Learning Proximal Operators to Discover Multiple Optima

• URL: http://arxiv.org/abs/2201.11945v1
• Date: Fri, 28 Jan 2022 05:53:28 GMT
• Title: Learning Proximal Operators to Discover Multiple Optima
• Authors: Lingxiao Li, Noam Aigerman, Vladimir G. Kim, Jiajin Li, Kristjan Greenewald, Mikhail Yurochkin, Justin Solomon
• Abstract summary: We present an end-to-end method to learn the proximal operator across non-family problems. We show that for weakly-ized objectives and under mild conditions, the method converges globally.
• Score: 66.98045013486794
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Typical existing solutions either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of found solutions using ad hoc heuristics. We present an end-to-end method to learn the proximal operator across a family of non-convex problems, which can then be used to recover multiple solutions for unseen problems at test time. Our method only requires access to the objectives without needing the supervision of ground truth solutions. Notably, the added proximal regularization term elevates the convexity of our formulation: by applying recent theoretical results, we show that for weakly-convex objectives and under mild regularity conditions, training of the proximal operator converges globally in the over-parameterized setting. We further present a benchmark for multi-solution optimization including a wide range of applications and evaluate our method to demonstrate its effectiveness.

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