arXiv subjects

Zhengling Qi

Publications and source records attributed to Zhengling Qi.

At least 37 records · Page 2Linked to original sources

arXiv2025

Reinforcement Learning with Continuous Actions Under Unmeasured Confounding

This paper addresses the challenge of offline policy learning in reinforcement learning with continuous action spaces when unmeasured confounders are present. While most existing research focuses on policy evaluation within partially observable Markov decision processes (POMDPs) and assumes discrete action spaces, we advance this field by establishing a novel identification result to enable the nonparametric estimation of policy value for a given target policy under an infinite-horizon framework. Leveraging this identification, we develop a minimax estimator and introduce a policy-gradient-based algorithm to identify the in-class optimal policy that maximizes the estimated policy value. Furthermore, we provide theoretical results regarding the consistency, finite-sample error bound, and regret bound of the resulting optimal policy. Extensive simulations and a real-world application using the German Family Panel data demonstrate the effectiveness of our proposed methodology.

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arXiv2025

Distributional Off-policy Evaluation with Bellman Residual Minimization

We study distributional off-policy evaluation (OPE), of which the goal is to learn the distribution of the return for a target policy using offline data generated by a different policy. The theoretical foundation of many existing work relies on the supremum-extended statistical distances such as supremum-Wasserstein distance, which are hard to estimate. In contrast, we study the more manageable expectation-extended statistical distances and provide a novel theoretical justification on their validity for learning the return distribution. Based on this attractive property, we propose a new method called Energy Bellman Residual Minimizer (EBRM) for distributional OPE. We provide corresponding in-depth theoretical analyses. We establish a finite-sample error bound for the EBRM estimator under the realizability assumption. Furthermore, we introduce a variant of our method based on a multi-step extension which improves the error bound for non-realizable settings. Notably, unlike prior distributional OPE methods, the theoretical guarantees of our method do not require the completeness assumption.

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arXiv2024

Two-way Deconfounder for Off-policy Evaluation in Causal Reinforcement Learning

This paper studies off-policy evaluation (OPE) in the presence of unmeasured confounders. Inspired by the two-way fixed effects regression model widely used in the panel data literature, we propose a two-way unmeasured confounding assumption to model the system dynamics in causal reinforcement learning and develop a two-way deconfounder algorithm that devises a neural tensor network to simultaneously learn both the unmeasured confounders and the system dynamics, based on which a model-based estimator can be constructed for consistent policy value estimation. We illustrate the effectiveness of the proposed estimator through theoretical results and numerical experiments.

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arXiv2024

Off-policy Evaluation in Doubly Inhomogeneous Environments

This work aims to study off-policy evaluation (OPE) under scenarios where two key reinforcement learning (RL) assumptions -- temporal stationarity and individual homogeneity are both violated. To handle the ``double inhomogeneities", we propose a class of latent factor models for the reward and observation transition functions, under which we develop a general OPE framework that consists of both model-based and model-free approaches. To our knowledge, this is the first paper that develops statistically sound OPE methods in offline RL with double inhomogeneities. It contributes to a deeper understanding of OPE in environments, where standard RL assumptions are not met, and provides several practical approaches in these settings. We establish the theoretical properties of the proposed value estimators and empirically show that our approach outperforms competing methods that ignore either temporal nonstationarity or individual heterogeneity. Finally, we illustrate our method on a data set from the Medical Information Mart for Intensive Care.

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arXiv2024

Sequential Knockoffs for Variable Selection in Reinforcement Learning

In real-world applications of reinforcement learning, it is often challenging to obtain a state representation that is parsimonious and satisfies the Markov property without prior knowledge. Consequently, it is common practice to construct a state larger than necessary, e.g., by concatenating measurements over contiguous time points. However, needlessly increasing the dimension of the state may slow learning and obfuscate the learned policy. We introduce the notion of a minimal sufficient state in a Markov decision process (MDP) as the subvector of the original state under which the process remains an MDP and shares the same reward function as the original process. We propose a novel SEquEntial Knockoffs (SEEK) algorithm that estimates the minimal sufficient state in a system with high-dimensional complex nonlinear dynamics. In large samples, the proposed method achieves selection consistency. As the method is agnostic to the reinforcement learning algorithm being applied, it benefits downstream tasks such as policy learning. Empirical experiments verify theoretical results and show the proposed approach outperforms several competing methods regarding variable selection accuracy and regret.

