Continuous Improvement and Parallel Autonomous Exploration: An LLM-Agent Framework for Searching Large Solution Spaces

We present a framework that gives LLM agents two mechanisms for searching large solution spaces autonomously. First, a leaderboard scored on held-out data acts as a reward signal that drives each agent to refine its solutions over repeated submissions, a loop that operates even with a single agent. Second, the framework enables running many agents in parallel, fully autonomously, with no human in the loop: agents independently analyze, survey methods, implement, self-evaluate, submit, and revise, while a moderator agent handles only logistics. Running agents in parallel under the shared reward broadens the explored region of the solution space rather than refining the single seeded paradigm. We instantiate the framework on product-to-catalog matching (a core e-commerce retrieval task with a large, category-structured solution space), posed as selective prediction with a precision-coverage operating point. A single agent refines within its seeded paradigm, whereas parallel autonomous agents surface qualitatively different solutions. On this testbed, best qualified coverage (>=95% P@1 per category) reaches 47.8-57.4% with a single agent and 62.8-69.4% with five, against a 33.3% baseline. Our contribution is the framework itself: a continuous-improvement reward loop and a substrate for fully autonomous parallel exploration, backed by case-study evidence.