Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes (1908.08526v3)

Abstract: Off-policy evaluation (OPE) in reinforcement learning allows one to evaluate novel decision policies without needing to conduct exploration, which is often costly or otherwise infeasible. We consider for the first time the semiparametric efficiency limits of OPE in Markov decision processes (MDPs), where actions, rewards, and states are memoryless. We show existing OPE estimators may fail to be efficient in this setting. We develop a new estimator based on cross-fold estimation of $q$-functions and marginalized density ratios, which we term double reinforcement learning (DRL). We show that DRL is efficient when both components are estimated at fourth-root rates and is also doubly robust when only one component is consistent. We investigate these properties empirically and demonstrate the performance benefits due to harnessing memorylessness.

• The paper establishes semiparametric efficiency limits for off-policy evaluation by exploiting the memoryless property of MDPs.
• The paper develops the DRL estimator that combines cross-fold q-function and density ratio estimation to achieve double robustness.
• The paper empirically validates DRL's efficiency and robustness, offering a practical solution for policy evaluation in cost-sensitive applications.

Summary of Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes

The paper, "Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes," by Nathan Kallus and Masatoshi Uehara, presents an advanced methodology for Off-Policy Evaluation (OPE) in the setting of Markov Decision Processes (MDPs). This work establishes theoretical efficiency limits and proposes a new estimator, termed Double Reinforcement Learning (DRL), that achieves these limits under certain conditions, addressing critical challenges in reinforcement learning (RL).

Key Contributions

1. Study of Semiparametric Efficiency in OPE: The paper investigates the semiparametric efficiency bounds for OPE in both Non-Markov Decision Processes (NMDPs) and MDPs. This analysis reveals that leveraging the memorylessness property of MDPs can reduce the asymptotic mean squared error (AMSE) of OPE, suggesting that the MDP model is more statistically efficient than the NMDP model.
2. Development of DRL Estimator: The paper introduces the DRL estimator, which combines cross-fold estimation of $q$-functions and marginalized density ratios. The key advantage of DRL is its efficiency when both components achieve estimation rates at a fourth-root rate. Additionally, DRL exhibits double robustness; it remains consistent when only one component (either $q$-functions or density ratios) is correctly specified.
3. Empirical Validation: Empirical investigations undertaken demonstrate the efficiency and robustness of DRL, especially in leveraging the Markov property to enhance performance in scenarios with memoryless data structures.

Implications

• Practical Applications: The development of DRL enables practitioners to evaluate decision-making policies more effectively in applications where data collection is constrained by cost or feasibility, such as in healthcare and educational settings where exploration can be ethically or logistically challenging.
• Theoretical Insights: By formalizing the use of semiparametric efficiency theory in reinforcement learning tasks, this work bridges a gap between theoretical statistics and practical RL applications—opening pathways for the deployment of statistically optimal policies in real-world settings.
• Future Work in AI: The results presented could inspire extensions to other decision-making frameworks, possibly offering insights into the development of more general learning algorithms that can exploit model-specific properties for efficiency gains.

In conclusion, the paper presents a substantial advancement in the methodological framework of OPE in MDPs. By establishing efficiency limits and developing an estimator that approaches these bounds, it offers both theoretical and practical pathways for the deployment of more reliable and efficient RL systems. This contribution holds potential implications for both current AI systems and future theoretical explorations in the field.