Code-Space Response Oracles: Generating Interpretable Multi-Agent Policies with Large Language Models

Multi-agent systems enable complex reasoning and tool use by coordinating agents that divide roles and refine candidate solutions. Existing methods typically update individual agent responses or treat a complete trajectory as one training example. However, these methods may produce misleading policy updates because they assign the same final outcome to responses or trajectory segments that may play different roles in different team decisions. This is because treating each response as an independent update may separate outputs that jointly determine the next action, while treating an entire trajectory as one update may combine decisions made after different observations. These limitations call for a policy update defined at the level of a team decision, outputs that lead to the same state transition are optimized under a shared objective. In this paper, we propose Setwise Relative Policy Optimization (SRPO) for multi-agent systems. We represent the outputs used together to produce one state transition as an active set. A singleton set covers division of labor, while a larger set covers joint co-evolution, and the set composition can change across decisions. SRPO assigns a shared advantage to each active set, clips the combined policy change, and normalizes its scale according to the set size. This ties each update to the decision that produced the next state. Experiments on mathematical reasoning and multi-turn search demonstrate the effectiveness of SRPO across both tasks. Additional ablation studies analyze the normalization choice and training behavior under changing active-set sizes.

Much of the advancement in Multi-Agent Reinforcement Learning (MARL) for imperfect-information games has historically depended on the manual, iterative refinement of algorithmic baselines. Recently, evolutionary coding agents powered by Large Language Models (LLMs) have emerged as powerful tools to automate this discovery process. In this work, we deploy one of such agentic frameworks, AlphaEvolve, to navigate the design spaces of two distinct game-theoretic paradigms: counterfactual regret minimization (CFR) and policy-space response oracles (PSRO). This automated search yielded two algorithms: Volatility-Adaptive Discounted (VAD-) CFR and Smoothed Hybrid Optimistic Regret (SHOR-) PSRO, which are consistently competitive with state-of-the-art human-designed baselines across an 18-game evaluation suite spanning Poker, Goofspiel, Liar's Dice, Blotto, and Battleship variants. However, because the LLM optimizes for fitness on a specific training set, it often constructs highly synergistic, complex mechanisms tailored to those environments. Through systematic ablation studies, we demonstrate that while these mechanisms are tightly coupled, the true driver of generalization lies in a minimal algorithmic core. By distilling the LLM's discoveries down to their most fundamental principles, we produce two minimal solvers: Warm-started Optimistic Predictive (WOP-)CFR and Projection Matching (PM-)PSRO. These distilled versions achieve superior performance on generalization with greatly reduced structural complexity, providing a clear methodology for using LLMs in algorithmic discovery.

Can a multimodal language model learn to manipulate physical objects by reasoning about its own failures-without gradient updates, demonstrations, or reward engineering? We argue the answer is yes, under conditions we characterise precisely. We present Act-Observe-Rewrite (AOR), a framework in which an LLM agent improves a robot manipulation policy by synthesising entirely new executable Python controller code between trials, guided by visual observations and structured episode outcomes. Unlike prior work that grounds LLMs in pre-defined skill libraries or uses code generation for one-shot plan synthesis, AOR makes the full low-level motor control implementation the unit of LLM reasoning, enabling the agent to change not just what the robot does, but how it does it. The central claim is that interpretable code as the policy representation creates a qualitatively different kind of in-context learning from opaque neural policies: the agent can diagnose systematic failures and rewrite their causes. We validate this across three robosuite manipulation tasks and report promising results, with the agent achieving high success rates without demonstrations, reward engineering, or gradient updates.