On the representation complexity of model-based and model-free reinforcement learning

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Complexity Theory

Background:

• Reinforcement learning (RL) algorithms are broadly categorized into model-based and model-free approaches.
• Understanding the representation complexity of these algorithms is crucial for improving sample efficiency and performance.
• Prior research has not extensively explored the link between circuit complexity and the differing sample complexities of RL paradigms.

Purpose of the Study:

• To investigate the representation complexity of model-based and model-free reinforcement learning using circuit complexity theory.
• To provide theoretical insights into why model-based RL algorithms often exhibit superior sample complexity compared to model-free methods.
• To establish a rigorous framework for analyzing the representational demands of RL components.

Main Methods:

• Analyzing the circuit complexity of transition and reward functions in Markov decision processes.
• Comparing the circuit complexity of optimal Q-functions with that of environment models.
• Empirically evaluating approximation errors of transition kernels, reward functions, and Q-functions in MuJoCo environments.

Main Results:

• Demonstrated that environment transition and reward functions can be represented by polynomial-sized, constant-depth circuits.
• Showed that optimal Q-functions require exponential circuit complexity in constant-depth models.
• Empirical results confirmed consistently lower approximation errors for transition kernels and reward functions compared to optimal Q-functions.

Conclusions:

• The inherent simplicity in representing environment dynamics (world models) contributes to the sample efficiency of model-based RL.
• Model-free RL's reliance on complex Q-functions, which are harder to represent, leads to higher sample complexity.
• This research highlights the significance of world models in AI and offers a novel perspective on RL algorithm design and analysis.