Experimenting on Markov Decision Processes with Local Treatments (2407.19618v2)

Abstract: Utilizing randomized experiments to evaluate the effect of short-term treatments on the short-term outcomes has been well understood and become the golden standard in industrial practice. However, as service systems become increasingly dynamical and personalized, much focus is shifting toward maximizing long-term cumulative outcomes, such as customer lifetime value, through lifetime exposure to interventions. To bridge this gap, we investigate the randomized experiments within dynamical systems modeled as Markov Decision Processes (MDPs). Our goal is to assess the impact of treatment and control policies on long-term cumulative rewards from relatively short-term observations. We first develop optimal inference techniques for assessing the effects of general treatment patterns. Furthermore, recognizing that many real-world treatments tend to be fine-grained and localized for practical efficiency and operational convenience, we then propose methods to harness this localized structure by sharing information on the non-targeted states. Our new estimator effectively overcomes the variance lower bound for general treatments while matching the more stringent lower bound incorporating the local treatment structure. Furthermore, our estimator can optimally achieve a linear reduction with the number of test arms for a major part of the variance. Finally, we explore scenarios with perfect knowledge of the control arm and design estimators that further improve inference efficiency.

• The paper’s main contribution is a variance reduction estimator that shares data across unaffected states to accurately measure local treatment effects.
• It combines classical inference methods with innovative techniques to enhance A/B testing reliability in dynamic decision processes.
• Empirical evaluations demonstrate substantial improvements in bias and variance reduction, informing better decision-making in practical applications.

Evaluating A/B Testing Frameworks in Markov Decision Processes with Local Treatments

This paper presents a comprehensive exploration of experimentation within Markov Decision Processes (MDPs) when interventions, or treatments, are applied locally to specific states. The paper introduces methodologies to optimize the evaluation of treatment effects using both classical and novel inference techniques. The authors focus on leveraging the local structure of treatments to enhance the efficiency of estimating average treatment effects (ATEs). This is achieved by developing a variance reduction technique that shares data between states unaffected by treatments, ensuring a more informed data-driven decision-making process.

Key Contributions

The paper investigates several aspects of A/B testing in the context of MDPs:

1. Classic Methods and Local Treatment Structure: The authors begin by assessing traditional inference methods such as model-based estimation and temporal difference (TD) learning. These methods were applied under a fixed policy framework and further extended to scenarios involving MDPs, indicating the potential for considerable variance limitations when ignoring treatment structures.
2. Variance Reduction via Information Sharing: A core innovation of the paper is the presentation of an estimator employing variance reduction. This method utilizes the local treatment structure by sharing information across states that remain unaffected by the treatment. By doing so, the estimator not only surpasses existing variance bounds for general treatments but also matches the stricter lower bounds associated with localized treatment effects. This aids in achieving an optimal linear relationship with the number of test arms concerning variance reduction.
3. Empirical and Theoretical Evaluation: The paper conducts extensive evaluations, including simulating customer scenarios of the business world. These empirical results verify the efficacy of information sharing and demonstrate significant performance improvements when dealing with local treatments. The findings further highlight the estimator's ability to reduce variance substantially while maintaining low bias—offering a clearer understanding of treatment benefits across different contexts.
4. Generalization to Local Treatment: Beyond single-state treatments, the framework is broadened for treatments affecting multiple states. This generalization increases the paper's applicability to broader real-world scenarios where interventions are often not limited to single states but rather distributed across a subset of states in the MDP.

Implications and Future Directions

This research has substantial implications for efficiently conducting experiments in dynamic MDP environments. By intelligently sharing information and reducing variance, businesses and organizations can make better-informed decisions based on more accurate predictions of long-term treatment effects. The ability to exploit local treatment structures offers a promising path to optimize decision-making strategies, crucial in areas like marketing, healthcare, and service industries.

The paper raises open questions for further exploration, particularly around more complex local treatment structures and how these might interact with other machine learning techniques such as reinforcement learning frameworks beyond TD learning. Moreover, examining the integration of these techniques with various function approximations may yield further efficiency in complex, high-dimensional state spaces.

Through its in-depth analysis and robust experimentation methodologies, this paper contributes significantly to the literature on MDPs, showcasing innovative solutions to longstanding problems in experimental design and analysis, paving the way for more nuanced and effective applications in artificial intelligence and operations research.