ACPO: Agent-Chained Policy Optimization for Multi-Agent Reinforcement Learning

Centralized training with decentralized execution (CTDE) is a standard framework for cooperative multi-agent policy-gradient reinforcement learning, allowing agents to learn from joint information while acting from local observations. Ratio-based trust-region methods such as Multi-Agent Proximal Policy Optimization (MAPPO) and Multi-Agent Simple Policy Optimization (MASPO) update decentralized actors using per-agent probability ratios weighted by joint advantage estimates. Teammate non-stationarity increases the variance of these advantages, which in turn increases the variance in the local ratio updates. This exposes two method-specific failure modes: MAPPO's additive clipping removes gradients for outlier samples and weakens recovery from policy drift, while MASPO's soft quadratic penalty can allow probability collapse. We introduce Multi-Agent Ratio Symmetry (MARS), a novel policy optimization objective that replaces these additive ratio-based trust-region mechanisms with a multiplicatively symmetric geometric barrier. MARS preserves corrective gradients while assigning unbounded cost as probability ratios approach zero. Across 47 tasks spanning eight multi-agent environments, including novel JAX benchmarks PaxMen and AeroJAX, MARS matches or exceeds MAPPO and MASPO in aggregate environment-level performance. Ablations show that these gains arise from the geometry of the symmetric barrier rather than from flexible trust-region boundaries alone.

Multi-agent policy optimization, exemplified by PPO-based methods, is a key branch of cooperative Multi-Agent Reinforcement Learning (MARL). A central design question is how many neighboring agents\footnote{In this paper, "neighbors" refer not only to physical proximity but also to agents whose actions influence one another.} to aggregate in order to effectively utilize global information for cooperation. This decision must be made along two dimensions: in the advantage (which agents' rewards contribute to the credit signal) and in the ratio (which agents' likelihood ratios form the clipped importance weight). Existing methods occupy scattered, underexplored points on these two axes: IPPO treats both separately; MAPPO pairs a team-level advantage with per-agent ratios; HAPPO employs sequential ratios with per-agent advantages; and single-agent reductions operating on factorized joint policies aggregate both into fully joint products. We formalize these two design choices as support matrices $\SA$ and $\SR$, and prove a canonical structure: the expected multi-agent policy optimization objective depends on the pair $(\SA,\SR)$ only through their matrix product $\tS=\SR\SA$. This yields two key consequences: (i) Redundancy: the two support matrices are interchangeable with respect to the signal, meaning neither aggregation pattern is inherently superior.(ii) Variance Ordering: the advantage aggregates rewards as a sum (additive variance with an interior bias-variance optimum at the coupling neighborhood), whereas the ratio aggregates likelihood ratios as a product (multiplicative variance that grows exponentially with support size, with no accompanying bias reduction). The resulting design principle is unambiguous: aggregate neighbors in the advantage, sized to the coupling neighborhood, and keep the ratio per-agent.

Cooperative multi-agent reinforcement learning (MARL) involves complex agent interactions and requires effective exploration strategies. A prominent class of MARL algorithms, decentralized softmax policy gradient (DecSPG), addresses this through energy-based policy updates. In practice, however, such energy-based policies are intractable to maintain and are commonly projected onto the Gaussian policy class. In this work, we show that the limited expressiveness of Gaussian policies severely hinders exploration in DecSPG, and this limitation worsens as the number of agents grows. To address this issue, we propose decentralized diffusion policy learning (DDPL), which parameterizes each agent's policy with a denoising diffusion probabilistic model, an expressive generative model that captures multi-modal action distributions for enhanced exploration. DDPL enables efficient online training of diffusion policies via importance sampling score matching (ISSM), a novel training method with theoretical guarantee. We evaluate DDPL on representative continuous-action MARL benchmarks, including multi-agent particle environment, multi-agent MuJoCo, IsaacLab, and JAX-reimplemented StarCraft multi-agent challenge, and observe consistently improved performance.