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Federated Learning

Main Challenges

  • Communication cost: In federated settings, clients communicate with a central server over limited-bandwidth links; transmission of dense vectors is infeasible at large scale.
  • Data heterogeneity: Client datasets are non-IID, causing client drift in local methods, which degrades the overall performance.
  • Privacy guarantees: To protect user data, privacy-preserving algorithms clip update magnitudes and add noise. This DP noise degrades model performance, making the privacy-utility tradeoff a key practical concern.

My Contributions

Analysis of Differential Private Algorithms

Standard analyses of DP-SGD rely on the unrealistic bounded-gradient assumption. We propose an algorithm with high-probability convergence guarantees that avoids this restriction while achieving an optimal privacy-utility tradeoff [13]. Complementary SDE analyses [19] show that adaptive methods such as DP-SignSGD and DP-Adam perform better under strong privacy constraints and are less sensitive to learning-rate tuning.

Non-smooth Distributed Optimization with Compression

Works on distributed RL remains limited, and such problems are inherently nonsmooth due to operations like maximization. In [15], we develop an algorithm with provable convergence for nonsmooth convex objectives that simultaneously handles both the objective and constraints. The method significantly outperforms several baselines in distributed training of humanoid agents.

Gradient Methods with Biased Compression and Convergence Guarantees

Compression is a practical approach to reducing communication overhead. Biased compressors (e.g., Top-K) are particularly effective in practice, but introduce bias that can degrade performance. We design provably convergent algorithms for smooth nonconvex, convex, and strongly convex objectives that achieve optimal asymptotic complexity while reducing communication in both centralized [9] and decentralized [10] settings. In [5], we further develop adaptive biased compressors that adjust compression strength during training.

Methods with Provable Improvements from Local Updates

Standard convergence guarantees for local methods do not capture the benefits of local updates, despite their strong empirical performance. In [6], we identified a class of functions for which local methods provably achieve faster convergence.

Second-order Algorithms for Federated Learning with Compression

Transmitting full Hessians in federated settings is impractical. We address this bottleneck by designing second-order methods that employ Hessian and gradient compression to reduce communication overhead [1-4]. Crucially, these methods retain the hallmark properties of Newton's method, achieving local superlinear convergence independent of the condition number.

Research Impact

These theoretical results advance the understanding of optimization algorithms in federated and distributed settings by providing stronger guarantees under realistic conditions, improving communication and computation efficiency, and explaining the robustness and effectiveness of modern methods in practice.

Selected Publications

2026
[19] Adaptive Methods Are Preferable in High Privacy Settings: An SDE Perspective.
14th International Conference on Learning Representations (ICLR 2026)
PDF arXiv ICLR Poster
Differential Privacy (DP) is becoming central to large-scale training as privacy regulations tighten. We revisit how DP noise interacts with adaptivity in optimization through the lens of stochastic differential equations, providing the first SDE-based analysis of private optimizers. Focusing on DP-SGD and DP-SignSGD under per-example clipping, we show a sharp contrast under fixed hyperparameters: DP-SGD converges at a Privacy-Utility Trade-Off of ${\small \mathcal{O}(1/\varepsilon^2)}$ with speed independent of ${\small \varepsilon}$, while DP-SignSGD converges at a speed linear in $\varepsilon$ with an ${\small \mathcal{O}(1/\varepsilon)}$ trade-off, dominating in high-privacy or large batch noise regimes. By contrast, under optimal learning rates, both methods achieve comparable theoretical asymptotic performance; however, the optimal learning rate of DP-SGD scales linearly with ${\small \varepsilon}$, while that of DP-SignSGD is essentially ${\small \varepsilon}$-independent. This makes adaptive methods far more practical, as their hyperparameters transfer across privacy levels with little or no re-tuning. Empirical results confirm our theory across training and test metrics, and empirically extend from DP-SignSGD to DP-Adam.

