Compact Optimality Verification for Optimization Proxies

• URL: http://arxiv.org/abs/2405.21023v1
• Date: Fri, 31 May 2024 17:11:39 GMT
• Title: Compact Optimality Verification for Optimization Proxies
• Authors: Wenbo Chen, Haoruo Zhao, Mathieu Tanneau, Pascal Van Hentenryck,
• Abstract summary: Recent years have witnessed increasing interest in machine learning models that approximate the input-output mapping of parametric optimization problems. The paper proposes a compact formulation for optimality verification that brings substantial computational benefits.
• Score: 15.761737742798157
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent years have witnessed increasing interest in optimization proxies, i.e., machine learning models that approximate the input-output mapping of parametric optimization problems and return near-optimal feasible solutions. Following recent work by (Nellikkath & Chatzivasileiadis, 2021), this paper reconsiders the optimality verification problem for optimization proxies, i.e., the determination of the worst-case optimality gap over the instance distribution. The paper proposes a compact formulation for optimality verification and a gradient-based primal heuristic that brings substantial computational benefits to the original formulation. The compact formulation is also more general and applies to non-convex optimization problems. The benefits of the compact formulation are demonstrated on large-scale DC Optimal Power Flow and knapsack problems.

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