A Communication-Efficient Algorithm for Federated Multilevel Stochastic Compositional Optimization

Recent literature shows a growing interest in the integration of federated learning (FL) and multilevel stochastic compositional optimization (MSCO), which arises in meta-learning and reinforcement learning. It is known that a bottleneck in FL is communication efficiency, when compared to fully dece...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 72; pp. 1 - 15
Main Authors: Yang, Shuoguang, Li, Fengpei
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Communication
Communication Efficient
Complexity
Complexity theory
Distributed Optimization
Extrapolation
Federated learning
Multilevel Stochastic Compositional Optimization
Optimization
Reinforcement learning
Signal processing algorithms
Stochastic processes
Task analysis
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:Recent literature shows a growing interest in the integration of federated learning (FL) and multilevel stochastic compositional optimization (MSCO), which arises in meta-learning and reinforcement learning. It is known that a bottleneck in FL is communication efficiency, when compared to fully decentralized methods. Yet, it remains unclear whether communication-efficient algorithms exist for MSCO in distributed settings. Single-loop optimizations, used in recent methods, structurally require communications per fixed samples generated, resulting in communication complexity being no less than sample complexity, hence lower bounded by <inline-formula><tex-math notation="LaTeX">\mathcal O (1/\epsilon)</tex-math></inline-formula>, for reaching an ε -accurate solution. This paper studies distibuted MSCO of a smooth, strongly convex objective with smooth gradients. Based on a double-loop strategy, we proposed Federated Stochastic Compositional Gradient Extrapolation (F ed SCGE), a federated MSCO method that attains an optimal <inline-formula><tex-math notation="LaTeX">\mathcal O(\log\frac{1}{\epsilon})</tex-math></inline-formula> communication complexity while maintaining an (almost) optimal <inline-formula><tex-math notation="LaTeX">\tilde{\mathcal O}(1/\epsilon)</tex-math></inline-formula> sample complexity, both of which independent of client number, making the approach scalable. Our analysis leverages the random gradient extrapolation method (RGEM) in [19] and generalizes it by overcoming the biased gradients of MSCO. To the best of our knowledge, our work is the first to show the simultaneous attainability of both complexity bounds for distributed MSCO.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2024.3392351