Amortized Implicit Differentiation for Stochastic Bilevel Optimization

• URL: http://arxiv.org/abs/2111.14580v2
• Date: Tue, 30 Nov 2021 04:43:47 GMT
• Title: Amortized Implicit Differentiation for Stochastic Bilevel Optimization
• Authors: Michael Arbel and Julien Mairal
• Abstract summary: We study a class of algorithms for solving bilevel optimization problems in both deterministic and deterministic settings. We exploit a warm-start strategy to amortize the estimation of the exact gradient. By using this framework, our analysis shows these algorithms to match the computational complexity of methods that have access to an unbiased estimate of the gradient.
• Score: 53.12363770169761
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit differentiation and we exploit a warm-start strategy to amortize the estimation of the exact gradient. We then introduce a unified theoretical framework inspired by the study of singularly perturbed systems (Habets, 1974) to analyze such amortized algorithms. By using this framework, our analysis shows these algorithms to match the computational complexity of oracle methods that have access to an unbiased estimate of the gradient, thus outperforming many existing results for bilevel optimization. We illustrate these findings on synthetic experiments and demonstrate the efficiency of these algorithms on hyper-parameter optimization experiments involving several thousands of variables.

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