A Spectral Revisit of the Distributional Bellman Operator under the Cramér Metric
Distributional reinforcement learning (DRL) studies the evolution of full return distributions under Bellman updates rather than focusing on expected values. A classical result is that the distributional Bellman operator is contractive under the Cramér metric, which corresponds to an $L^2$ geometry on differences of cumulative distribution functions (CDFs). While this contraction ensures stability of policy evaluation, existing analyses remain largely metric, focusing on contraction properties without elucidating the structural action of the Bellman update on distributions. In this work, we analyse distributional Bellman dynamics directly at the level of CDFs, treating the Cramér geometry...
| Authors | Keru Wang, Yixin Deng, Yao Lyu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 13 March 2026 |
| Last updated at source | 13 March 2026 |
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