Compositional federated learning: Applications in distributionally robust averaging and meta learning

TL;DR

This paper introduces ComFedL, a novel compositional federated learning algorithm that addresses hierarchical data problems like distributionally robust FL and MAML, with proven convergence and practical applications.

Contribution

It is the first to connect federated learning with compositional stochastic optimization, transforming complex problems into simpler composition optimization tasks.

Findings

Achieves a convergence rate of O(1/√T).

Effectively applies to distributionally robust FL and MAML.

Demonstrates practical effectiveness on real tasks.

Abstract

In the paper, we propose an effective and efficient Compositional Federated Learning (ComFedL) algorithm for solving a new compositional Federated Learning (FL) framework, which frequently appears in many data mining and machine learning problems with a hierarchical structure such as distributionally robust FL and model-agnostic meta learning (MAML). Moreover, we study the convergence analysis of our ComFedL algorithm under some mild conditions, and prove that it achieves a convergence rate of $O(\frac{1}{\sqrt{T}})$, where $T$ denotes the number of iteration. To the best of our knowledge, our new Compositional FL framework is the first work to bridge federated learning with composition stochastic optimization. In particular, we first transform the distributionally robust FL (i.e., a minimax optimization problem) into a simple composition optimization problem by using KL divergence regularization. At the same time, we also first transform the distribution-agnostic MAML problem (i.e., a minimax optimization problem) into a simple yet effective composition optimization problem. Finally, we apply two popular machine learning tasks, i.e., distributionally robust FL and MAML to demonstrate the effectiveness of our algorithm.