Distributed Personalized Empirical Risk Minimization

This paper advocates a new paradigm Personalized Empirical Risk Minimization (PERM) to facilitate learning from heterogeneous data sources without imposing stringent constraints on computational resources shared by participating devices. In PERM, we aim to learn a distinct model for each client by learning who to learn with and personalizing the aggregation of local empirical losses by effectively estimating the statistical discrepancy among data distributions, which entails optimal statistical accuracy for all local distributions and overcomes the data heterogeneity issue. To learn personalized models at scale, we propose a distributed algorithm that replaces the standard model averaging with model shuffling to simultaneously optimize PERM objectives for all devices. This also allows us to learn distinct model architectures (e.g., neural networks with different numbers of parameters) for different clients, thus confining underlying memory and compute resources of individual clients. We rigorously analyze the convergence of the proposed algorithm and conduct experiments that corroborate the effectiveness of the proposed paradigm.

Tight Analysis of Extra-gradient and Optimistic Gradient Methods For Nonconvex Minimax Problems

Despite the established convergence theory of Optimistic Gradient Descent Ascent (OGDA) and Extragradient (EG) methods for the convex-concave minimax problems, little is known about the theoretical guarantees of these methods in nonconvex settings. To bridge this gap, for the first time, this paper establishes the convergence of OGDA and EG methods under the nonconvex-strongly-concave (NC-SC) and nonconvex-concave (NC-C) settings by providing a unified analysis through the lens of single-call extra-gradient methods. We further establish lower bounds on the convergence of GDA/OGDA/EG, shedding light on the tightness of our analysis. We also conduct experiments supporting our theoretical results. We believe our results will advance the theoretical understanding of OGDA and EG methods for solving complicated nonconvex minimax real-world problems, e.g., Generative Adversarial Networks (GANs) or robust neural networks training.