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arXiv2024

STEEL: Singularity-aware Reinforcement Learning

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.

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arXiv2024

A Fine-grained Analysis of Fitted Q-evaluation: Beyond Parametric Models

In this paper, we delve into the statistical analysis of the fitted Q-evaluation (FQE) method, which focuses on estimating the value of a target policy using offline data generated by some behavior policy. We provide a comprehensive theoretical understanding of FQE estimators under both parameteric and nonparametric models on the $Q$-function. Specifically, we address three key questions related to FQE that remain largely unexplored in the current literature: (1) Is the optimal convergence rate for estimating the policy value regarding the sample size $n$ ($n^{-1/2}$) achievable for FQE under a non-parametric model with a fixed horizon ($T$)? (2) How does the error bound depend on the horizon $T$? (3) What is the role of the probability ratio function in improving the convergence of FQE estimators? Specifically, we show that under the completeness assumption of $Q$-functions, which is mild in the non-parametric setting, the estimation errors for policy value using both parametric and non-parametric FQE estimators can achieve an optimal rate in terms of $n$. The corresponding error bounds in terms of both $n$ and $T$ are also established. With an additional realizability assumption on ratio functions, the rate of estimation errors can be improved from $T^{1.5}/\sqrt{n}$ to $T/\sqrt{n}$, which matches the sharpest known bound in the current literature under the tabular setting.

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arXiv2024

Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach

We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we propose a tail-adaptive method for change point detection and estimation. We use a weighted combination of composite quantile and least squared losses to build a new loss function, allowing us to leverage information from both conditional means and quantiles. For change point testing, we develop a family of individual testing statistics with different weights to account for unknown tail structures. These individual tests are further aggregated to construct a powerful tail-adaptive test for sparse regression coefficient changes. For change point estimation, we propose a family of argmax-based individual estimators. We provide theoretical justifications for the validity of these tests and change point estimators. Additionally, we introduce a new algorithm for detecting multiple change points in a tail-adaptive manner using the wild binary segmentation. Extensive numerical results show the effectiveness of our method. Lastly, an R package called ``TailAdaptiveCpt" is developed to implement our algorithms.

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arXiv2024

Robust Offline Reinforcement learning with Heavy-Tailed Rewards

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.

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arXiv2023

A Policy Gradient Method for Confounded POMDPs

In this paper, we propose a policy gradient method for confounded partially observable Markov decision processes (POMDPs) with continuous state and observation spaces in the offline setting. We first establish a novel identification result to non-parametrically estimate any history-dependent policy gradient under POMDPs using the offline data. The identification enables us to solve a sequence of conditional moment restrictions and adopt the min-max learning procedure with general function approximation for estimating the policy gradient. We then provide a finite-sample non-asymptotic bound for estimating the gradient uniformly over a pre-specified policy class in terms of the sample size, length of horizon, concentratability coefficient and the measure of ill-posedness in solving the conditional moment restrictions. Lastly, by deploying the proposed gradient estimation in the gradient ascent algorithm, we show the global convergence of the proposed algorithm in finding the history-dependent optimal policy under some technical conditions. To the best of our knowledge, this is the first work studying the policy gradient method for POMDPs under the offline setting.

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arXiv2023

Personalized Pricing with Invalid Instrumental Variables: Identification, Estimation, and Policy Learning

Pricing based on individual customer characteristics is widely used to maximize sellers' revenues. This work studies offline personalized pricing under endogeneity using an instrumental variable approach. Standard instrumental variable methods in causal inference/econometrics either focus on a discrete treatment space or require the exclusion restriction of instruments from having a direct effect on the outcome, which limits their applicability in personalized pricing. In this paper, we propose a new policy learning method for Personalized pRicing using Invalid iNsTrumental variables (PRINT) for continuous treatment that allow direct effects on the outcome. Specifically, relying on the structural models of revenue and price, we establish the identifiability condition of an optimal pricing strategy under endogeneity with the help of invalid instrumental variables. Based on this new identification, which leads to solving conditional moment restrictions with generalized residual functions, we construct an adversarial min-max estimator and learn an optimal pricing strategy. Furthermore, we establish an asymptotic regret bound to find an optimal pricing strategy. Finally, we demonstrate the effectiveness of the proposed method via extensive simulation studies as well as a real data application from an US online auto loan company.

