Quotient-Categorical Representations for Bellman-Compatible Average-Reward Distributional Reinforcement Learning
Average-reward reinforcement learning requires estimating the gain and the bias, which is defined only up to an additive constant. This makes direct distributional analogues ill-posed on the real line. We introduce a quotient-space formulation in which state-indexed bias laws are identified up to a common translation, together with a categorical parameterization that respects this symmetry. On this quotient-categorical space, we define a projected average-reward distributional operator and show that it is well-defined, non-expansive in a coordinate Cramér metric, and admits fixed points. We then study sampled recursions whose mean-field maps are asynchronous relaxations of this operator. ...
| Authors | Ege C. Kaya, Aliasghar Pourghani, Vijay Gupta et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 May 2026 |
| Last updated at source | 11 May 2026 |
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