A Unified Bellman Equation for Causal Information and Value in Markov Decision Processes

TL;DR

This paper introduces a unified Bellman equation that combines causal information and value functions in Markov Decision Processes, addressing information-theoretic constraints in reinforcement learning.

Contribution

It derives a novel Bellman-type recursive equation for causal information, integrating it with the value function for the first time in RL.

Findings

Unified framework for information and reward optimization

Insights into agent-environment interaction dynamics

Potential for improved RL algorithms under information constraints

Abstract

The interaction between an artificial agent and its environment is bi-directional. The agent extracts relevant information from the environment, and affects the environment by its actions in return to accumulate high expected reward. Standard reinforcement learning (RL) deals with the expected reward maximization. However, there are always information-theoretic limitations that restrict the expected reward, which are not properly considered by the standard RL. In this work we consider RL objectives with information-theoretic limitations. For the first time we derive a Bellman-type recursive equa- tion for the causal information between the environment and the agent, which is combined plausibly with the Bellman recursion for the value function. The unified equitation serves to explore the typical behavior of artificial agents in an infinite time horizon.