Compact Optimality Verification for Optimization Proxies

TL;DR

This paper introduces a compact and general approach for verifying the near-optimality of optimization proxies, significantly improving computational efficiency and applicability to non-convex problems like power flow and knapsack.

Contribution

It proposes a novel compact formulation for optimality verification and a gradient-based heuristic, enhancing efficiency and extending applicability to non-convex optimization problems.

Findings

Demonstrated on large-scale DC Optimal Power Flow problems.

Validated on knapsack problems.

Achieved substantial computational benefits.

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.