Hongchang Gao

Hongchang Gao

In this paper, we studied the federated bilevel optimization problem, which has widespread applications in machine learning. In particular, we developed two momentum-based algorithms for optimizing this kind of problem and established the convergence rate of our two algorithms, providing the sample and communication complexities. Importantly, to the best of our knowledge, our convergence rate is the first one achieving the linear speedup with respect to the number of devices for federated bilevel optimization algorithms. At last, our extensive experimental results confirm the effectiveness of our two algorithms.

Xinwen Zhang, Yihan Zhang, Hongchang Gao

Existing decentralized stochastic optimization methods assume the lower-level loss function is strongly convex and the stochastic gradient noise has finite variance. These strong assumptions typically are not satisfied in real-world machine learning models. To address these limitations, we develop a novel decentralized stochastic bilevel optimization algorithm for the nonconvex bilevel optimization problem under heavy-tailed noises. Specifically, we develop a normalized stochastic variance-reduced bilevel gradient descent algorithm, which does not rely on any clipping operation. Moreover, we establish its convergence rate by innovatively bounding interdependent gradient sequences under heavy-tailed noises for nonconvex decentralized bilevel optimization problems. As far as we know, this is the first decentralized bilevel optimization algorithm with rigorous theoretical guarantees under heavy-tailed noises. The extensive experimental results confirm the effectiveness of our algorithm in handling heavy-tailed noises.