Active Model Estimation in Markov Decision Processes
This addresses the challenge of model estimation in MDPs for reinforcement learning agents, with incremental improvements in early-stage exploration.
The paper tackles the problem of efficient exploration to learn an accurate model of a Markov decision process (MDP), introducing an algorithm with sample complexity guarantees for ε-accurate dynamics estimation and a heuristic-based algorithm that outperforms others in small sample regimes while matching asymptotic performance.
We study the problem of efficient exploration in order to learn an accurate model of an environment, modeled as a Markov decision process (MDP). Efficient exploration in this problem requires the agent to identify the regions in which estimating the model is more difficult and then exploit this knowledge to collect more samples there. In this paper, we formalize this problem, introduce the first algorithm to learn an $ε$-accurate estimate of the dynamics, and provide its sample complexity analysis. While this algorithm enjoys strong guarantees in the large-sample regime, it tends to have a poor performance in early stages of exploration. To address this issue, we propose an algorithm that is based on maximum weighted entropy, a heuristic that stems from common sense and our theoretical analysis. The main idea here is to cover the entire state-action space with the weight proportional to the noise in the transitions. Using a number of simple domains with heterogeneous noise in their transitions, we show that our heuristic-based algorithm outperforms both our original algorithm and the maximum entropy algorithm in the small sample regime, while achieving similar asymptotic performance as that of the original algorithm.