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

Mao Ye, Bo Liu, Stephen Wright, Peter Stone, qiang liu

Keywords: bilevel optimization

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.

Community Implementations: [ 5 code implementations](https://www.catalyzex.com/paper/bome-bilevel-optimization-made-easy-a-simple/code)