Provably Faster Algorithms for Bilevel Optimization and Applications to Meta-Learning

10/15/2020 ∙ by Kaiyi Ji, et al. ∙ 0

Bilevel optimization has arisen as a powerful tool for many machine learning problems such as meta-learning, hyper-parameter optimization, reinforcement learning, etc. In this paper, we investigate the nonconvex-strongly-convex bilevel optimization problem, and propose two novel algorithms named deterBiO and stocBiO respectively for the deterministic and stochastic settings. At the core design of deterBiO is the construction of a low-cost and easy-to-implement hyper-gradient estimator via a simple back-propagation. In addition, stocBiO updates with the mini-batch data sampling rather than the existing single-sample schemes, where a sample-efficient Hessian inverse estimator is proposed. We provide the finite-time convergence guarantee for both algorithms, and show that they outperform the best known computational complexities orderwisely with respect to the condition number κ and/or the target accuracy ϵ. We further demonstrate the superior efficiency of the proposed algorithms by the experiments on meta-learning and hyper-parameter optimization.

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