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.

翻译：摘要：许多分散决策问题要求多方在共享决策上进行协调，同时保持目标、约束和数据的私有性。大语言模型通过从自然语言规范生成本地优化代理，为降低参与门槛提供了有前景的途径。然而，在协调场景中，可执行性并不足够：生成的代理可能通过编译、求解和局部检查，但在语义上仍存在错误，例如成本误述、约束范围错配或对激励的响应不正确。此类错误通常仅在协调过程中显现，表现为系统性行为失效而非不可行性。我们提出面向LLM生成优化代理的协调内循环验证与修复方法。通过交替方向乘子法风格共识协议实例化该思想，并引入OptiLoop流水线：从文本生成本地优化代理，通过针对固定参考对手的短时、有界协调运行进行验证，提取结构化行为与静态证据，并实施基于证据的修复。当失效属于结构性问题而非实现性问题时，OptiLoop从局部代码修复升级为修正表达式的修复，并可复用先前实例的经验教训。在40个保留测试场景中，相较于强局部验证基线，OptiLoop完整版本将目标匹配率从66.0%提升至93.0%，社会匹配率从68.5%提升至89.0%，同时将平均目标差距从15.3%降至3.5%，平均社会差距从7.6%降至2.0%。这些结果表明，对于部署在分散决策循环中的生成优化代理，正确性应在循环内部而非仅通过孤立执行进行验证。