An Emphatic Approach to the Problem of Off-policy Temporal-Difference Learning (1503.04269v2)

Abstract: In this paper we introduce the idea of improving the performance of parametric temporal-difference (TD) learning algorithms by selectively emphasizing or de-emphasizing their updates on different time steps. In particular, we show that varying the emphasis of linear TD($\lambda$)'s updates in a particular way causes its expected update to become stable under off-policy training. The only prior model-free TD methods to achieve this with per-step computation linear in the number of function approximation parameters are the gradient-TD family of methods including TDC, GTD($\lambda$), and GQ($\lambda$). Compared to these methods, our emphatic TD($\lambda$) is simpler and easier to use; it has only one learned parameter vector and one step-size parameter. Our treatment includes general state-dependent discounting and bootstrapping functions, and a way of specifying varying degrees of interest in accurately valuing different states.

• The paper introduces emphatic TD learning, which dynamically weights off-policy updates to ensure stability.
• It simplifies the algorithm by maintaining a single parameter vector and step size, reducing complexity compared to gradient TD methods.
• The method is theoretically validated through positive definiteness of the update matrix, paving the way for robust off-policy learning.

Emphatic Approach to Off-policy Temporal-Difference Learning: A Detailed Examination

The paper "An Emphatic Approach to the Problem of Off-policy Temporal-Difference Learning," authored by Richard S. Sutton, A. Rupam Mahmood, and Martha White, explores the challenges and advancements in temporal-difference (TD) learning, particularly in off-policy settings with function approximation. Off-policy TD learning is a foundational aspect of reinforcement learning that allows learning optimal policies or value functions from observations gathered under a different policy, typically termed as the behavior policy.

Introduction and Context

Temporal-difference learning, introduced by Sutton (1988), has been a central concept in reinforcement learning for predicting future rewards in Markov decision processes. The TD learning algorithm makes updates based on differences between successive predictions rather than waiting for final outcomes, providing certain computational and statistical advantages.

Off-policy learning, however, introduces additional complexity. Unlike on-policy learning, where the policy used to generate data aligns with the one being evaluated, off-policy learning separates these, enabling learning from historical or exploratory data. Yet, this flexibility often comes with stability concerns, notably exposed in Baird's counterexamples (1995), where off-policy TD methods have shown divergence with function approximation.

Main Contribution

The emphatic TD (ETD) method proposed in this paper builds on ideas of importance sampling and traces, determining how updates should be weighted across different time steps to ensure stability. In particular, ETD solves stability issues inherent in off-policy TD learning by introducing an emphasis term that dynamically adjusts the weight of updates. This approach relies on followon traces, a mechanism that accounts for both the inherent interest in certain states and the trajectory deviations introduced by the behavior policy.

The key innovations of the ETD algorithm include:

• Stability under Off-policy Training: ETD achieves stability under off-policy training by ensuring the expected updates remain contraction mappings. This is achieved through the strategic weighting of the updates using followon traces.
• Lower Complexity: Compared to other gradient-based TD algorithms (like gradient TD algorithms), ETD simplifies parameters by reducing the need for additional parameter vectors and step sizes associated with gradient correction methods.
• Algorithm Simplicity: ETD maintains a single parameter vector and step size, easing the deployment and tuning in practical scenarios.

Theoretical Implications

This work offers new insights into the convergence properties of TD algorithms under off-policy conditions. The authors demonstrate the convergence of the algorithm in expectation by showing the positive definiteness of the matrix involved in the update, which is critical, given TD update's reliance on contraction mappings for stability.

The introduction of state-dependent discounting and interest functions further generalizes TD methods, making them more versatile for a wider range of learning scenarios, including non-episodic tasks. The ETD methodology shows that careful design of weightings (emphases) with respect to state visitations and policy deviations can remedy instability issues that traditional off-policy methods encounter.

Practical Implications and Future Directions

While the paper primarily focuses on theoretical foundations and stability assurances, there are clear indications for future empirical validation and comparative studies against existing methods such as gradient TD approaches. The authors remark on the potential for extending emphatic approaches to control settings, action-value functions, and adaptations to current importance-sampling methods for variance reduction.

The simplicity and theoretical stability of ETD suggest promising applications in real-world scenarios where learning from large datasets, historical data, or simulations under different policies is paramount. This includes settings like robotics, game-playing algorithms, and complex decision systems benefiting from improved efficiency and reduced parameter tuning efforts.

Future research could explore empirical performance on large-scale benchmarks, extensions to non-linear function approximations such as neural networks, and integration with existing RL frameworks to leverage ETD's favorable properties.

In conclusion, the emphatic TD method represents a significant evolution in TD learning's ability to stabilize and process off-policy updates effectively. This research broadens the applicability of TD methods in reinforcement learning, addressing longstanding stability concerns with innovative theoretical constructs.