Paper ID: 2402.08530

A Distributional Analogue to the Successor Representation

Harley Wiltzer, Jesse Farebrother, Arthur Gretton, Yunhao Tang, André Barreto, Will Dabney, Marc G. Bellemare, Mark Rowland

This paper contributes a new approach for distributional reinforcement learning which elucidates a clean separation of transition structure and reward in the learning process. Analogous to how the successor representation (SR) describes the expected consequences of behaving according to a given policy, our distributional successor measure (SM) describes the distributional consequences of this behaviour. We formulate the distributional SM as a distribution over distributions and provide theory connecting it with distributional and model-based reinforcement learning. Moreover, we propose an algorithm that learns the distributional SM from data by minimizing a two-level maximum mean discrepancy. Key to our method are a number of algorithmic techniques that are independently valuable for learning generative models of state. As an illustration of the usefulness of the distributional SM, we show that it enables zero-shot risk-sensitive policy evaluation in a way that was not previously possible.

Submitted: Feb 13, 2024