Approximate information state based convergence analysis of recurrent Q-learning
This provides theoretical convergence guarantees for recurrent Q-learning in POMDPs, addressing a gap in RL theory for partially observable environments.
The paper tackles the lack of theoretical understanding for reinforcement learning in partially observable settings by proving that recurrent Q-learning converges in tabular cases, with convergence quality depending on approximate information state representation, and presents a variant using AIS losses that outperforms a strong baseline.
In spite of the large literature on reinforcement learning (RL) algorithms for partially observable Markov decision processes (POMDPs), a complete theoretical understanding is still lacking. In a partially observable setting, the history of data available to the agent increases over time so most practical algorithms either truncate the history to a finite window or compress it using a recurrent neural network leading to an agent state that is non-Markovian. In this paper, it is shown that in spite of the lack of the Markov property, recurrent Q-learning (RQL) converges in the tabular setting. Moreover, it is shown that the quality of the converged limit depends on the quality of the representation which is quantified in terms of what is known as an approximate information state (AIS). Based on this characterization of the approximation error, a variant of RQL with AIS losses is presented. This variant performs better than a strong baseline for RQL that does not use AIS losses. It is demonstrated that there is a strong correlation between the performance of RQL over time and the loss associated with the AIS representation.