Solver-in-the-Loop: MDP-Based Benchmarks for Self-Correction and Behavioral Rationality in Operations Research

• URL: http://arxiv.org/abs/2601.21008v1
• Date: Wed, 28 Jan 2026 20:02:44 GMT
• Title: Solver-in-the-Loop: MDP-Based Benchmarks for Self-Correction and Behavioral Rationality in Operations Research
• Authors: Ruicheng Ao, David Simchi-Levi, Xinshang Wang,
• Abstract summary: Operations Research practitioners routinely debug infeasible models through an iterative process.<n>We introduce two benchmarks that place the textbfsolver in the evaluation loop<n>We find that domain-specific RLVR training enables an 8B model to surpass frontier APIs.
• Score: 19.31559944205485
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Operations Research practitioners routinely debug infeasible models through an iterative process: analyzing Irreducible Infeasible Subsystems (\IIS{}), identifying constraint conflicts, and systematically repairing formulations until feasibility is achieved. Yet existing LLM benchmarks evaluate OR as one-shot translation -- given a problem description, generate solver code -- ignoring this diagnostic loop entirely. We introduce two benchmarks that place the \textbf{solver in the evaluation loop}. \textbf{\ORDebug{}} evaluates iterative self-correction through 5,000+ problems spanning 9 error types; each repair action triggers solver re-execution and \IIS{} recomputation, providing deterministic, verifiable feedback. \textbf{\ORBias{}} evaluates behavioral rationality through 2,000 newsvendor instances (1,000 ID + 1,000 OOD), measuring systematic deviations from closed-form optimal policies. Across 26 models and 12,000+ samples, we find that domain-specific RLVR training enables an 8B model to surpass frontier APIs: 95.3\% vs 86.2\% recovery rate (+9.1\%), 62.4\% vs 47.8\% diagnostic accuracy (+14.6\%), and 2.25 vs 3.78 steps to resolution (1.7$\times$ faster). On \ORBias{}, curriculum training achieves the only negative ID$\rightarrow$OOD bias drift among models evaluated (-9.6\%), reducing systematic bias by 48\% (from 20.0\% to 10.4\%). These results demonstrate that process-level evaluation with verifiable oracles enables targeted training that outperforms scale.

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