The Role of Environment Access in Agnostic Reinforcement Learning
This addresses the challenge of sample-efficient learning in RL when optimal policies are not guaranteed, which is incremental as it builds on prior work on environment access and function approximation.
The paper tackles the problem of agnostic policy learning in reinforcement learning with large state spaces, showing that it remains statistically intractable under local simulator or reset distribution access, but becomes tractable for Block MDPs with both reset models via a new algorithm that constructs a policy emulator.
We study Reinforcement Learning (RL) in environments with large state spaces, where function approximation is required for sample-efficient learning. Departing from a long history of prior work, we consider the weakest possible form of function approximation, called agnostic policy learning, where the learner seeks to find the best policy in a given class $Π$, with no guarantee that $Π$ contains an optimal policy for the underlying task. Although it is known that sample-efficient agnostic policy learning is not possible in the standard online RL setting without further assumptions, we investigate the extent to which this can be overcome with stronger forms of access to the environment. Specifically, we show that: 1. Agnostic policy learning remains statistically intractable when given access to a local simulator, from which one can reset to any previously seen state. This result holds even when the policy class is realizable, and stands in contrast to a positive result of [MFR24] showing that value-based learning under realizability is tractable with local simulator access. 2. Agnostic policy learning remains statistically intractable when given online access to a reset distribution with good coverage properties over the state space (the so-called $μ$-reset setting). We also study stronger forms of function approximation for policy learning, showing that PSDP [BKSN03] and CPI [KL02] provably fail in the absence of policy completeness. 3. On a positive note, agnostic policy learning is statistically tractable for Block MDPs with access to both of the above reset models. We establish this via a new algorithm that carefully constructs a policy emulator: a tabular MDP with a small state space that approximates the value functions of all policies $π\in Π$. These values are approximated without any explicit value function class.