arXiv subjects

Chengchun Shi

Publications and source records attributed to Chengchun Shi.

At least 73 records · Page 4Linked to original sources

arXiv2023

Future-Dependent Value-Based Off-Policy Evaluation in POMDPs

We study off-policy evaluation (OPE) for partially observable MDPs (POMDPs) with general function approximation. Existing methods such as sequential importance sampling estimators and fitted-Q evaluation suffer from the curse of horizon in POMDPs. To circumvent this problem, we develop a novel model-free OPE method by introducing future-dependent value functions that take future proxies as inputs. Future-dependent value functions play similar roles as classical value functions in fully-observable MDPs. We derive a new Bellman equation for future-dependent value functions as conditional moment equations that use history proxies as instrumental variables. We further propose a minimax learning method to learn future-dependent value functions using the new Bellman equation. We obtain the PAC result, which implies our OPE estimator is consistent as long as futures and histories contain sufficient information about latent states, and the Bellman completeness. Finally, we extend our methods to learning of dynamics and establish the connection between our approach and the well-known spectral learning methods in POMDPs.

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arXiv2023

Optimal Treatment Allocation for Efficient Policy Evaluation in Sequential Decision Making

A/B testing is critical for modern technological companies to evaluate the effectiveness of newly developed products against standard baselines. This paper studies optimal designs that aim to maximize the amount of information obtained from online experiments to estimate treatment effects accurately. We propose three optimal allocation strategies in a dynamic setting where treatments are sequentially assigned over time. These strategies are designed to minimize the variance of the treatment effect estimator when data follow a non-Markov decision process or a (time-varying) Markov decision process. We further develop estimation procedures based on existing off-policy evaluation (OPE) methods and conduct extensive experiments in various environments to demonstrate the effectiveness of the proposed methodologies. In theory, we prove the optimality of the proposed treatment allocation design and establish upper bounds for the mean squared errors of the resulting treatment effect estimators.

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arXiv2023

A Reinforcement Learning Framework for Dynamic Mediation Analysis

Mediation analysis learns the causal effect transmitted via mediator variables between treatments and outcomes and receives increasing attention in various scientific domains to elucidate causal relations. Most existing works focus on point-exposure studies where each subject only receives one treatment at a single time point. However, there are a number of applications (e.g., mobile health) where the treatments are sequentially assigned over time and the dynamic mediation effects are of primary interest. Proposing a reinforcement learning (RL) framework, we are the first to evaluate dynamic mediation effects in settings with infinite horizons. We decompose the average treatment effect into an immediate direct effect, an immediate mediation effect, a delayed direct effect, and a delayed mediation effect. Upon the identification of each effect component, we further develop robust and semi-parametrically efficient estimators under the RL framework to infer these causal effects. The superior performance of the proposed method is demonstrated through extensive numerical studies, theoretical results, and an analysis of a mobile health dataset.

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arXiv2023

Testing for the Markov Property in Time Series via Deep Conditional Generative Learning

The Markov property is widely imposed in analysis of time series data. Correspondingly, testing the Markov property, and relatedly, inferring the order of a Markov model, are of paramount importance. In this article, we propose a nonparametric test for the Markov property in high-dimensional time series via deep conditional generative learning. We also apply the test sequentially to determine the order of the Markov model. We show that the test controls the type-I error asymptotically, and has the power approaching one. Our proposal makes novel contributions in several ways. We utilize and extend state-of-the-art deep generative learning to estimate the conditional density functions, and establish a sharp upper bound on the approximation error of the estimators. We derive a doubly robust test statistic, which employs a nonparametric estimation but achieves a parametric convergence rate. We further adopt sample splitting and cross-fitting to minimize the conditions required to ensure the consistency of the test. We demonstrate the efficacy of the test through both simulations and the three data applications.

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arXiv2023

Testing Directed Acyclic Graph via Structural, Supervised and Generative Adversarial Learning

In this article, we propose a new hypothesis testing method for directed acyclic graph (DAG). While there is a rich class of DAG estimation methods, there is a relative paucity of DAG inference solutions. Moreover, the existing methods often impose some specific model structures such as linear models or additive models, and assume independent data observations. Our proposed test instead allows the associations among the random variables to be nonlinear and the data to be time-dependent. We build the test based on some highly flexible neural networks learners. We establish the asymptotic guarantees of the test, while allowing either the number of subjects or the number of time points for each subject to diverge to infinity. We demonstrate the efficacy of the test through simulations and a brain connectivity network analysis.