2025
[15] Safe-EF: Error Feedback for Nonsmooth Constrained Optimization.
42nd International Conference on Machine Learning (ICML 2025)
PDF arXiv ICML Poster
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.

[14] Unbiased and Sign Compression in Distributed Learning: Comparing Noise Resilience via SDEs.
28th International Conference on Artificial Intelligence and Statistics (Oral, AISTATS 2025)
PDF arXiv AISTATS Poster
Distributed methods are essential for handling machine learning pipelines comprising large-scale models and datasets. However, their benefits often come at the cost of increased communication overhead between the central server and agents, which can become the main bottleneck, making training costly or even unfeasible in such systems. Compression methods such as quantization and sparsification can alleviate this issue. Still, their robustness to large and heavy-tailed gradient noise, a phenomenon sometimes observed in language modeling, remains poorly understood. This work addresses this gap by analyzing Distributed Compressed SGD (DCSGD) and Distributed SignSGD (DSignSGD) using stochastic differential equations (SDEs). Our results show that DCSGD with unbiased compression is more vulnerable to noise in stochastic gradients, while DSignSGD remains robust, even under large and heavy-tailed noise. Additionally, we propose new scaling rules for hyperparameter tuning to mitigate performance degradation due to compression. These findings are empirically validated across multiple deep learning architectures and datasets, providing practical recommendations for distributed optimization.

[13] Double Momentum and Error Feedback for Clipping with Fast Rates and Differential Privacy.

PDF arXiv

Strong Differential Privacy (DP) and Optimization guarantees are two desirable properties for a method in Federated Learning (FL). However, existing algorithms do not achieve both properties at once: they either have optimal DP guarantees but rely on restrictive assumptions such as bounded gradients/bounded data heterogeneity, or they ensure strong optimization performance but lack DP guarantees. To address this gap in the literature, we propose and analyze a new method called Clip21-SGD2M based on a novel combination of clipping, heavy-ball momentum, and Error Feedback. In particular, for non-convex smooth distributed problems with clients having arbitrarily heterogeneous data, we prove that Clip21-SGD2M has optimal convergence rate and also near optimal (local-)DP neighborhood. Our numerical experiments on non-convex logistic regression and training of neural networks highlight the superiority of Clip21-SGD2M over baselines in terms of the optimization performance for a given DP-budget.

2024
[10] Towards Faster Decentralized Stochastic Optimization with Communication Compression.
13th International Conference on Learning Representations (ICLR 2025)
PDF arXiv ICLR Poster
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 quantized 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, the current results suffer from various issues such as non-scalability with the number of clients, requirements for large batches, or bounded gradient assumption. In this paper, we introduce MoTEF, a novel approach that integrates communication compression with Momentum Tracking and Error Feedback. Our analysis demonstrates that MoTEF achieves most of the desired properties, and significantly outperforms existing methods under arbitrary data heterogeneity. We provide numerical experiments to validate our theoretical findings and confirm the practical superiority of MoTEF.

2023
[9] EControl: Fast Distributed Optimization with Compression and Error Control.
12th International Conference on Learning Representations (ICLR 2025)
PDF arXiv ICLR Poster
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.

[8] AsGrad: A Sharp Unified Analysis of Asynchronous-SGD Algorithms.
27th International Conference on Artificial Intelligence and Statistics (AISTATS 2024)
PDF arXiv AISTATS Poster
We analyze asynchronous-type algorithms for distributed SGD in the heterogeneous setting, where each worker has its own computation and communication speeds, as well as data distribution. In these algorithms, workers compute possibly stale and stochastic gradients associated with their local data at some iteration back in history and then return those gradients to the server without synchronizing with other workers. We present a unified convergence theory for non-convex smooth functions in the heterogeneous regime. The proposed analysis provides convergence for pure asynchronous SGD and its various modifications. Moreover, our theory explains what affects the convergence rate and what can be done to improve the performance of asynchronous algorithms. In particular, we introduce a novel asynchronous method based on worker shuffling. As a by-product of our analysis, we also demonstrate convergence guarantees for gradient-type algorithms such as SGD with random reshuffling and shuffle-once mini-batch SGD. The derived rates match the best-known results for those algorithms, highlighting the tightness of our approach. Finally, our numerical evaluations support theoretical findings and show the good practical performance of our method.

