A Sojourn-Based Approach to Semi-Markov Reinforcement Learning

Abstract

In this paper we introduce a new approach to discrete-time semi-Markov decision processes based on the sojourn time process. Different characterizations of discrete-time semi-Markov processes are exploited and decision processes are constructed by their means. With this new approach, the agent is allowed to consider different actions depending also on the sojourn time of the process in the current state. A numerical method based on Q-learning algorithms for finite horizon reinforcement learning and stochastic recursive relations is investigated. Finally, we consider two toy examples: one in which the reward depends on the sojourn-time, according to the gambler’s fallacy; the other in which the environment is semi-Markov even if the reward function does not depend on the sojourn time. These are used to carry on some numerical evaluations on the previously presented Q-learning algorithm and on a different naive method based on deep reinforcement learning.

Intelligent air defense task assignment based on hierarchical reinforcement learning

“…The idea of this method is to decompose a whole task into multi-level subtasks by introducing mechanisms such as State space decomposition ( Takahashi, 2001 ), State abstraction ( Abel, 2019 ), and Temporal abstraction ( Bacon and Precup, 2018 ) so that each subtask can be solved in a small-scale state space, thus speeding up the solution of the whole task. To model these abstract mechanisms, researchers introduced the semi-Markov Decision Process (SMDP) ( Ascione and Cuomo, 2022 ) model to handle actions that must be completed at multiple time steps. The state space decomposition approach decomposes the state space into different subsets.…”