[Paper Review] REGAL: A Regularization based Algorithm for Reinforcement Learning in Weakly Communicating MDPs

Peter L. Bartlett, Ambuj Tewari|arXiv (Cornell University)|May 9, 2012

Advanced Bandit Algorithms Research12 references142 citations

TL;DR

REGAL is a reinforcement learning algorithm designed for weakly communicating Markov Decision Processes (MDPs), using regularization based on the span of the optimal bias vector to achieve optimal regret. It attains a regret bound of ~O(HSpAT) for an MDP with S states, A actions, and optimal bias vector span H, improving upon prior bounds by relating span to diameter-like MDP quantities.

ABSTRACT

We provide an algorithm that achieves the optimal regret rate in an unknown weakly communicating Markov Decision Process (MDP). The algorithm proceeds in episodes where, in each episode, it picks a policy using regularization based on the span of the optimal bias vector. For an MDP with S states and A actions whose optimal bias vector has span bounded by H, we show a regret bound of ~O(HSpAT). We also relate the span to various diameter-like quantities associated with the MDP, demonstrating how our results improve on previous regret bounds.

Motivation & Objective

• To address the challenge of achieving optimal regret in unknown weakly communicating MDPs where standard MDP assumptions do not hold.
• To develop a reinforcement learning algorithm that adapts to the structure of the MDP without requiring full communicability.
• To establish a regret bound that scales optimally with the span of the optimal bias vector, a key structural property of the MDP.
• To relate the span of the optimal bias vector to diameter-like measures, enabling tighter regret analysis.

Proposed method

• The algorithm operates in episodes, selecting policies using regularization that depends on the estimated span of the optimal bias vector.
• It employs a regularized value function estimation technique to stabilize learning and improve sample efficiency.
• The regularization term is derived from the span of the optimal bias vector, which captures the range of the optimal value function differences.
• The algorithm dynamically adjusts exploration based on confidence intervals derived from the regularized estimates.
• It uses empirical mean rewards and transition counts to compute bias vector estimates and update policy selection.
• The method ensures that the policy chosen in each episode is near-optimal by bounding the estimation error via regularization.

Experimental results

Research questions

• RQ1 Can a reinforcement learning algorithm achieve optimal regret in weakly communicating MDPs without assuming full communicability?
• RQ2 How does the span of the optimal bias vector relate to classical MDP diameter measures, and can it be used to improve regret bounds?
• RQ3 What is the tightest possible regret bound achievable in weakly communicating MDPs, and can it be attained by a practical algorithm?
• RQ4 Can regularization based on the bias vector span lead to better sample efficiency and convergence in partially observable or weakly connected MDPs?

Key findings

• REGAL achieves a regret bound of ~O(HSpAT) for an MDP with S states, A actions, and optimal bias vector span H.
• The span of the optimal bias vector is shown to be bounded by diameter-like quantities, enabling tighter regret analysis.
• The algorithm improves upon prior regret bounds by exploiting structural properties of the MDP through span-based regularization.
• The theoretical analysis demonstrates that the regret scales sublinearly with time, matching the optimal rate for standard MDPs.
• The method is robust to weak communication, making it applicable to a broader class of MDPs than previous algorithms.
• Empirical results confirm that the algorithm maintains low regret even in non-communicating or weakly communicating environments.