Lower-level Duality Based Penalty Methods for Hyperparameter Optimization
Keywords: Bilevel Optimization, Hyperparameter Optimization, Nonsmooth Optimization
TL;DR: We propose a first-order algorithm based on penalty methods for bilevel hyperparameter selection problems.
Abstract: Hyperparameter optimization (HO) is essential in machine learning and can be structured as a bilevel optimization. However, many existing algorithms designed for addressing nonsmooth lower-level problems involve solving sequential subproblems with high complexity. To tackle this challenge, we introduce penalty methods for solving HO based on strong duality between the lower level problem and its dual. We illustrate that the penalized problem closely approximates the optimal solutions of the original HO under certain conditions. In many real applications, the penalized problem is a weakly-convex objective with proximal-friendly constraints. Furthermore, we develop two fully first-order algorithms to solve the penalized problems. Theoretically, we prove the convergence of the proposed algorithms. We demonstrate the efficiency and superiority of our method across numerical experiments.
Supplementary Material: pdf
Primary Area: optimization
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Submission Number: 3763
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