Author name cluster

Filip Hanzely

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9 papers

2 author rows

TMLR Journal 2023 Journal Article

Personalized Federated Learning: A Unified Framework and Universal Optimization Techniques

Filip Hanzely
Boxin Zhao
Mladen Kolar

We investigate the optimization aspects of personalized Federated Learning (FL). We propose general optimizers that can be applied to numerous existing personalized FL objectives, specifically a tailored variant of Local SGD and variants of accelerated coordinate descent/accelerated SVRCD. By examining a general personalized objective capable of recovering many existing personalized FL objectives as special cases, we develop a comprehensive optimization theory applicable to a wide range of strongly convex personalized FL models in the literature. We showcase the practicality and/or optimality of our methods in terms of communication and local computation. Remarkably, our general optimization solvers and theory can recover the best-known communication and computation guarantees for addressing specific personalized FL objectives. Consequently, our proposed methods can serve as universal optimizers, rendering the design of task-specific optimizers unnecessary in many instances.

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NeurIPS Conference 2021 Conference Paper

Smoothness Matrices Beat Smoothness Constants: Better Communication Compression Techniques for Distributed Optimization

Mher Safaryan
Filip Hanzely
Peter Richtarik

Large scale distributed optimization has become the default tool for the training of supervised machine learning models with a large number of parameters and training data. Recent advancements in the field provide several mechanisms for speeding up the training, including {\em compressed communication}, {\em variance reduction} and {\em acceleration}. However, none of these methods is capable of exploiting the inherently rich data-dependent smoothness structure of the local losses beyond standard smoothness constants. In this paper, we argue that when training supervised models, {\em smoothness matrices}---information-rich generalizations of the ubiquitous smoothness constants---can and should be exploited for further dramatic gains, both in theory and practice. In order to further alleviate the communication burden inherent in distributed optimization, we propose a novel communication sparsification strategy that can take full advantage of the smoothness matrices associated with local losses. To showcase the power of this tool, we describe how our sparsification technique can be adapted to three distributed optimization algorithms---DCGD, DIANA and ADIANA---yielding significant savings in terms of communication complexity. The new methods always outperform the baselines, often dramatically so.

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UAI Conference 2020 Conference Paper

99% of Worker-Master Communication in Distributed Optimization Is Not Needed

Konstantin Mishchenko
Filip Hanzely
Peter Richtárik

In this paper we discuss sparsification of worker-to-server communication in large distributed systems. We improve upon algorithms that fit the following template: a local gradient estimate is computed independently by each worker, then communicated to a master, which subsequently performs averaging. The average is broadcast back to the workers, which use it to perform a gradient-type step to update the local version of the model. We observe that the above template is fundamentally inefficient in that too much data is unnecessarily communicated from the workers to the server, which slows down the overall system. We propose a fix based on a new update-sparsification method we develop in this work, which we suggest be used on top of existing methods. Namely, we develop a new variant of parallel block coordinate descent based on independent sparsification of the local gradient estimates before communication. We demonstrate that with only $m/n$ blocks sent by each of $n$ workers, where $m$ is the total number of parameter blocks, the theoretical iteration complexity of the underlying distributed methods is essentially unaffected. As an illustration, this means that when $n=100$ parallel workers are used, the communication of 99% blocks is redundant, and hence a waste of time. Our theoretical claims are supported through extensive numerical experiments which demonstrate an almost perfect match with our theory on a number of synthetic and real datasets.

