BOME! Bilevel Optimization Made Easy: A Simple First-Order Approach

• URL: http://arxiv.org/abs/2209.08709v1
• Date: Mon, 19 Sep 2022 01:51:12 GMT
• Title: BOME! Bilevel Optimization Made Easy: A Simple First-Order Approach
• Authors: Mao Ye, Bo Liu, Stephen Wright, Peter Stone and Qiang Liu
• Abstract summary: Bilevel optimization (BO) is useful for solving a variety important machine learning problems. Conventional methods need to differentiate through the low-level optimization process with implicit differentiation. First-order BO depends only on first-order information, requires no implicit differentiation.
• Score: 46.457298683984924
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bilevel optimization (BO) is useful for solving a variety of important machine learning problems including but not limited to hyperparameter optimization, meta-learning, continual learning, and reinforcement learning. Conventional BO methods need to differentiate through the low-level optimization process with implicit differentiation, which requires expensive calculations related to the Hessian matrix. There has been a recent quest for first-order methods for BO, but the methods proposed to date tend to be complicated and impractical for large-scale deep learning applications. In this work, we propose a simple first-order BO algorithm that depends only on first-order gradient information, requires no implicit differentiation, and is practical and efficient for large-scale non-convex functions in deep learning. We provide non-asymptotic convergence analysis of the proposed method to stationary points for non-convex objectives and present empirical results that show its superior practical performance.

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