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arXiv2023

Evaluating Dynamic Conditional Quantile Treatment Effects with Applications in Ridesharing

Many modern tech companies, such as Google, Uber, and Didi, utilize online experiments (also known as A/B testing) to evaluate new policies against existing ones. While most studies concentrate on average treatment effects, situations with skewed and heavy-tailed outcome distributions may benefit from alternative criteria, such as quantiles. However, assessing dynamic quantile treatment effects (QTE) remains a challenge, particularly when dealing with data from ride-sourcing platforms that involve sequential decision-making across time and space. In this paper, we establish a formal framework to calculate QTE conditional on characteristics independent of the treatment. Under specific model assumptions, we demonstrate that the dynamic conditional QTE (CQTE) equals the sum of individual CQTEs across time, even though the conditional quantile of cumulative rewards may not necessarily equate to the sum of conditional quantiles of individual rewards. This crucial insight significantly streamlines the estimation and inference processes for our target causal estimand. We then introduce two varying coefficient decision process (VCDP) models and devise an innovative method to test the dynamic CQTE. Moreover, we expand our approach to accommodate data from spatiotemporal dependent experiments and examine both conditional quantile direct and indirect effects. To showcase the practical utility of our method, we apply it to three real-world datasets from a ride-sourcing platform. Theoretical findings and comprehensive simulation studies further substantiate our proposal.

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arXiv2023

A Multi-Agent Reinforcement Learning Framework for Off-Policy Evaluation in Two-sided Markets

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.

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arXiv2023

Optimizing Pessimism in Dynamic Treatment Regimes: A Bayesian Learning Approach

In this article, we propose a novel pessimism-based Bayesian learning method for optimal dynamic treatment regimes in the offline setting. When the coverage condition does not hold, which is common for offline data, the existing solutions would produce sub-optimal policies. The pessimism principle addresses this issue by discouraging recommendation of actions that are less explored conditioning on the state. However, nearly all pessimism-based methods rely on a key hyper-parameter that quantifies the degree of pessimism, and the performance of the methods can be highly sensitive to the choice of this parameter. We propose to integrate the pessimism principle with Thompson sampling and Bayesian machine learning for optimizing the degree of pessimism. We derive a credible set whose boundary uniformly lower bounds the optimal Q-function, and thus we do not require additional tuning of the degree of pessimism. We develop a general Bayesian learning method that works with a range of models, from Bayesian linear basis model to Bayesian neural network model. We develop the computational algorithm based on variational inference, which is highly efficient and scalable. We establish the theoretical guarantees of the proposed method, and show empirically that it outperforms the existing state-of-the-art solutions through both simulations and a real data example.

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arXiv2023

Conformal Off-policy Prediction

Off-policy evaluation is critical in a number of applications where new policies need to be evaluated offline before online deployment. Most existing methods focus on the expected return, define the target parameter through averaging and provide a point estimator only. In this paper, we develop a novel procedure to produce reliable interval estimators for a target policy's return starting from any initial state. Our proposal accounts for the variability of the return around its expectation, focuses on the individual effect and offers valid uncertainty quantification. Our main idea lies in designing a pseudo policy that generates subsamples as if they were sampled from the target policy so that existing conformal prediction algorithms are applicable to prediction interval construction. Our methods are justified by theories, synthetic data and real data from short-video platforms.

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arXiv2023

An Instrumental Variable Approach to Confounded Off-Policy Evaluation

Off-policy evaluation (OPE) is a method for estimating the return of a target policy using some pre-collected observational data generated by a potentially different behavior policy. In some cases, there may be unmeasured variables that can confound the action-reward or action-next-state relationships, rendering many existing OPE approaches ineffective. This paper develops an instrumental variable (IV)-based method for consistent OPE in confounded Markov decision processes (MDPs). Similar to single-stage decision making, we show that IV enables us to correctly identify the target policy's value in infinite horizon settings as well. Furthermore, we propose an efficient and robust value estimator and illustrate its effectiveness through extensive simulations and analysis of real data from a world-leading short-video platform.

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arXiv2023

Jump Interval-Learning for Individualized Decision Making

An individualized decision rule (IDR) is a decision function that assigns each individual a given treatment based on his/her observed characteristics. Most of the existing works in the literature consider settings with binary or finitely many treatment options. In this paper, we focus on the continuous treatment setting and propose a jump interval-learning to develop an individualized interval-valued decision rule (I2DR) that maximizes the expected outcome. Unlike IDRs that recommend a single treatment, the proposed I2DR yields an interval of treatment options for each individual, making it more flexible to implement in practice. To derive an optimal I2DR, our jump interval-learning method estimates the conditional mean of the outcome given the treatment and the covariates via jump penalized regression, and derives the corresponding optimal I2DR based on the estimated outcome regression function. The regressor is allowed to be either linear for clear interpretation or deep neural network to model complex treatment-covariates interactions. To implement jump interval-learning, we develop a searching algorithm based on dynamic programming that efficiently computes the outcome regression function. Statistical properties of the resulting I2DR are established when the outcome regression function is either a piecewise or continuous function over the treatment space. We further develop a procedure to infer the mean outcome under the (estimated) optimal policy. Extensive simulations and a real data application to a warfarin study are conducted to demonstrate the empirical validity of the proposed I2DR.