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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 2020 Conference Paper

Stochastic Subspace Cubic Newton Method

Filip Hanzely
Nikita Doikov
Yurii E. Nesterov
Peter Richtárik

In this paper, we propose a new randomized second-order optimization algorithm—Stochastic Subspace Cubic Newton (SSCN)—for minimizing a high dimensional convex function $f$. Our method can be seen both as a \emph{stochastic} extension of the cubically-regularized Newton method of Nesterov and Polyak (2006), and a \emph{second-order} enhancement of stochastic subspace descent of Kozak et al. (2019). We prove that as we vary the minibatch size, the global convergence rate of SSCN interpolates between the rate of stochastic coordinate descent (CD) and the rate of cubic regularized Newton, thus giving new insights into the connection between first and second-order methods. Remarkably, the local convergence rate of SSCN matches the rate of stochastic subspace descent applied to the problem of minimizing the quadratic function $\frac12 (x-x^*)^\top \nabla^2f(x^*)(x-x^*)$, where $x^*$ is the minimizer of $f$, and hence depends on the properties of $f$ at the optimum only. Our numerical experiments show that SSCN outperforms non-accelerated first-order CD algorithms while being competitive to their accelerated variants.

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ICML Conference 2020 Conference Paper

Variance Reduced Coordinate Descent with Acceleration: New Method With a Surprising Application to Finite-Sum Problems

Filip Hanzely
Dmitry Kovalev
Peter Richtárik

We propose an accelerated version of stochastic variance reduced coordinate descent – ASVRCD. As other variance reduced coordinate descent methods such as SEGA or SVRCD, our method can deal with problems that include a non-separable and non-smooth regularizer, while accessing a random block of partial derivatives in each iteration only. However, ASVRCD incorporates Nesterov’s momentum, which offers favorable iteration complexity guarantees over both SEGA and SVRCD. As a by-product of our theory, we show that a variant of Katyusha (Allen-Zhu, 2017) is a specific case of ASVRCD, recovering the optimal oracle complexity for the finite sum objective.

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AAAI Conference 2019 Conference Paper

A Nonconvex Projection Method for Robust PCA

Aritra Dutta
Filip Hanzely
Peter Richtàrik

Robust principal component analysis (RPCA) is a well-studied problem whose goal is to decompose a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and apply an alternating projection method to solve it. To the best of our knowledge, this is the first paper proposing a method that solves RPCA problem without considering any objective function, convex relaxation, or surrogate convex constraints. We demonstrate through extensive numerical experiments on a variety of applications, including shadow removal, background estimation, face detection, and galaxy evolution, that our approach matches and often significantly outperforms current state-of-the-art in various ways.

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NeurIPS Conference 2018 Conference Paper

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

Robert Gower
Filip Hanzely
Peter Richtarik
Sebastian Stich

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices in such a way that all iterates (approximate solutions) generated by the algorithm are positive definite matrices themselves. This opens the way for many applications in the field of optimization and machine learning. As an application of our general theory, we develop the first accelerated (deterministic and stochastic) quasi-Newton updates. Our updates lead to provably more aggressive approximations of the inverse Hessian, and lead to speed-ups over classical non-accelerated rules in numerical experiments. Experiments with empirical risk minimization show that our rules can accelerate training of machine learning models.

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NeurIPS Conference 2018 Conference Paper

SEGA: Variance Reduction via Gradient Sketching

Filip Hanzely
Konstantin Mishchenko
Peter Richtarik

We propose a novel randomized first order optimization method---SEGA (SkEtched GrAdient method)---which progressively throughout its iterations builds a variance-reduced estimate of the gradient from random linear measurements (sketches) of the gradient provided at each iteration by an oracle. In each iteration, SEGA updates the current estimate of the gradient through a sketch-and-project operation using the information provided by the latest sketch, and this is subsequently used to compute an unbiased estimate of the true gradient through a random relaxation procedure. This unbiased estimate is then used to perform a gradient step. Unlike standard subspace descent methods, such as coordinate descent, SEGA can be used for optimization problems with a non-separable proximal term. We provide a general convergence analysis and prove linear convergence for strongly convex objectives. In the special case of coordinate sketches, SEGA can be enhanced with various techniques such as importance sampling, minibatching and acceleration, and its rate is up to a small constant factor identical to the best-known rate of coordinate descent.

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