Theoretical results on the effect of ‘shortcut’ actions in MDPs

Temporally extended actions have been used extensively in reinforcement learning in order to speed up the process of learning good behaviours. While such actions are intuitively appealing, very little work has provided a formal analysis of the advantage that can be obtained by using such actions. In this paper, we tackle this problem using the methodology of stochastic processes. We present case studies of Markov decision processes with actions that allow ‘shortcuts’ between different parts of the environment, and show how such actions affect the travel time between states. Our main finding is that such actions allow for provably quicker travel around the environment, and the benefit increases with the dimensionality of the state space. Hence, extended actions help in efficiently exploring large, high-dimensional domains.