Reward Shaping via Diffusion Process in Reinforcement Learning

In this article, I take inspiration from stochastic thermodynamics to derive a problem formulation for online learning in uncertain MDPs while grounded in system dynamics. The system balances the diffusion process with drif dynamics as a way to formulate the explorationexploitation trade-off. To this effect, I make an explicit link between the information entropy and the stochastic dynamics of a system coupled to an environment. I analyze various sources of entropy production: due to the decision-maker's uncertainty about the system-environment interaction characteristics; due to the stochastic nature of system dynamics; and the interaction of the decision maker's knowledge with system dynamics. This analysis provides a framework that can be formulated either as a maximum entropy program to derive efficient policies that balance the exploration and exploitation trade-off, or as a modified cost optimization program that includes informational costs and benefits.