Quantifying the stochasticity of policy parameters in reinforcement learning problems.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Neuroscience

Background:

• Reinforcement learning (RL) models exhibit complex stochastic dynamics.
• Understanding these dynamics is crucial for developing robust learning algorithms.
• Existing methods may not fully capture the intricacies of policy parameter evolution.

Purpose of the Study:

• To investigate the stochastic dynamics of reinforcement learning using a master equation formalism.
• To apply this formalism to Q-learning in two-agent games and the multi-armed bandit problem.
• To develop accurate methods for estimating policy variable (co)variances.

Main Methods:

• Constructing a master equation with probability distributions over policy parameters.
• Employing moment closure approximation to solve the stochastic dynamics.
• Analyzing Q-learning and multi-armed bandit problems with policy gradients.

Main Results:

• Accurate estimation of the mean and (co)variance of policy variables.
• Demonstration of finite steady-state variance terms in the two-agent game.
• Derivation of algebraic equations for direct computation of steady-state variances.

Conclusions:

• The master equation formalism provides an effective framework for analyzing RL stochastic dynamics.
• The moment closure approximation yields accurate estimations for policy variable statistics.
• The findings offer insights into the stability and convergence properties of RL algorithms.