Runzhe Wan

Jin Zhu, Runzhe Wan, Zhengling Qi et al.

This paper endeavors to augment the robustness of offline reinforcement learning (RL) in scenarios laden with heavy-tailed rewards, a prevalent circumstance in real-world applications. We propose two algorithmic frameworks, ROAM and ROOM, for robust off-policy evaluation and offline policy optimization (OPO), respectively. Central to our frameworks is the strategic incorporation of the median-of-means method with offline RL, enabling straightforward uncertainty estimation for the value function estimator. This not only adheres to the principle of pessimism in OPO but also adeptly manages heavy-tailed rewards. Theoretical results and extensive experiments demonstrate that our two frameworks outperform existing methods on the logged dataset exhibits heavy-tailed reward distributions. The implementation of the proposal is available at https://github.com/Mamba413/ROOM.

Runzhe Wan, Yingying Li, Wenbin Lu et al.

Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the former approach may suffer from the bias while the latter can not incorporate additional information. We propose to bridge these two approaches while allowing the number of factor proxies to diverge, and hence make the latent factor model estimation robust, flexible, and statistically more accurate. As a bonus, the number of factors is also allowed to grow. At the heart of our method is a penalized reduced rank regression to combine information. To further deal with heavy-tailed data, a computationally attractive penalized robust reduced rank regression method is proposed. We establish faster rates of convergence compared with the benchmark. Extensive simulations and real examples are used to illustrate the advantages.

Runzhe Wan, Haoyu Wei, Branislav Kveton et al.

Despite the great interest in the bandit problem, designing efficient algorithms for complex models remains challenging, as there is typically no analytical way to quantify uncertainty. In this paper, we propose Multiplier Bootstrap-based Exploration (MBE), a novel exploration strategy that is applicable to any reward model amenable to weighted loss minimization. We prove both instance-dependent and instance-independent rate-optimal regret bounds for MBE in sub-Gaussian multi-armed bandits. With extensive simulation and real data experiments, we show the generality and adaptivity of MBE.

Runzhe Wan, Yu Liu, James McQueen et al.

With the growing needs of online A/B testing to support the innovation in industry, the opportunity cost of running an experiment becomes non-negligible. Therefore, there is an increasing demand for an efficient continuous monitoring service that allows early stopping when appropriate. Classic statistical methods focus on hypothesis testing and are mostly developed for traditional high-stake problems such as clinical trials, while experiments at online service companies typically have very different features and focuses. Motivated by the real needs, in this paper, we introduce a novel framework that we developed in Amazon to maximize customer experience and control opportunity cost. We formulate the problem as a Bayesian optimal sequential decision making problem that has a unified utility function. We discuss extensively practical design choices and considerations. We further introduce how to solve the optimal decision rule via Reinforcement Learning and scale the solution. We show the effectiveness of this novel approach compared with existing methods via a large-scale meta-analysis on experiments in Amazon.

Xiaohong Chen, Zhengling Qi, Runzhe Wan

Batch reinforcement learning (RL) aims at leveraging pre-collected data to find an optimal policy that maximizes the expected total rewards in a dynamic environment. The existing methods require absolutely continuous assumption (e.g., there do not exist non-overlapping regions) on the distribution induced by target policies with respect to the data distribution over either the state or action or both. We propose a new batch RL algorithm that allows for singularity for both state and action spaces (e.g., existence of non-overlapping regions between offline data distribution and the distribution induced by the target policies) in the setting of an infinite-horizon Markov decision process with continuous states and actions. We call our algorithm STEEL: SingulariTy-awarE rEinforcement Learning. Our algorithm is motivated by a new error analysis on off-policy evaluation, where we use maximum mean discrepancy, together with distributionally robust optimization, to characterize the error of off-policy evaluation caused by the possible singularity and to enable model extrapolation. By leveraging the idea of pessimism and under some technical conditions, we derive a first finite-sample regret guarantee for our proposed algorithm under singularity. Compared with existing algorithms,by requiring only minimal data-coverage assumption, STEEL improves the applicability and robustness of batch RL. In addition, a two-step adaptive STEEL, which is nearly tuning-free, is proposed. Extensive simulation studies and one (semi)-real experiment on personalized pricing demonstrate the superior performance of our methods in dealing with possible singularity in batch RL.

Ye Shen, Runzhe Wan, Hengrui Cai et al.

In the new era of personalization, learning the heterogeneous treatment effect (HTE) becomes an inevitable trend with numerous applications. Yet, most existing HTE estimation methods focus on independently and identically distributed observations and cannot handle the non-stationarity and temporal dependency in the common panel data setting. The treatment evaluators developed for panel data, on the other hand, typically ignore the individualized information. To fill the gap, in this paper, we initialize the study of HTE estimation in panel data. Under different assumptions for HTE identifiability, we propose the corresponding heterogeneous one-side and two-side synthetic learner, namely H1SL and H2SL, by leveraging the state-of-the-art HTE estimator for non-panel data and generalizing the synthetic control method that allows flexible data generating process. We establish the convergence rates of the proposed estimators. The superior performance of the proposed methods over existing ones is demonstrated by extensive numerical studies.

