Bayesian Reinforcement Learning: A Survey (1609.04436v1)

Abstract: Bayesian methods for machine learning have been widely investigated, yielding principled methods for incorporating prior information into inference algorithms. In this survey, we provide an in-depth review of the role of Bayesian methods for the reinforcement learning (RL) paradigm. The major incentives for incorporating Bayesian reasoning in RL are: 1) it provides an elegant approach to action-selection (exploration/exploitation) as a function of the uncertainty in learning; and 2) it provides a machinery to incorporate prior knowledge into the algorithms. We first discuss models and methods for Bayesian inference in the simple single-step Bandit model. We then review the extensive recent literature on Bayesian methods for model-based RL, where prior information can be expressed on the parameters of the Markov model. We also present Bayesian methods for model-free RL, where priors are expressed over the value function or policy class. The objective of the paper is to provide a comprehensive survey on Bayesian RL algorithms and their theoretical and empirical properties.

• The paper presents Bayesian reinforcement learning as a framework that integrates Bayesian inference into RL to manage uncertainty in action selection via posterior distributions.
• It details both model-based and model-free methods, including BAMDP and GPSARSA, which boost sample efficiency and performance in uncertain environments.
• The survey discusses risk-aware approaches and multi-task extensions, highlighting open challenges and future directions for scaling BRL to complex, high-dimensional problems.

Bayesian Reinforcement Learning: A Survey

Bayesian Reinforcement Learning (BRL) lies at the confluence of Bayesian inference and reinforcement learning, offering a principled framework that incorporates uncertainties into the learning process. This comprehensive survey by Ghavamzadeh et al. explores the theoretical underpinnings and practical implementations of BRL, examining the integration of prior knowledge into reinforcement learning algorithms.

Theoretical Foundation

The survey outlines the advantages of employing Bayesian methods within RL, primarily leveraging Bayesian inference for optimal action-selection based on the uncertainty of the learning process. In contrast to traditional methods focusing solely on model estimation, BRL utilizes posterior distributions as representations of uncertainty, enabling informed exploration-exploitation trade-offs.

Bayesian Bandits

In the context of multi-armed bandits (MAB), BRL offers sophisticated methods for parameterizing outcome probabilities. Techniques such as Thompson Sampling and Bayes-UCB provide robust means of uncertainty quantification and action-selection, yielding regret bounds that demonstrate the efficiency of Bayesian strategies over traditional frequentist methods.

Model-based BRL

The paper extensively covers model-based Bayesian RL, emphasizing the Bayes-Adaptive Markov Decision Process (BAMDP). Here, the exploration dilemma is approached through intricate modeling of uncertainty in transition dynamics using Dirichlet distributions. Methods like Bayesian dynamic programming and Bayesian sparse sampling are shown to provide effective means of balancing model learning and exploitation.

Advanced approaches like BAMCP (Bayes-Adaptive Monte Carlo Planning) leverage Monte Carlo tree search principles, aligning computational efficiency with theoretical convergence properties. Algorithms within this space exhibit improved sample efficiency through strategic posterior sampling and value estimation.

Model-free BRL

For cases where explicit model representation is infeasible, the authors discuss model-free BRL leveraging Gaussian processes for approximating value functions. Techniques like Gaussian Process SARSA (GPSARSA) and Bayesian Policy Gradient (BPG) methods illustrate how uncertainty in value function estimation can guide policy improvement with reduced sample needs.

Risk-Aware BRL

The survey touches upon risk-aware Bayesian RL, where parametric uncertainty is explicitly managed to optimize for both expected performance and risk. Methods incorporating variance-based rewards and percentile-based optimization underscore BRL's capability to address risk-sensitive settings, particularly relevant in domains like finance.

Extensions and Implications

The discussion extends to multi-task and multi-agent settings, highlighting BRL's adaptability in leveraging shared structural information across tasks and agents. PAC-Bayes analyses provide robust theoretical backing, ensuring model selection that can accommodate mis-specified priors.

Future Directions

The authors argue for further research in scaling BRL to large-scale problems, emphasizing the need for novel priors based on empirical Bayes techniques. The integration with deep learning models to manage high-dimensional data and leverage transfer learning is identified as a promising avenue.

Overall, while BRL offers powerful tools for handling uncertainty in RL, its practical implementation in large systems remains a significant challenge. However, its coherent framework, capable of embedding domain knowledge, provides a strong foundation for advancing both theoretical research and practical applications in reinforcement learning.