method can have dramatically superior convergence behavior when compared to state-of-the-art methods. Finally, we develop a globalization strategy using cubic regularization which leads to our next method, CUBIC-NEWTON-LEARN, for which we prove global sublinear and linear convergence rates, and a fast superlinear rate. Our results are supported with experimental results on real datasets, and show several orders of magnitude improvement on baseline and state-of-the-art methods in terms of communication complexity.

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