Posterior Sampling-based Online Learning for Episodic POMDPs
This addresses the challenge of learning in POMDPs, which is harder than in MDPs, by providing a more implementable algorithm for researchers and practitioners in reinforcement learning, though it is incremental as it builds on existing posterior sampling methods.
The paper tackles online learning in episodic POMDPs with unknown models by proposing a simpler posterior sampling algorithm (PS4POMDPs), achieving Bayesian regret scaling as the square root of episodes and polynomial in other parameters, with exponential regret in horizon length shown inevitable but polynomial under common assumptions like undercomplete and weakly revealing POMDPs.
Learning in POMDPs is known to be significantly harder than in MDPs. In this paper, we consider the online learning problem for episodic POMDPs with unknown transition and observation models. We propose a Posterior Sampling-based reinforcement learning algorithm for POMDPs (PS4POMDPs), which is much simpler and more implementable compared to state-of-the-art optimism-based online learning algorithms for POMDPs. We show that the Bayesian regret of the proposed algorithm scales as the square root of the number of episodes and is polynomial in the other parameters. In a general setting, the regret scales exponentially in the horizon length $H$, and we show that this is inevitable by providing a lower bound. However, when the POMDP is undercomplete and weakly revealing (a common assumption in the recent literature), we establish a polynomial Bayesian regret bound. We finally propose a posterior sampling algorithm for multi-agent POMDPs, and show it too has sublinear regret.