Off-Policy Actor-Critic (1205.4839v5)

Abstract: This paper presents the first actor-critic algorithm for off-policy reinforcement learning. Our algorithm is online and incremental, and its per-time-step complexity scales linearly with the number of learned weights. Previous work on actor-critic algorithms is limited to the on-policy setting and does not take advantage of the recent advances in off-policy gradient temporal-difference learning. Off-policy techniques, such as Greedy-GQ, enable a target policy to be learned while following and obtaining data from another (behavior) policy. For many problems, however, actor-critic methods are more practical than action value methods (like Greedy-GQ) because they explicitly represent the policy; consequently, the policy can be stochastic and utilize a large action space. In this paper, we illustrate how to practically combine the generality and learning potential of off-policy learning with the flexibility in action selection given by actor-critic methods. We derive an incremental, linear time and space complexity algorithm that includes eligibility traces, prove convergence under assumptions similar to previous off-policy algorithms, and empirically show better or comparable performance to existing algorithms on standard reinforcement-learning benchmark problems.

Off-Policy Actor-Critic: An Analysis

The paper under consideration introduces a novel actor-critic algorithm tailored for off-policy reinforcement learning (RL), expanding the horizons of existing actor-critic methods which are traditionally confined to on-policy settings. In particular, this development is significant because it aligns with the recent progress in off-policy gradient temporal-difference (TD) learning, such as techniques embodied by Greedy-GQ. Off-policy RL methods offer greater generality as they allow the learning of a target policy while deriving data from a different behavior policy. This capability is vital for applications requiring exploration strategies different from the optimal policy pursuit, such as learning from demonstrations or multitask learning.

Contributions and Algorithmic Overview

This work introduces the Off-Policy Actor-Critic (Off-PAC) algorithm, marking a pivotal contribution as it extends actor-critic strategies into the off-policy field. This extension incorporates the essentiality of off-policy learning’s flexibility while maintaining the inherent robustness provided by actor-critic’s explicit policy representation. The algorithm leverages eligibility traces—an elegant solution for managing the balance between bias and variance—and demonstrates linear time and space complexity. Crucially, Off-PAC maintains convergence under standard off-policy learning assumptions.

The authors deliver a comprehensive framework for Off-PAC by:

1. Proposing an off-policy policy gradient theorem.
2. Establishing convergence proofs for the gradient updates when the $\lambda$ parameter equals zero.
3. Providing empirical evidence that Off-PAC outshines several established algorithms on benchmark RL problems.

Empirical Evaluation

Off-PAC's superiority is substantiated through rigorous empirical comparison against Q($\lambda$), Greedy-GQ, and Softmax-GQ across benchmark scenarios including mountain car, pendulum, and continuous grid world tasks. Noteworthy results are highlighted with Off-PAC demonstrating reliably better performance and displaying significantly lower variance in outcomes compared to its counterparts.

It is essential to recognize that the empirical evaluation focuses on environments with discrete actions and continuous states, which inherently push the limits of conventional off-policy methods. Off-PAC stands out especially in the continuous grid world environment, achieving the set goal reliably, a feat unachieved by other algorithms.

Theoretical Insights and Limitations

The paper methodically lays the theoretical foundation for off-policy actor-critic approaches, presenting a robust convergence analysis under simplifying assumptions. However, the framework partially hinges on the confines of tabular representation for some theoretical assurances. Overcoming such limitations, especially for function approximation scenarios, necessitates further investigation and refinement.

Furthermore, the discussion section provides practical insights into the sensitivity of parameter settings. This area remains a critical focus for real-world applicability, especially when extending the framework to include more complex, real-time, or higher-dimensional systems.

Future Directions

The implications of Off-PAC are promising yet invite numerous avenues for future exploration. Key areas include:

• Extending off-policy actor-critic methods to settings with continuous action spaces, which could revolutionize applications in robotics and autonomous systems.
• Enhancing stability and efficiency through natural actor-critic extensions.
• Addressing the challenges of high-dimensional function approximations to harness the full potential of off-policy learning.

Conclusion

Overall, the introduction of the Off-PAC algorithm represents a noteworthy advance in the reinforcement learning paradigm by effectively bridging the gap between the benefits of actor-critics and the generality of off-policy learning. This work provides a solid theoretical and empirical bedrock that establishes Off-PAC as an attractive option for researchers and practitioners focusing on scalable and robust off-policy RL solutions.