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PEARL: Solver-in-the-Loop Interactive Optimization Modeling from Natural Language

NeurIPS 2026 · Large language models › Agents, code and math · approach: LLMs for optimization and heuristics · 0 citations (OpenAlex)

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Proposes PEARL, a multi-turn tool-integrated agentic RL method that trains an LLM to interactively formulate and solve optimization models with Python/solver feedback, yielding a 4B model that beats DeepSeek-V3.2-685B on macro-averaged pass@1.

Problem

Optimization modeling from natural language is typically treated as one-shot generation, without executing partial models, using solver feedback, or revising errors. Existing RL methods mostly score completed outputs post hoc.

Approach

Formulate optimization modeling as a POMDP where Execute and Validate tools are first-class environment actions, and train the policy with GRPO-style agentic RL (decoupled clipping, observation loss masking) on format and solver-verified objective rewards, so the model learns when to test, revise, and terminate.

Key results

• PEARL-Qwen3-4B reaches 69.71 macro average pass@1 vs 66.51 for DeepSeek-V3.2-685B and 22.20 for Qwen3-4B-Instruct direct prompting.
• PEARL-Qwen3-4B micro average 79.84 vs 77.07 for DeepSeek-V3.2-685B; GPT-5 leads macro average at 71.40.
• On MAMO ComplexLP, PEARL-4B reaches 76.12 vs 50.75 for DeepSeek-V3.2-685B.

Surprising findings

• GPT-5 and GPT-5-Codex (and DeepSeek-V3.2-Think) remain competitive or stronger than PEARL-4B on some aggregate metrics, so small models do not universally dominate.
• Aggressive trajectory filtering of truncated or format-violating trajectories did not help and slightly hurt performance in this setting.

Limitations

• Bounded interaction budget (8 turns) and limited benchmark coverage; stochastic, robust, and domain-specific settings not covered.
• Solver-based validation is only a partial oracle; objective match against references is the main correctness signal.
• Reported results for GPT-5 and some baselines come from different settings and are not fully controlled comparisons.

Experimental setup

Datasets: OR-Instruct/ORLM data OptMATH OptiBench-style data NL4Opt MAMO EasyLP MAMO ComplexLP NLP4LP IndustryOR ComplexOR Resocratic

Benchmarks: NL4Opt MAMO EasyLP MAMO ComplexLP NLP4LP OptMATH IndustryOR ComplexOR Resocratic

Metrics: pass@1 accuracy macro average micro average

Baselines: Qwen-3-4B-Instruct Qwen-3-4B-Think Qwen3-235B-A22B DeepSeek-V3.2-685B GPT-5 GPT-5-Codex SIRL-Qwen2.5-32B ORLM-LLaMA-3-8B OptMATH-Qwen2.5-32B

Builds on: GRPO DAPO SIRL ORLM OptMATH

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• MM-OptBench: A Solver-Grounded Benchmark for Multimodal Optimization Modeling (NeurIPS 2026 · similarity 0.90)
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