Truncating Trajectories in Monte Carlo Policy Evaluation: an Adaptive Approach

Policy evaluation via Monte Carlo (MC) simulation is at the core of many MC Reinforcement Learning (RL) algorithms (e.g., policy gradient methods). In this context, the designer of the learning system specifies an interaction budget that the agent usually spends by collecting trajectories of within a simulator. However, is this data collection strategy the best option? To answer this question, in this paper, we consider as quality index the variance of an unbiased policy return estimator that uses trajectories of different lengths, i.e., . We first derive a closed-form expression of this variance that clearly shows the sub-optimality of the fixed-length trajectory schedule. Furthermore, it suggests that adaptive data collection strategies that spend the available budget sequentially might be able to allocate a larger portion of transitions in timesteps in which more accurate sampling is required to reduce the variance of the final estimate.