Approximate Policy Iteration With Deep Minimax Average Bellman Error Minimization.

Area of Science:

• Reinforcement Learning
• Deep Learning Theory
• Markov Decision Processes

Background:

• Deep approximate policy iteration (DAPI) is a powerful technique for reinforcement learning.
• Estimating the optimal action-value function is crucial for effective policy learning.
• Rectified linear unit (ReLU) ResNet architectures offer potential for complex function approximation.

Purpose of the Study:

• To investigate the use of DAPI with ReLU ResNet for optimal action-value function estimation.
• To derive nonasymptotic error bounds for the DAPI algorithm.
• To establish theoretical guidelines for hyperparameter selection in DAPI.

Main Methods:

• Utilizing deep approximate policy iteration (DAPI) with ReLU ResNet.
• Applying minimax average Bellman error minimization.
• Employing empirical process and deep approximation theory for error analysis.
• Deriving generalization and approximation bounds for ReLU ResNet with dependent data.

Main Results:

• Established nonasymptotic error bounds for DAPI, dependent on sample size, dimension, and network architecture.
• Developed a novel generalization bound for ReLU ResNet with dependent data.
• Achieved an improved polynomial dependence on ambient dimension in approximation bounds.
• Demonstrated theoretical guidelines for hyperparameter tuning in DAPI.

Conclusions:

• The study provides a robust theoretical framework for DAPI using ReLU ResNet.
• The derived error bounds offer practical insights for optimizing DAPI training.
• The improved approximation bounds advance the understanding of deep learning in reinforcement learning contexts.