Bilevel Optimization: Convergence Analysis and Enhanced Design

arXiv2010.07962MaRDI QIDQ6351428

Author name not available (Why is that?)

Publication date: 15 October 2020

Abstract: Bilevel optimization has arisen as a powerful tool for many machine learning problems such as meta-learning, hyperparameter optimization, and reinforcement learning. In this paper, we investigate the nonconvex-strongly-convex bilevel optimization problem. For deterministic bilevel optimization, we provide a comprehensive convergence rate analysis for two popular algorithms respectively based on approximate implicit differentiation (AID) and iterative differentiation (ITD). For the AID-based method, we orderwisely improve the previous convergence rate analysis due to a more practical parameter selection as well as a warm start strategy, and for the ITD-based method we establish the first theoretical convergence rate. Our analysis also provides a quantitative comparison between ITD and AID based approaches. For stochastic bilevel optimization, we propose a novel algorithm named stocBiO, which features a sample-efficient hypergradient estimator using efficient Jacobian- and Hessian-vector product computations. We provide the convergence rate guarantee for stocBiO, and show that stocBiO outperforms the best known computational complexities orderwisely with respect to the condition number $kappa$ and the target accuracy $epsilon$. We further validate our theoretical results and demonstrate the efficiency of bilevel optimization algorithms by the experiments on meta-learning and hyperparameter optimization.

Has companion code repository: https://github.com/JunjieYang97/stocBiO

This page was built for publication: Bilevel Optimization: Convergence Analysis and Enhanced Design

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6351428)