Causal inference explores the causation between actions and the consequent rewards on a covariate set. Recently deep learning has achieved a remarkable performance in causal inference, but existing statistical theories cannot well explain such an empirical success, especially when the covariates are high-dimensional. Most theoretical results in causal inference are asymptotic, suffer from the curse of dimensionality, and only work for the finite-action scenario. To bridge such a gap between theory and practice, this paper studies doubly robust off-policy learning by deep neural networks. When the covariates lie on a low-dimensional manifold, we prove nonasymptotic regret bounds, which converge at a fast rate depending on the intrinsic dimension of the manifold. Our results cover both the finite- and continuous-action scenarios. Our theory shows that deep neural networks are adaptive to the low-dimensional geometric structures of the covariates, and partially explains the success of deep learning for causal inference.
Adaptive experiments, including efficient average treatment effect estimation and multi-armed bandit algorithms, have garnered attention in various applications, such as social experiments, clinical trials, and online advertisement optimization. This paper considers estimating the mean outcome of an action from samples obtained in adaptive experiments. In causal inference, the mean outcome of an action has a crucial role, and the estimation is an essential task, where the average treatment effect estimation and off-policy value estimation are its variants. In adaptive experiments, the probabil…
We study the problem of off-policy critic evaluation in several variants of value-based off-policy actor-critic algorithms. Off-policy actor-critic algorithms require an off-policy critic evaluation step, to estimate the value of the new policy after every policy gradient update. Despite enormous success of off-policy policy gradients on control tasks, existing general methods suffer from high variance and instability, partly because the policy improvement depends on gradient of the estimated value function. In this work, we present a new way of off-policy policy evaluation in actor-critic, ba…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We show that on-policy policy gradient (PG) and its variance reduction variants can be derived by taking finite difference of function evaluations supplied by estimators from the importance sampling (IS) family for off-policy evaluation (OPE). Starting from the doubly robust (DR) estimator (Jiang & Li, 2016), we provide a simple derivation of a very general and flexible form of PG, which subsumes the state-of-the-art variance reduction technique (Cheng et al., 2019) as its special case and immediately hints at further variance reduction opportunities overlooked by existing literature. We analy…
We propose a new framework for designing estimators for off-policy evaluation in contextual bandits. Our approach is based on the asymptotically optimal doubly robust estimator, but we shrink the importance weights to minimize a bound on the mean squared error, which results in a better bias-variance tradeoff in finite samples. We use this optimization-based framework to obtain three estimators: (a) a weight-clipping estimator, (b) a new weight-shrinkage estimator, and (c) the first shrinkage-based estimator for combinatorial action sets. Extensive experiments in both standard and combinatoria…
The Ohio State University（俄亥俄州立大学）；Princeton University（普林斯顿大学）；Northwestern University（西北大学）
Designing off-policy reinforcement learning algorithms is typically a very challenging task, because a desirable iteration update often involves an expectation over an on-policy distribution. Prior off-policy actor-critic (AC) algorithms have introduced a new critic that uses the density ratio for adjusting the distribution mismatch in order to stabilize the convergence, but at the cost of potentially introducing high biases due to the estimation errors of both the density ratio and value function. In this paper, we develop a doubly robust off-policy AC (DR-Off-PAC) for discounted MDP, which c…
Offline reinforcement learning, wherein one uses off-policy data logged by a fixed behavior policy to evaluate and learn new policies, is crucial in applications where experimentation is limited such as medicine. We study the estimation of policy value and gradient of a deterministic policy from off-policy data when actions are continuous. Targeting deterministic policies, for which action is a deterministic function of state, is crucial since optimal policies are always deterministic (up to ties). In this setting, standard importance sampling and doubly robust estimators for policy value and …
We present a new approach to the problems of evaluating and learning personalized decision policies from observational data of past contexts, decisions, and outcomes. Only the outcome of the enacted decision is available and the historical policy is unknown. These problems arise in personalized medicine using electronic health records and in internet advertising. Existing approaches use inverse propensity weighting (or, doubly robust versions) to make historical outcome (or, residual) data look like it were generated by a new policy being evaluated or learned. But this relies on a plug-in appr…
