# OptiLoop: Coordination-in-the-Loop Verification and Repair for LLM-Generated Optimization Agents

arXiv: https://arxiv.org/abs/2605.27630 · HTML: https://mlsanity.com/paper/2605.27630/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use.
- Builds on 7 of its 13 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)

## Builds on (most cited first, 7 of 7)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimization](https://mlsanity.com/paper/2602.15983/) (2026)
- [Leveraging Large Language Models for Risk Assessment in Hyperconnected Logistic Hub Network Deployment](https://mlsanity.com/paper/2503.21115/) (2025)
- [OptiHive: Ensemble Selection for LLM-Based Optimization via Statistical Modeling](https://mlsanity.com/paper/2508.02503/) (2025)

## Built on by (most cited first, 2 of 2)

- [Falsification-Based Verification of LLM-Generated Optimization Models: Sound Test Batteries and Their Detection Limits](https://mlsanity.com/paper/2607.16646/) (2026)
- [YUKTI: From Natural-Language Situations to Robust, Verifiable Decisions An Uncertainty-Typed Proposition IR, Assumption-Robust Pareto Frontiers, and a Regret Certificate](https://mlsanity.com/paper/2607.09706/) (2026)

## Abstract (arXiv)

Many decentralized decision problems require multiple parties to coordinate on shared decisions while keeping objectives, constraints, and data private. Large language models (LLMs) offer a promising way to lower the barrier to participation by generating local optimization agents from natural-language specifications. In coordination settings, however, executability is not enough: a generated agent may compile, solve, and pass local checks while still being semantically wrong, for example by misrepresenting costs, mis-scoping constraints, or responding incorrectly to incentives. Such errors often surface only during coordination, as systematic behavioral failures rather than infeasibility. We propose coordination-in-the-loop verification and repair for LLM-generated optimization agents. We instantiate this idea with an Alternating Direction Method of Multipliers (ADMM)-style consensus protocol and introduce OptiLoop, a pipeline that generates local optimization agents from text, verifies them through short, bounded coordination runs against a fixed reference counterparty, extracts structured behavioral and static evidence, and applies evidence-driven repair. When failures are structural rather than implementational, OptiLoop escalates from localized code fixes to corrected-formulation repair, and it can additionally reuse episodic lessons from prior instances. On 40 held-out test scenarios, OptiLoop-Full improves objective match from 66.0% to 93.0% and social match from 68.5% to 89.0% relative to a strong local-validation baseline, while reducing mean objective gap from 15.3% to 3.5% and mean social gap from 7.6% to 2.0%. These results show that, for generated optimization agents deployed inside decentralized decision loops, correctness should be validated in the loop itself rather than through isolated execution alone.