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arXiv2023

Value Enhancement of Reinforcement Learning via Efficient and Robust Trust Region Optimization

Reinforcement learning (RL) is a powerful machine learning technique that enables an intelligent agent to learn an optimal policy that maximizes the cumulative rewards in sequential decision making. Most of methods in the existing literature are developed in \textit{online} settings where the data are easy to collect or simulate. Motivated by high stake domains such as mobile health studies with limited and pre-collected data, in this paper, we study \textit{offline} reinforcement learning methods. To efficiently use these datasets for policy optimization, we propose a novel value enhancement method to improve the performance of a given initial policy computed by existing state-of-the-art RL algorithms. Specifically, when the initial policy is not consistent, our method will output a policy whose value is no worse and often better than that of the initial policy. When the initial policy is consistent, under some mild conditions, our method will yield a policy whose value converges to the optimal one at a faster rate than the initial policy, achieving the desired ``value enhancement" property. The proposed method is generally applicable to any parametrized policy that belongs to certain pre-specified function class (e.g., deep neural networks). Extensive numerical studies are conducted to demonstrate the superior performance of our method.

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arXiv2023

Deep Spectral Q-learning with Application to Mobile Health

Dynamic treatment regimes assign personalized treatments to patients sequentially over time based on their baseline information and time-varying covariates. In mobile health applications, these covariates are typically collected at different frequencies over a long time horizon. In this paper, we propose a deep spectral Q-learning algorithm, which integrates principal component analysis (PCA) with deep Q-learning to handle the mixed frequency data. In theory, we prove that the mean return under the estimated optimal policy converges to that under the optimal one and establish its rate of convergence. The usefulness of our proposal is further illustrated via simulations and an application to a diabetes dataset.

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arXiv2022

Quantile Off-Policy Evaluation via Deep Conditional Generative Learning

Off-Policy evaluation (OPE) is concerned with evaluating a new target policy using offline data generated by a potentially different behavior policy. It is critical in a number of sequential decision making problems ranging from healthcare to technology industries. Most of the work in existing literature is focused on evaluating the mean outcome of a given policy, and ignores the variability of the outcome. However, in a variety of applications, criteria other than the mean may be more sensible. For example, when the reward distribution is skewed and asymmetric, quantile-based metrics are often preferred for their robustness. In this paper, we propose a doubly-robust inference procedure for quantile OPE in sequential decision making and study its asymptotic properties. In particular, we propose utilizing state-of-the-art deep conditional generative learning methods to handle parameter-dependent nuisance function estimation. We demonstrate the advantages of this proposed estimator through both simulations and a real-world dataset from a short-video platform. In particular, we find that our proposed estimator outperforms classical OPE estimators for the mean in settings with heavy-tailed reward distributions.

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arXiv2022

A Review of Off-Policy Evaluation in Reinforcement Learning

Reinforcement learning (RL) is one of the most vibrant research frontiers in machine learning and has been recently applied to solve a number of challenging problems. In this paper, we primarily focus on off-policy evaluation (OPE), one of the most fundamental topics in RL. In recent years, a number of OPE methods have been developed in the statistics and computer science literature. We provide a discussion on the efficiency bound of OPE, some of the existing state-of-the-art OPE methods, their statistical properties and some other related research directions that are currently actively explored.

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arXiv2022

Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process

This paper is concerned with constructing a confidence interval for a target policy's value offline based on a pre-collected observational data in infinite horizon settings. Most of the existing works assume no unmeasured variables exist that confound the observed actions. This assumption, however, is likely to be violated in real applications such as healthcare and technological industries. In this paper, we show that with some auxiliary variables that mediate the effect of actions on the system dynamics, the target policy's value is identifiable in a confounded Markov decision process. Based on this result, we develop an efficient off-policy value estimator that is robust to potential model misspecification and provide rigorous uncertainty quantification. Our method is justified by theoretical results, simulated and real datasets obtained from ridesharing companies. A Python implementation of the proposed procedure is available at https://github.com/Mamba413/cope.

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arXiv2022

Dynamic Causal Effects Evaluation in A/B Testing with a Reinforcement Learning Framework

A/B testing, or online experiment is a standard business strategy to compare a new product with an old one in pharmaceutical, technological, and traditional industries. Major challenges arise in online experiments of two-sided marketplace platforms (e.g., Uber) where there is only one unit that receives a sequence of treatments over time. In those experiments, the treatment at a given time impacts current outcome as well as future outcomes. The aim of this paper is to introduce a reinforcement learning framework for carrying A/B testing in these experiments, while characterizing the long-term treatment effects. Our proposed testing procedure allows for sequential monitoring and online updating. It is generally applicable to a variety of treatment designs in different industries. In addition, we systematically investigate the theoretical properties (e.g., size and power) of our testing procedure. Finally, we apply our framework to both simulated data and a real-world data example obtained from a technological company to illustrate its advantage over the current practice. A Python implementation of our test is available at https://github.com/callmespring/CausalRL.

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arXiv2022

Sure Screening for Transelliptical Graphical Models

We propose a sure screening approach for recovering the structure of a transelliptical graphical model in the high dimensional setting. We estimate the partial correlation graph by thresholding the elements of an estimator of the sample correlation matrix obtained using Kendall's tau statistic. Under a simple assumption on the relationship between the correlation and partial correlation graphs, we show that with high probability, the estimated edge set contains the true edge set, and the size of the estimated edge set is controlled. We develop a threshold value that allows for control of the expected false positive rate. In simulation and on an equities data set, we show that transelliptical graphical sure screening performs quite competitively with more computationally demanding techniques for graph estimation.

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