In many areas, practitioners seek to use observational data to learn a treatment assignment policy that satisfies application-specific constraints, such as budget, fairness, simplicity, or other functional form constraints. For example, policies may be restricted to take the form of decision trees based on a limited set of easily observable individual characteristics. We propose a new approach to this problem motivated by the theory of semiparametrically efficient estimation. Our method can be used to optimize either binary treatments or infinitesimal nudges to continuous treatments, and can l…
Randomized trials, also known as A/B tests, are used to select between two policies: a control and a treatment. Given a corresponding set of features, we can ideally learn an optimized policy P that maps the A/B test data features to action space and optimizes reward. However, although A/B testing provides an unbiased estimator for the value of deploying B (i.e., switching from policy A to B), direct application of those samples to learn the the optimized policy P generally does not provide an unbiased estimator of the value of P as the samples were observed when constructing P. In situations …
The doubly robust (DR) estimator, which consists of two nuisance parameters, the conditional mean outcome and the logging policy (the probability of choosing an action), is crucial in causal inference. This paper proposes a DR estimator for dependent samples obtained from adaptive experiments. To obtain an asymptotically normal semiparametric estimator from dependent samples with non-Donsker nuisance estimators, we propose adaptive-fitting as a variant of sample-splitting. We also report an empirical paradox that our proposed DR estimator tends to show better performances compared to other est…
University of Texas at Austin（得克萨斯大学奥斯汀分校）；Google Research（谷歌研究院）
Infinite horizon off-policy policy evaluation is a highly challenging task due to the excessively large variance of typical importance sampling (IS) estimators. Recently, Liu et al. (2018a) proposed an approach that significantly reduces the variance of infinite-horizon off-policy evaluation by estimating the stationary density ratio, but at the cost of introducing potentially high biases due to the error in density ratio estimation. In this paper, we develop a bias-reduced augmentation of their method, which can take advantage of a learned value function to obtain higher accuracy. Our method …
We study decision making in environments where the reward is only partially observed, but can be modeled as a function of an action and an observed context. This setting, known as contextual bandits, encompasses a wide variety of applications including health-care policy and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previous approaches rely either on models of rewards or m…
Tokyo Institute of Technology（东京工业大学）；Cornell University（康奈尔大学）；Yahoo Japan Corporation（雅虎日本公司）；Yale University（耶鲁大学）
In real-world recommender systems and search engines, optimizing ranking decisions to present a ranked list of relevant items is critical. Off-policy evaluation (OPE) for ranking policies is thus gaining a growing interest because it enables performance estimation of new ranking policies using only logged data. Although OPE in contextual bandits has been studied extensively, its naive application to the ranking setting faces a critical variance issue due to the huge item space. To tackle this problem, previous studies introduce some assumptions on user behavior to make the combinatorial item s…
Policy interventions can spill over to units of a population that are not directly exposed to the policy but are geographically close to the units receiving the intervention. In recent work, investigations of spillover effects on neighboring regions have focused on estimating the average treatment effect of a particular policy in an observed setting. Our research question broadens this scope by asking what policy consequences would the treated units have experienced under hypothetical exposure settings. When we only observe treated unit(s) surrounded by controls -- as is common when a policy i…
When evaluating the effectiveness of a treatment, policy, or intervention, the desired measure of effectiveness may be expensive to collect, not routinely available, or may take a long time to occur. In these cases, it is sometimes possible to identify a surrogate outcome that can more easily/quickly/cheaply capture the effect of interest. Theory and methods for evaluating the strength of surrogate markers have been well studied in the context of a single surrogate marker measured in the course of a randomized clinical study. However, methods are lacking for quantifying the utility of surrogat…
Cornell University（康奈尔大学）；Cornell Tech（康奈尔科技校区）；Tsinghua University（清华大学）；Arena Technologies（Arena科技公司）；New York University（纽约大学）
