Sample-Efficient Reinforcement Learning for Linearly-Parameterized MDPs with a Generative Model.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Control Theory

Background:

• The curse of dimensionality poses a significant challenge in reinforcement learning (RL), particularly in tabular settings with large state and action spaces.
• Obtaining near-optimal policies in such environments requires sample complexities that scale linearly with the size of the state and action spaces, often proving computationally infeasible.
• Existing methods struggle with the high sample requirements when dealing with large state-action spaces in Markov decision processes (MDPs).

Purpose of the Study:

• To investigate sample-efficient learning algorithms for large-scale Markov decision processes (MDPs).
• To analyze the impact of feature representations on the sample complexity of reinforcement learning.
• To develop provably efficient model-based and Q-learning approaches for MDPs with feature approximations of the transition kernel.

Main Methods:

• The study analyzes a feature-based representation of the probability transition kernel in MDPs.
• Theoretical analysis is applied to a model-based approach and Q-learning algorithm.
• Sample complexity bounds are derived for learning ε-optimal policies and Q-functions with high probability.

Main Results:

• A feature-based approach reduces sample complexity for model-based RL and Q-learning in MDPs.
• The derived sample complexity scales with the feature dimension (K) and discount factor (γ), not the state-action space size.
• The bounds are shown to be tight, with the model-based approach matching the minimax lower bound.

Conclusions:

• Model-based RL and Q-learning are sample-efficient for large-scale MDPs when using a small set of state-action features.
• Feature engineering is crucial for overcoming the curse of dimensionality in reinforcement learning.
• The findings provide theoretical guarantees for efficient learning in complex RL environments.