arXiv:2505.04310cs.AIcs.LG2025-05

用连续流模型高效建模强化学习回报分布,参数量远低于传统方法。

Parameter-Efficient Distributional RL via Normalizing Flows and a Geometry-Aware Cramér Surrogate

  • 基于连续归一化流构建回报分布,支持自适应动态支撑点。
  • 在Atari-5上性能媲美经典方法,参数量显著减少。
  • 新度量保证收敛性与无偏梯度,适合追求效率的强化学习研究者。

分布式强化学习(DistRL)通过建模完整回报分布而非仅期望值来提升性能,但现有方法常参数冗余。分类法(如C51)依赖固定支撑集,参数量随分辨率线性增长;分位数法将分布近似为分段常数密度,对复杂多模态或重尾回报建模低效。本文提出NFDRL,采用连续归一化流建模回报分布。与分类基线不同,该流模型保持紧凑参数量,不随分布有效分辨率增加而增长,同时提供动态自适应支撑。为训练该连续表示,我们提出一种基于Cramér的几何感知距离,定义于流生成的概率质量上。证明该距离是真正的概率度量,相关分布贝尔曼算子为sqrt(gamma)-收缩,且目标函数可得无偏样本梯度,这些性质在以往基于概率密度的DistRL方法中通常无法同时满足。实验表明,NFDRL在玩具MDP上能恢复丰富的多模态回报结构,在Atari-5基准上表现媲美分类基线,且参数效率显著更优。

原文摘要 · Abstract (English)

Distributional Reinforcement Learning (DistRL) improves upon expectation-based methods by modeling full return distributions, but standard approaches often remain far from parsimonious. Categorical methods (e.g., C51) rely on fixed supports where parameter counts scale linearly with resolution, while quantile methods approximate distributions as discrete mixtures whose piecewise-constant densities can be wasteful when modeling complex multi-modal or heavy-tailed returns. We introduce NFDRL, a parsimonious architecture that models return distributions using continuous normalizing flows. Unlike categorical baselines, our flow-based model maintains a compact parameter footprint that does not grow with the effective resolution of the distribution, while providing a dynamic, adaptive support for returns. To train this continuous representation, we propose a Cramér-inspired, geometry-aware distance defined over probability masses obtained from the flow. We show that this distance is a true probability metric, that the associated distributional Bellman operator is a sqrt(gamma)-contraction, and that the resulting objective admits unbiased sample gradients, properties that are typically not simultaneously guaranteed in prior PDF-based DistRL methods. Empirically, NFDRL recovers rich, multi-modal return landscapes on toy MDPs and achieves performance competitive with categorical baselines on the Atari-5 benchmark, while offering substantially better parameter efficiency.

强化学习分布建模参数效率归一化流

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