Off-policy evaluation and learning (OPE/L) use offline observational data to make better decisions, which is crucial in applications where online experimentation is limited. However, depending entirely on logged data, OPE/L is sensitive to environment distribution shifts -- discrepancies between the data-generating environment and that where policies are deployed. \citet{si2020distributional} proposed distributionally robust OPE/L (DROPE/L) to address this, but the proposal relies on inverse-propensity weighting, whose estimation error and regret will deteriorate if propensities are nonparamet…
Department of Statistics（统计系）；LSE London, UK（伦敦大学学院）；Department of Mathematics（数学系）；Tsinghua University（清华大学）；School of Design LCC, UAL London, UK（伦敦艺术大学设计学院）；Department of Engineering Science（工程科学系）；University of Oxford（牛津大学）
Are Good Generators Good Decision-Makers? Policy Learning for General Interventions via Retargeted Counterfactual Generation
Cornell Tech（康奈尔科技）；Cornell University（康奈尔大学）；Department of Biostatistics, Department of Population Health（生物统计学系、人口健康系）；New York University Grossman School of Medicine（纽约大学格罗斯曼医学院）
Amazon Web Services（亚马逊云科技）；University of Pennsylvania（宾夕法尼亚大学）
Reliant on too many experiments to learn good actions, current Reinforcement Learning (RL) algorithms have limited applicability in real-world settings, which can be too expensive to allow exploration. We propose an algorithm for batch RL, where effective policies are learned using only a fixed offline dataset instead of online interactions with the environment. The limited data in batch RL produces inherent uncertainty in value estimates of states/actions that were insufficiently represented in the training data. This leads to particularly severe extrapolation when our candidate policies dive…
We propose a robust regression approach to off-policy evaluation (OPE) for contextual bandits. We frame OPE as a covariate-shift problem and leverage modern robust regression tools. Ours is a general approach that can be used to augment any existing OPE method that utilizes the direct method. When augmenting doubly robust methods, we call the resulting method Triply Robust. We prove upper bounds on the resulting bias and variance, as well as derive novel minimax bounds based on robust minimax analysis for covariate shift. Our robust regression method is compatible with deep learning, and is th…
Columbia IEOR and DSI（哥伦比亚大学工业工程与运筹学系和数据科学研究所）；USC Marshall（南加州大学马歇尔商学院）；Columbia IEOR（哥伦比亚大学工业工程与运筹学系）
We consider a personalized pricing problem in which we have data consisting of feature information, historical pricing decisions, and binary realized demand. The goal is to perform off-policy evaluation for a new personalized pricing policy that maps features to prices. Methods based on inverse propensity weighting (including doubly robust methods) for off-policy evaluation may perform poorly when the logging policy has little exploration or is deterministic, which is common in pricing applications. Building on the balanced policy evaluation framework of Kallus (2018), we propose a new approac…
Even when unable to run experiments, practitioners can evaluate prospective policies, using previously logged data. However, while the bandits literature has adopted a diverse set of objectives, most research on off-policy evaluation to date focuses on the expected reward. In this paper, we introduce Lipschitz risk functionals, a broad class of objectives that subsumes conditional value-at-risk (CVaR), variance, mean-variance, many distorted risks, and CPT risks, among others. We propose Off-Policy Risk Assessment (OPRA), a framework that first estimates a target policy's CDF and then generate…
We study the off-policy evaluation problem---estimating the value of a target policy using data collected by another policy---under the contextual bandit model. We consider the general (agnostic) setting without access to a consistent model of rewards and establish a minimax lower bound on the mean squared error (MSE). The bound is matched up to constants by the inverse propensity scoring (IPS) and doubly robust (DR) estimators. This highlights the difficulty of the agnostic contextual setting, in contrast with multi-armed bandits and contextual bandits with access to a consistent reward model…
London School of Economics and Political Science（伦敦政治经济学院）；Cornell University（康奈尔大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes (POMDPs), where the evaluation policy depends only on observable variables and the behavior policy depends on unobservable latent variables. Existing works either assume no unmeasured confounders, or focus on settings where both the observation and the state spaces are tabular. In this work, we first propose novel identification methods for OPE in POMDPs with latent confounders, by introducing bridge functions that link the target policy's value and the observed data distribution. We next propose minimax …
Harvard University（哈佛大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We provide theoretical investigations into off-policy evaluation in reinforcement learning using function approximators for (marginalized) importance weights and value functions. Our contributions include: (1) A new estimator, MWL, that directly estimates importance ratios over the state-action distributions, removing the reliance on knowledge of the behavior policy as in prior work (Liu et al., 2018). (2) Another new estimator, MQL, obtained by swapping the roles of importance weights and value-functions in MWL. MQL has an intuitive interpretation of minimizing average Bellman errors and can …