[7] Clip21: Error Feedback for Gradient Clipping.

PDF arXiv

Motivated by the increasing popularity and importance of large-scale training under differential privacy (DP) constraints, we study distributed gradient methods with gradient clipping, i.e., clipping applied to the gradients computed from local information at the nodes. While gradient clipping is an essential tool for injecting formal DP guarantees into gradient-based methods [Abadi et al., 2016], it also induces bias which causes serious convergence issues specific to the distributed setting. Inspired by recent progress in the error-feedback literature which is focused on taming the bias/error introduced by communication compression operators such as Top-k [Richtárik et al., 2021], and mathematical similarities between the clipping operator and contractive compression operators, we design Clip21 -- the first provably effective and practically useful error feedback mechanism for distributed methods with gradient clipping. We prove that our method converges at the same ${\tiny \mathcal{O}(1/K)}$ rate as distributed gradient descent in the smooth nonconvex regime, which improves the previous best ${\tiny \mathcal{O}(1/\sqrt{K})}$ rate which was obtained under significantly stronger assumptions. Our method converges significantly faster in practice than competing methods.

[6] Partially Personalized Federated Learning: Breaking the Curse of Data Heterogeneity.
Transactions on Machine Learning Research (TMLR 2025)
PDF arXiv TMLR
We present 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.

2022
[5] Adaptive Compression for Communication-Efficient Distributed Training.

Transactions on Machine Learning Research (TMLR 2023)
PDF arXiv TMLR

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 extremes only, our proposal is to perform a much finer adaptation. In particular, we allow the user to choose any number of arbitrarily chosen 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., we 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.

[4] Distributed Newton-Type Methods with Communication Compression and Bernoulli Aggregation.
Transactions on Machine Learning Research (TMLR 2023)
PDF arXiv TMLR poster HOO-22 NeurIPS
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.

2021
[3] Basis Matters: Better Communication-Efficient Second Order Methods for Federated Learning.
25th International Conference on Artificial Intelligence and Statistics (AISTATS 2022)
PDF arXiv AISTATS Poster
Recent advances in distributed optimization have shown that Newton-type methods with proper communication compression mechanisms can guarantee fast local rates and low communication cost compared to first order methods. We discover that the communication cost of these methods can be further reduced, sometimes dramatically so, with a surprisingly simple trick: Basis Learn (BL). The idea is to transform the usual representation of the local Hessians via a change of basis in the space of matrices and apply compression tools to the new representation. To demonstrate the potential of using custom bases, we design a new Newton-type method (BL1), which reduces communication cost via both BL technique and bidirectional compression mechanism. Furthermore, we present two alternative extensions (BL2 and BL3) to partial participation to accommodate federated learning applications. We prove local linear and superlinear rates independent of the condition number. Finally, we support our claims with numerical experiments by comparing several first and second-order methods.

[2] FedNL: Making Newton-Type Methods Applicable to Federated Learning.
39th International Conference on Machine Learning (ICML 2022)
PDF arXiv ICML FL-ICML BFOM-ICML Poster 3-min video
Inspired by recent work of Islamov et al (2021), we propose a family of Federated Newton Learn (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, 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 FedNL-PP, FedNL-CR and FedNL-LS, which are variants of FedNL that support partial participation, and globalization via cubic regularization and line search, respectively, and 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 FedNL methods have state-of-the-art communication complexity when compared to key baselines.

[1] Distributed Second Order Methods with Fast Rates and Compressed Communication.
38th International Conference on Machine Learning (ICML 2021)
PDF arXiv ICML NSF-TRIPODS Poster 5-min video
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 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.