A Unified Bellman Equation for Causal Information and Value in Markov Decision Processes
For reinforcement learning researchers, it provides a theoretical framework to incorporate information constraints into value-based RL, but the contribution is incremental as it extends existing Bellman recursions.
This paper derives a unified Bellman equation that combines causal information and value in Markov decision processes, enabling exploration of agent behavior under information-theoretic constraints over an infinite horizon.
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.