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Bilevel optimization have gained growing interests, with numerousapplications found in meta learning, minimax games, reinforcement learning, andnested composition optimization. This paper studies the problem of distributedbilevel optimization over a network where agents can only communicate withneighbors, including examples from multi-task, multi-agent learning andfederated learning. In this paper, we propose a gossip-based distributedbilevel learning algorithm that allows networked agents to solve both the innerand outer optimization problems in a single timescale and share information vianetwork propagation. We show that our algorithm enjoys the$\mathcal{O}(\frac{1}{K \epsilon^2})$ per-agent sample complexity for generalnonconvex bilevel optimization and $\mathcal{O}(\frac{1}{K \epsilon})$ forstrongly convex objective, achieving a speedup that scales linearly with thenetwork size. The sample complexities are optimal in both $\epsilon$ and $K$.We test our algorithm on the examples of hyperparameter tuning anddecentralized reinforcement learning. Simulated experiments confirmed that ouralgorithm achieves the state-of-the-art training efficiency and test accuracy.

Decentralized Gossip-Based Stochastic Bilevel Optimization over Communication Networks