FEDNEST: Federated Bilevel, Minimax, and Compositional Optimization

• URL: http://arxiv.org/abs/2205.02215v1
• Date: Wed, 4 May 2022 17:48:55 GMT
• Title: FEDNEST: Federated Bilevel, Minimax, and Compositional Optimization
• Authors: Davoud Ataee Tarzanagh, Mingchen Li, Christos Thrampoulidis, Samet Oymak
• Abstract summary: Many contemporary ML problems fall under nested bilevel programming that subsumes minimax and compositional optimization. We propose FedNest: A federated alternating gradient method to address general nested problems.
• Score: 53.78643974257301
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Standard federated optimization methods successfully apply to stochastic problems with \textit{single-level} structure. However, many contemporary ML problems -- including adversarial robustness, hyperparameter tuning, and actor-critic -- fall under nested bilevel programming that subsumes minimax and compositional optimization. In this work, we propose FedNest: A federated alternating stochastic gradient method to address general nested problems. We establish provable convergence rates for FedNest in the presence of heterogeneous data and introduce variations for bilevel, minimax, and compositional optimization. FedNest introduces multiple innovations including federated hypergradient computation and variance reduction to address inner-level heterogeneity. We complement our theory with experiments on hyperparameter \& hyper-representation learning and minimax optimization that demonstrate the benefits of our method in practice. Code is available at https://github.com/mc-nya/FedNest.

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