Chengchun Shi, Runzhe Wan, Ge Song et al.

The two-sided markets such as ride-sharing companies often involve a group of subjects who are making sequential decisions across time and/or location. With the rapid development of smart phones and internet of things, they have substantially transformed the transportation landscape of human beings. In this paper we consider large-scale fleet management in ride-sharing companies that involve multiple units in different areas receiving sequences of products (or treatments) over time. Major technical challenges, such as policy evaluation, arise in those studies because (i) spatial and temporal proximities induce interference between locations and times; and (ii) the large number of locations results in the curse of dimensionality. To address both challenges simultaneously, we introduce a multi-agent reinforcement learning (MARL) framework for carrying policy evaluation in these studies. We propose novel estimators for mean outcomes under different products that are consistent despite the high-dimensionality of state-action space. The proposed estimator works favorably in simulation experiments. We further illustrate our method using a real dataset obtained from a two-sided marketplace company to evaluate the effects of applying different subsidizing policies. A Python implementation of our proposed method is available at https://github.com/RunzheStat/CausalMARL.

Chengchun Shi, Runzhe Wan, Victor Chernozhukov et al.

Off-policy evaluation learns a target policy's value with a historical dataset generated by a different behavior policy. In addition to a point estimate, many applications would benefit significantly from having a confidence interval (CI) that quantifies the uncertainty of the point estimate. In this paper, we propose a novel deeply-debiasing procedure to construct an efficient, robust, and flexible CI on a target policy's value. Our method is justified by theoretical results and numerical experiments. A Python implementation of the proposed procedure is available at https://github.com/RunzheStat/D2OPE.

Yahui Bai, Yuhe Gao, Runzhe Wan et al.

In recent years, there has been a growing trend of applying Reinforcement Learning (RL) in financial applications. This approach has shown great potential to solve decision-making tasks in finance. In this survey, we present a comprehensive study of the applications of RL in finance and conduct a series of meta-analyses to investigate the common themes in the literature, such as the factors that most significantly affect RL's performance compared to traditional methods. Moreover, we identify challenges including explainability, Markov Decision Process (MDP) modeling, and robustness that hinder the broader utilization of RL in the financial industry and discuss recent advancements in overcoming these challenges. Finally, we propose future research directions, such as benchmarking, contextual RL, multi-agent RL, and model-based RL to address these challenges and to further enhance the implementation of RL in finance.

Lin Ge, Hengrui Cai, Runzhe Wan et al.

To make effective decisions, it is important to have a thorough understanding of the causal relationships among actions, environments, and outcomes. This review aims to surface three crucial aspects of decision-making through a causal lens: 1) the discovery of causal relationships through causal structure learning, 2) understanding the impacts of these relationships through causal effect learning, and 3) applying the knowledge gained from the first two aspects to support decision making via causal policy learning. Moreover, we identify challenges that hinder the broader utilization of causal decision-making and discuss recent advances in overcoming these challenges. Finally, we provide future research directions to address these challenges and to further enhance the implementation of causal decision-making in practice, with real-world applications illustrated based on the proposed causal decision-making. We aim to offer a comprehensive methodology and practical implementation framework by consolidating various methods in this area into a Python-based collection. URL: https://causaldm.github.io/Causal-Decision-Making.

Haoyu Wei, Runzhe Wan, Lei Shi et al.

Many real-world bandit applications are characterized by sparse rewards, which can significantly hinder learning efficiency. Leveraging problem-specific structures for careful distribution modeling is recognized as essential for improving estimation efficiency in statistics. However, this approach remains under-explored in the context of bandits. To address this gap, we initiate the study of zero-inflated bandits, where the reward is modeled using a classic semi-parametric distribution known as the zero-inflated distribution. We develop algorithms based on the Upper Confidence Bound and Thompson Sampling frameworks for this specific structure. The superior empirical performance of these methods is demonstrated through extensive numerical studies.

Yu Liu, Runzhe Wan, James McQueen et al.

The selection of the assumed effect size (AES) critically determines the duration of an experiment, and hence its accuracy and efficiency. Traditionally, experimenters determine AES based on domain knowledge. However, this method becomes impractical for online experimentation services managing numerous experiments, and a more automated approach is hence of great demand. We initiate the study of data-driven AES selection in for online experimentation services by introducing two solutions. The first employs a three-layer Gaussian Mixture Model considering the heteroskedasticity across experiments, and it seeks to estimate the true expected effect size among positive experiments. The second method, grounded in utility theory, aims to determine the optimal effect size by striking a balance between the experiment's cost and the precision of decision-making. Through comparisons with baseline methods using both simulated and real data, we showcase the superior performance of the proposed approaches.

