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arXiv · 2307.00126

Accelerating Inexact HyperGradient Descent for Bilevel Optimization

Haikuo Yang·Luo Luo·Chris Junchi Li·Michael I. Jordan
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Abstract

We present a method for solving general nonconvex-strongly-convex bilevel optimization problems. Our method -- the \emph{Restarted Accelerated HyperGradient Descent} (\texttt{RAHGD}) method -- finds an $\epsilon$-first-order stationary point of the objective with $\tilde{\mathcal{O}}(\kappa^{3.25}\epsilon^{-1.75})$ oracle complexity, where $\kappa$ is the condition number of the lower-level objective and $\epsilon$ is the desired accuracy. We also propose a perturbed variant of \texttt{RAHGD} for finding an $\big(\epsilon,\mathcal{O}(\kappa^{2.5}\sqrt{\epsilon}\,)\big)$-second-order stationary point within the same order of oracle complexity. Our results achieve the best-known theoretical guarantees for finding stationary points in bilevel optimization and also improve upon the existing upper complexity bound for finding second-order stationary points in nonconvex-strongly-concave minimax optimization problems, setting a new state-of-the-art benchmark. Empirical studies are conducted to validate the theoretical results in this paper.

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Haikuo Yang, Luo Luo, Chris Junchi Li, Michael I. Jordan. 2023-06-30. Accelerating Inexact HyperGradient Descent for Bilevel Optimization. https://arxiv.org/abs/2307.00126

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