多智能体强化学习中,应只在奖励信号上聚合邻居,而非重要性权重。
Aggregate in the Advantage, Not the Ratio: A Canonical-Form Analysis of Cooperative Multi-Agent Policy Optimization

- 通过支持矩阵分析,发现奖励聚合与权重聚合可分离设计。
- 奖励聚合为加法,方差可控;权重聚合为乘法,方差随规模指数增长。
- 建议仅在优势函数中聚合邻居,大小以耦合邻域为准,权重保持个体化。
多智能体策略优化(如基于PPO的方法)是合作式多智能体强化学习的核心分支。关键设计问题在于:应聚合多少邻近智能体的信息以有效利用全局协作信息?该决策需同时考虑两个维度:在优势(哪些智能体的奖励贡献于信用信号)和在比率(哪些智能体的似然比构成裁剪的重要性权重)。现有方法分布在两个轴上的多个未充分探索点:IPPO对两者分别处理;MAPPO采用团队级优势与个体比率;HAPPO使用序列比率与个体优势;单智能体简化方法则将二者合并为完全联合形式。本文形式化这两个选择为支持矩阵$\ ext{SA}$和$\ ext{SR}$,并证明其目标函数仅依赖于它们的矩阵积$\ ext{tS} = \ ext{SR} ext{SA}$。由此得出两个关键结论:(i) 冗余性:两支持矩阵在信号传递上可互换,无固有优劣之分;(ii) 方差排序:优势聚合以求和方式处理奖励(加性方差,存在内部偏差-方差最优解于耦合邻域);比率聚合以乘积方式处理似然比(乘性方差随支持规模指数增长,无伴随偏差降低)。最终的设计原则清晰明确:应在优势中聚合邻居,规模定为耦合邻域大小,并保持比率个体化。
原文摘要 · Abstract (English)
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.
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