Runzhe Wan, Branislav Kveton, Rui Song

High-quality data plays a central role in ensuring the accuracy of policy evaluation. This paper initiates the study of efficient and safe data collection for bandit policy evaluation. We formulate the problem and investigate its several representative variants. For each variant, we analyze its statistical properties, derive the corresponding exploration policy, and design an efficient algorithm for computing it. Both theoretical analysis and experiments support the usefulness of the proposed methods.

Runzhe Wan, Lin Ge, Rui Song

Online learning in large-scale structured bandits is known to be challenging due to the curse of dimensionality. In this paper, we propose a unified meta-learning framework for a general class of structured bandit problems where the parameter space can be factorized to item-level. The novel bandit algorithm is general to be applied to many popular problems,scalable to the huge parameter and action spaces, and robust to the specification of the generalization model. At the core of this framework is a Bayesian hierarchical model that allows information sharing among items via their features, upon which we design a meta Thompson sampling algorithm. Three representative examples are discussed thoroughly. Both theoretical analysis and numerical results support the usefulness of the proposed method.

Runzhe Wan, Lin Ge, Rui Song

How to explore efficiently is a central problem in multi-armed bandits. In this paper, we introduce the metadata-based multi-task bandit problem, where the agent needs to solve a large number of related multi-armed bandit tasks and can leverage some task-specific features (i.e., metadata) to share knowledge across tasks. As a general framework, we propose to capture task relations through the lens of Bayesian hierarchical models, upon which a Thompson sampling algorithm is designed to efficiently learn task relations, share information, and minimize the cumulative regrets. Two concrete examples for Gaussian bandits and Bernoulli bandits are carefully analyzed. The Bayes regret for Gaussian bandits clearly demonstrates the benefits of information sharing with our algorithm. The proposed method is further supported by extensive experiments.

Runzhe Wan, Sheng Zhang, Chengchun Shi et al.

Order dispatch is one of the central problems to ride-sharing platforms. Recently, value-based reinforcement learning algorithms have shown promising performance on this problem. However, in real-world applications, the non-stationarity of the demand-supply system poses challenges to re-utilizing data generated in different time periods to learn the value function. In this work, motivated by the fact that the relative relationship between the values of some states is largely stable across various environments, we propose a pattern transfer learning framework for value-based reinforcement learning in the order dispatch problem. Our method efficiently captures the value patterns by incorporating a concordance penalty. The superior performance of the proposed method is supported by experiments.

Runzhe Wan, Xinyu Zhang, Rui Song

Severe infectious diseases such as the novel coronavirus (COVID-19) pose a huge threat to public health. Stringent control measures, such as school closures and stay-at-home orders, while having significant effects, also bring huge economic losses. In the face of an emerging infectious disease, a crucial question for policymakers is how to make the trade-off and implement the appropriate interventions timely given the huge uncertainty. In this work, we propose a Multi-Objective Model-based Reinforcement Learning framework to facilitate data-driven decision-making and minimize the overall long-term cost. Specifically, at each decision point, a Bayesian epidemiological model is first learned as the environment model, and then the proposed model-based multi-objective planning algorithm is applied to find a set of Pareto-optimal policies. This framework, combined with the prediction bands for each policy, provides a real-time decision support tool for policymakers. The application is demonstrated with the spread of COVID-19 in China.

Peng Liao, Zhengling Qi, Runzhe Wan et al.

We consider the batch (off-line) policy learning problem in the infinite horizon Markov Decision Process. Motivated by mobile health applications, we focus on learning a policy that maximizes the long-term average reward. We propose a doubly robust estimator for the average reward and show that it achieves semiparametric efficiency. Further we develop an optimization algorithm to compute the optimal policy in a parameterized stochastic policy class. The performance of the estimated policy is measured by the difference between the optimal average reward in the policy class and the average reward of the estimated policy and we establish a finite-sample regret guarantee. The performance of the method is illustrated by simulation studies and an analysis of a mobile health study promoting physical activity.

Chengchun Shi, Runzhe Wan, Rui Song et al.

The Markov assumption (MA) is fundamental to the empirical validity of reinforcement learning. In this paper, we propose a novel Forward-Backward Learning procedure to test MA in sequential decision making. The proposed test does not assume any parametric form on the joint distribution of the observed data and plays an important role for identifying the optimal policy in high-order Markov decision processes and partially observable MDPs. We apply our test to both synthetic datasets and a real data example from mobile health studies to illustrate its usefulness.