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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

PASTA: Pessimistic Assortment Optimization

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

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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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arXiv2022

Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding

Data-driven individualized decision making has recently received increasing research interests. Most existing methods rely on the assumption of no unmeasured confounding, which unfortunately cannot be ensured in practice especially in observational studies. Motivated by the recent proposed proximal causal inference, we develop several proximal learning approaches to estimating optimal individualized treatment regimes (ITRs) in the presence of unmeasured confounding. In particular, we establish several identification results for different classes of ITRs, exhibiting the trade-off between the risk of making untestable assumptions and the value function improvement in decision making. Based on these results, we propose several classification-based approaches to finding a variety of restricted in-class optimal ITRs and develop their theoretical properties. The appealing numerical performance of our proposed methods is demonstrated via an extensive simulation study and one real data application.

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arXiv2022

Offline Reinforcement Learning for Human-Guided Human-Machine Interaction with Private Information

Motivated by the human-machine interaction such as training chatbots for improving customer satisfaction, we study human-guided human-machine interaction involving private information. We model this interaction as a two-player turn-based game, where one player (Alice, a human) guides the other player (Bob, a machine) towards a common goal. Specifically, we focus on offline reinforcement learning (RL) in this game, where the goal is to find a policy pair for Alice and Bob that maximizes their expected total rewards based on an offline dataset collected a priori. The offline setting presents two challenges: (i) We cannot collect Bob's private information, leading to a confounding bias when using standard RL methods, and (ii) a distributional mismatch between the behavior policy used to collect data and the desired policy we aim to learn. To tackle the confounding bias, we treat Bob's previous action as an instrumental variable for Alice's current decision making so as to adjust for the unmeasured confounding. We develop a novel identification result and use it to propose a new off-policy evaluation (OPE) method for evaluating policy pairs in this two-player turn-based game. To tackle the distributional mismatch, we leverage the idea of pessimism and use our OPE method to develop an off-policy learning algorithm for finding a desirable policy pair for both Alice and Bob. Finally, we prove that under mild assumptions such as partial coverage of the offline data, the policy pair obtained through our method converges to the optimal one at a satisfactory rate.

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arXiv2022

RISE: Robust Individualized Decision Learning with Sensitive Variables

This paper introduces RISE, a robust individualized decision learning framework with sensitive variables, where sensitive variables are collectible data and important to the intervention decision, but their inclusion in decision making is prohibited due to reasons such as delayed availability or fairness concerns. A naive baseline is to ignore these sensitive variables in learning decision rules, leading to significant uncertainty and bias. To address this, we propose a decision learning framework to incorporate sensitive variables during offline training but not include them in the input of the learned decision rule during model deployment. Specifically, from a causal perspective, the proposed framework intends to improve the worst-case outcomes of individuals caused by sensitive variables that are unavailable at the time of decision. Unlike most existing literature that uses mean-optimal objectives, we propose a robust learning framework by finding a newly defined quantile- or infimum-optimal decision rule. The reliable performance of the proposed method is demonstrated through synthetic experiments and three real-world applications.

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arXiv2022

Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Models

We study the problem of off-policy evaluation (OPE) for episodic Partially Observable Markov Decision Processes (POMDPs) with continuous states. Motivated by the recently proposed proximal causal inference framework, we develop a non-parametric identification result for estimating the policy value via a sequence of so-called V-bridge functions with the help of time-dependent proxy variables. We then develop a fitted-Q-evaluation-type algorithm to estimate V-bridge functions recursively, where a non-parametric instrumental variable (NPIV) problem is solved at each step. By analyzing this challenging sequential NPIV problem, we establish the finite-sample error bounds for estimating the V-bridge functions and accordingly that for evaluating the policy value, in terms of the sample size, length of horizon and so-called (local) measure of ill-posedness at each step. To the best of our knowledge, this is the first finite-sample error bound for OPE in POMDPs under non-parametric models.

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