An information-theoretic analysis of return maximization in reinforcement learning.

Area of Science:

• Reinforcement Learning
• Information Theory
• Decision Processes

Background:

• Traditional reinforcement learning analysis relies on Markovian, stationary, and ergodic assumptions.
• These assumptions limit the applicability of existing models to complex sequential decision problems.

Purpose of the Study:

• To present a general analysis of return maximization in reinforcement learning.
• To relax restrictive assumptions like Markovianity, stationarity, and ergodicity.
• To introduce a novel perspective using the asymptotic equipartition property from information theory.

Main Methods:

• Analysis of stochastic sequential decision processes.
• Application of the asymptotic equipartition property.
• Identification of typical and best sequence sets.

Main Results:

• Demonstrated that return maximization occurs through the overlap of typical and best sequence sets.
• Presented a class of stochastic sequential decision processes satisfying a necessary condition for return maximization.
• Provided examples of optimal sequences within this class.

Conclusions:

• The asymptotic equipartition property offers a powerful framework for analyzing return maximization.
• The findings provide a new theoretical foundation for reinforcement learning without traditional restrictive assumptions.
• This work advances the understanding of optimal strategies in complex decision-making environments.