Decentralized Gossip-Based Stochastic Bilevel Optimization over Communication Networks
This addresses distributed optimization problems in multi-task, multi-agent, and federated learning, offering incremental improvements in efficiency for networked agents.
The paper tackles decentralized bilevel optimization over communication networks by proposing a gossip-based algorithm that solves inner and outer problems in a single timescale, achieving optimal sample complexities of O(1/(Kε^2)) for nonconvex and O(1/(Kε)) for strongly convex objectives, with linear speedup in network size.
Bilevel optimization have gained growing interests, with numerous applications found in meta learning, minimax games, reinforcement learning, and nested composition optimization. This paper studies the problem of distributed bilevel optimization over a network where agents can only communicate with neighbors, including examples from multi-task, multi-agent learning and federated learning. In this paper, we propose a gossip-based distributed bilevel learning algorithm that allows networked agents to solve both the inner and outer optimization problems in a single timescale and share information via network propagation. We show that our algorithm enjoys the $\mathcal{O}(\frac{1}{K ε^2})$ per-agent sample complexity for general nonconvex bilevel optimization and $\mathcal{O}(\frac{1}{K ε})$ for strongly convex objective, achieving a speedup that scales linearly with the network size. The sample complexities are optimal in both $ε$ and $K$. We test our algorithm on the examples of hyperparameter tuning and decentralized reinforcement learning. Simulated experiments confirmed that our algorithm achieves the state-of-the-art training efficiency and test accuracy.