Foundations of Multivariate Distributional Reinforcement Learning
This addresses a foundational problem in reinforcement learning for researchers and practitioners working with multi-objective decision-making, transfer learning, and representation learning, representing a novel method for a known bottleneck rather than an incremental advance.
The paper tackles the problem of developing provably convergent algorithms for multivariate distributional reinforcement learning, introducing the first oracle-free and computationally-tractable methods with convergence rates matching scalar reward settings and revealing that standard categorical TD learning fails for reward dimensions larger than 1, which they resolve with a novel projection technique.
In reinforcement learning (RL), the consideration of multivariate reward signals has led to fundamental advancements in multi-objective decision-making, transfer learning, and representation learning. This work introduces the first oracle-free and computationally-tractable algorithms for provably convergent multivariate distributional dynamic programming and temporal difference learning. Our convergence rates match the familiar rates in the scalar reward setting, and additionally provide new insights into the fidelity of approximate return distribution representations as a function of the reward dimension. Surprisingly, when the reward dimension is larger than $1$, we show that standard analysis of categorical TD learning fails, which we resolve with a novel projection onto the space of mass-$1$ signed measures. Finally, with the aid of our technical results and simulations, we identify tradeoffs between distribution representations that influence the performance of multivariate distributional RL in practice.