36d373e4aabf0ba9b6fa65b0133cdafa-Paper-Conference.pdf

We aim to provide a unified convergence analysis for permutation-based Stochastic Gradient Descent (SGD), where data examples are permuted before each epoch. By examining the relations among permutations, we classify existing permutation-based SGD algorithms into three categories: Arbitrary Permutations, Independent Permutations (including Random Reshuffling and FlipFlop [Rajput et al., 2022]), Dependent Permutations (including GraBs [Lu et al., 2022a; Cooper et al., 2023]). Existing unified analyses failed to encompass the Dependent Permutations category due to the inter-epoch permutation dependency. In this work, we propose a generalized assumption that explicitly characterizes the dependence of permutations across epochs. Building upon this assumption, we develop a unified framework for permutation-based SGD with arbitrary permutations of examples, incorporating all the existing permutation-based SGD algorithms. Furthermore, we adapt our framework for Federated Learning (FL), developing a unified framework for regularized client participation FL with arbitrary permutations of clients.