Off-policy evaluation (OPE) in both contextual bandits and reinforcement learning allows one to evaluate novel decision policies without needing to conduct exploration, which is often costly or otherwise infeasible. The problem's importance has attracted many proposed solutions, including importance sampling (IS), self-normalized IS (SNIS), and doubly robust (DR) estimates. DR and its variants ensure semiparametric local efficiency if Q-functions are well-specified, but if they are not they can be worse than both IS and SNIS. It also does not enjoy SNIS's inherent stability and boundedness. We…
Cornell University（康奈尔大学）；Cornell TRIPODS Center for Data Science（康奈尔大学TRIPODS数据科学中心）
The ability to perform offline A/B-testing and off-policy learning using logged contextual bandit feedback is highly desirable in a broad range of applications, including recommender systems, search engines, ad placement, and personalized health care. Both offline A/B-testing and off-policy learning require a counterfactual estimator that evaluates how some new policy would have performed, if it had been used instead of the logging policy. In this paper, we identify a family of counterfactual estimators which subsumes most such estimators proposed to date. Our analysis of this family identifie…
We study off-policy evaluation and learning from sequential data in a structured class of Markov decision processes that arise from repeated interactions with an exogenous sequence of arrivals with contexts, which generate unknown individual-level responses to agent actions. This model can be thought of as an offline generalization of contextual bandits with resource constraints. We formalize the relevant causal structure of problems such as dynamic personalized pricing and other operations management problems in the presence of potentially high-dimensional user types. The key insight is that …
North Carolina State University（北卡罗来纳州立大学）；London School of Economics and Political Science（伦敦政治经济学院）；ByteDance（字节跳动）；University of Miami（迈阿密大学）
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 ofte…
Cost-optimal Sequential Testing via Doubly Robust Q-learning
Department of Statistics and Data Science, National University of Singapore（国立新加坡大学统计与数据科学系）；Public Health Sciences Division, Fred Hutch（Fred Hutch公共卫生科学系）；Department of Biomedical Data Science, Stanford University School of Medicine（斯坦福大学医学院生物医学数据科学系）；Department of Biostatistics, Harvard T.H. Chan School of Public Health（哈佛大学T.H. Chan公共卫生学院生物统计学系）
Stony Brook University（石溪大学）；Princeton University（普林斯顿大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Northwestern University（西北大学）
This paper extends off-policy reinforcement learning to the multi-agent case in which a set of networked agents communicating with their neighbors according to a time-varying graph collaboratively evaluates and improves a target policy while following a distinct behavior policy. To this end, the paper develops a multi-agent version of emphatic temporal difference learning for off-policy policy evaluation, and proves convergence under linear function approximation. The paper then leverages this result, in conjunction with a novel multi-agent off-policy policy gradient theorem and recent work in…
In this paper we present a new way of predicting the performance of a reinforcement learning policy given historical data that may have been generated by a different policy. The ability to evaluate a policy from historical data is important for applications where the deployment of a bad policy can be dangerous or costly. We show empirically that our algorithm produces estimates that often have orders of magnitude lower mean squared error than existing methods---it makes more efficient use of the available data. Our new estimator is based on two advances: an extension of the doubly robust estim…
On-policy reinforcement learning (RL) algorithms have high sample complexity while off-policy algorithms are difficult to tune. Merging the two holds the promise to develop efficient algorithms that generalize across diverse environments. It is however challenging in practice to find suitable hyper-parameters that govern this trade off. This paper develops a simple algorithm named P3O that interleaves off-policy updates with on-policy updates. P3O uses the effective sample size between the behavior policy and the target policy to control how far they can be from each other and does not introdu…
Auburn University（奥本大学）；University of Iowa（爱荷华大学）；Facebook AI Research（Facebook 人工智能研究院）；Huawei Inc.（华为公司）
Off-policy policy optimization is a challenging problem in reinforcement learning (RL). The algorithms designed for this problem often suffer from high variance in their estimators, which results in poor sample efficiency, and have issues with convergence. A few variance-reduced on-policy policy gradient algorithms have been recently proposed that use methods from stochastic optimization to reduce the variance of the gradient estimate in the REINFORCE algorithm. However, these algorithms are not designed for the off-policy setting and are memory-inefficient, since they need to collect and stor…
