Spectral Decomposition Representation for Reinforcement Learning

TL;DR

This paper introduces SPEDER, a spectral decomposition method for reinforcement learning that improves state-action representations by addressing policy dependence and exploration issues, leading to better sample efficiency and performance.

Contribution

The paper proposes SPEDER, a novel spectral method that extracts state-action abstractions without policy dependence and balances exploration, with theoretical and empirical validation.

Findings

SPEDER achieves superior performance on benchmark tasks.

Theoretical analysis confirms sample efficiency in online and offline settings.

Addresses limitations of previous spectral methods by incorporating exploration considerations.

Abstract

Representation learning often plays a critical role in reinforcement learning by managing the curse of dimensionality. A representative class of algorithms exploits a spectral decomposition of the stochastic transition dynamics to construct representations that enjoy strong theoretical properties in an idealized setting. However, current spectral methods suffer from limited applicability because they are constructed for state-only aggregation and derived from a policy-dependent transition kernel, without considering the issue of exploration. To address these issues, we propose an alternative spectral method, Spectral Decomposition Representation (SPEDER), that extracts a state-action abstraction from the dynamics without inducing spurious dependence on the data collection policy, while also balancing the exploration-versus-exploitation trade-off during learning. A theoretical analysis establishes the sample efficiency of the proposed algorithm in both the online and offline settings. In addition, an experimental investigation demonstrates superior performance over current state-of-the-art algorithms across several benchmarks.