A unified view of entropy-regularized Markov decision processes (1705.07798v1)

Abstract: We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to accommodate convex regularization functions. Our key result is showing that using the conditional entropy of the joint state-action distributions as regularization yields a dual optimization problem closely resembling the BeLLMan optimality equations. This result enables us to formalize a number of state-of-the-art entropy-regularized reinforcement learning algorithms as approximate variants of Mirror Descent or Dual Averaging, and thus to argue about the convergence properties of these methods. In particular, we show that the exact version of the TRPO algorithm of Schulman et al. (2015) actually converges to the optimal policy, while the entropy-regularized policy gradient methods of Mnih et al. (2016) may fail to converge to a fixed point. Finally, we illustrate empirically the effects of using various regularization techniques on learning performance in a simple reinforcement learning setup.

• The paper unifies entropy-regularized MDPs by framing policy optimization through convex regularization and duality theory.
• It recasts key reinforcement learning algorithms using Mirror Descent and Dual Averaging to provide theoretical consistency and convergence guarantees.
• The work demonstrates how conditional entropy shapes the exploration-exploitation trade-off, informing the design of robust policies.

A Unified View of Entropy-Regularized Markov Decision Processes

The paper "A Unified View of Entropy-Regularized Markov Decision Processes" by Gergely Neu, Vicenç Gómez, and Anders Jonsson offers a comprehensive framework for entropy-regularized reinforcement learning primarily focused on Markov Decision Processes (MDPs). The discussion leverages a convex optimization perspective, extending classical policy optimization through regularization. This approach is particularly centered on using the conditional entropy in conjunction with state-action distributions, thereby bridging the gap between existing methodologies.

The authors creatively apply convex regularization within the field of policy optimization in MDPs by extending the linear programming formulations prevalent in classical settings. By introducing regularization through entropy, a dual optimization problem akin to BeLLMan's optimality equations emerges. This connection allows various entropy-regularized reinforcement learning algorithms to be reframed as variants of established optimization techniques such as Mirror Descent and Dual Averaging.

One significant contribution of this work lies in formally justifying existing algorithms deemed state-of-the-art through this unified framework. Notably, the authors prove that the exact form of the Trust Region Policy Optimization (TRPO) algorithm converges to the optimal policy. This conception of TRPO, reframed as a regularized policy iteration method, offers a broader and theoretically sound convergence guarantee. Conversely, the paper identifies limitations in entropy-regularized policy gradient methods; for instance, the policies derived may not necessarily converge to an optimal solution.

The paper’s analytical framework is further augmented with empirical insights illustrating how various regularization techniques influence learning performances. These applications underscore how strategic regularization can shape the learning landscape within simple reinforcement learning settings.

Theoretical and Practical Implications

Theoretical Implications:

1. Unified Framework: Offering a cohesive view of entropy-regularized MDPs through duality theory paves the way for consistent analysis of reinforcement learning algorithms.
2. Optimization Insights: Bridging a connection to convex optimization techniques (i.e., Mirror Descent and Dual Averaging) extends the arsenal of tools available for tackling decision-making in uncertain environments.
3. Algorithmic Generalization: This unified approach prompts a deeper understanding of how different algorithms relate, ensuring generalization across various forms and settings.

Practical Implications:

1. Algorithmic Development: By elucidating convergence conditions and impacts of regularization, this framework supports the development of more reliable and efficient reinforcement learning algorithms.
2. Exploration-Exploitation Trade-off: The usage of conditional entropy aids in the exploration-exploitation paradigm, ensuring that robust policies are developed in uncertain or partially-known environments.
3. Policy Optimization: Practical endorsements of regularization techniques can inform hyperparameter tuning, leading to more effective deployments in real-world scenarios.

Prospective Directions and Future Developments

Continued exploration into entropy-regularized MDPs could provoke further advances in reinforcement learning. Future research may look into statistical validations of regularization benefits, primarily in dynamic and unknown environments. Moreover, leveraging these insights to devise policy models that adaptively adjust regularization parameters based on environmental feedback could yield significant advancements in adaptive learning systems.

This theoretical backdrop may spur interdisciplinary interest, where fields such as decision theory, artificial intelligence, and operations research converge to innovate on applications from robotics to strategic planning in complex domains. By charting new directions through a comprehensive mathematical foundation, this framework serves as a keystone in the normative and descriptive development of reinforcement learning methodologies.