我们研究了一个定价设置，其中每个客户都基于客户和/或产品特征提供了一种预测客户对该产品的估值的产品特征。通常只有历史销售记录，我们遵守每个客户是否以规定的价格购买产品，而不是客户的真实估值。因此，数据受到历史销售政策的影响，历史销售政策在没有进行实际实验的可能性的情况下估算未来损失/遗憾的困难/遗憾的损失/遗憾，而是优化诸如收入管理等下游任务的新政策。我们研究如何制定损失功能，该功能可用于直接优化定价策略，而不是通过中间需求估计阶段，这可能在实践中被偏见，因为模型拼写，正常化或校准差。虽然在估值数据可用时提出了现有方法，但我们提出了观察数据设置的损失函数。为实现这一目标，我们将机器学习的想法适应损坏的标签，我们可以考虑每个观察到的客户的结果（购买或不按规定的价格购买），作为客户估值的（已知）概率转变。从这种转变，我们派生了一类合适的无偏损失功能。在此类中，我们识别最小方差估计器，那些对不良需求函数估计的稳健性，并在估计的需求功能有用时提供指导。此外，我们还表明，当应用于我们的上下文定价环境时，在违规评估文学中流行的估计人员在这类损失职能范围内，并且当每个估算师在实践中可能表现良好时，还提供管理层。

与传统的监督学习不同，在许多设置中，只有部分反馈。我们只能遵守所选行动的结果，但不是与其他替代方案相关的反事成员。此类环境包括各种应用，包括定价，在线营销和精密药。关键挑战是观察数据受到系统部署的历史政策的影响，产生了偏置数据分布。我们将此任务作为域适应问题，提出了一种自我训练算法，其在观察数据中为有限的未经验证行动的分类值释放结果，以模拟通过伪标记的随机试验，我们称之为反事实自我训练（CST） 。 CST迭代地赋予伪标签并检测模型。此外，我们显示输入一致性损失可以进一步提高CST性能，这是近伪标签的理论分析中所示的。我们展示了合成和实时数据集在合成和实际数据集上的提出算法的有效性。

在上下文土匪中，非政策评估（OPE）已在现实世界中迅速采用，因为它仅使用历史日志数据就可以离线评估新政策。不幸的是，当动作数量较大时，现有的OPE估计器（其中大多数是基于反相反的得分加权）会严重降解，并且可能会遭受极端偏见和差异。这挫败了从推荐系统到语言模型的许多应用程序中使用OPE。为了克服这个问题，我们提出了一个新的OPE估计器，即当动作嵌入在动作空间中提供结构时，利用边缘化的重要性权重。我们表征了所提出的估计器的偏差，方差和平方平方误差，并分析了动作嵌入提供了比常规估计器提供统计益处的条件。除了理论分析外，我们还发现，即使由于大量作用，现有估计量崩溃，经验性绩效的改善也可以实现可靠的OPE。

我们探索了一个新的强盗实验模型，其中潜在的非组织序列会影响武器的性能。上下文 - 统一算法可能会混淆，而那些执行正确的推理面部信息延迟的算法。我们的主要见解是，我们称之为Deconfounst Thompson采样的算法在适应性和健壮性之间取得了微妙的平衡。它的适应性在易于固定实例中带来了最佳效率，但是在硬性非平稳性方面显示出令人惊讶的弹性，这会导致其他自适应算法失败。

We consider the problem of dynamic pricing of a product in the presence of feature-dependent price sensitivity. Developing practical algorithms that can estimate price elasticities robustly, especially when information about no purchases (losses) is not available, to drive such automated pricing systems is a challenge faced by many industries. Based on the Poisson semi-parametric approach, we construct a flexible yet interpretable demand model where the price related part is parametric while the remaining (nuisance) part of the model is non-parametric and can be modeled via sophisticated machine learning (ML) techniques. The estimation of price-sensitivity parameters of this model via direct one-stage regression techniques may lead to biased estimates due to regularization. To address this concern, we propose a two-stage estimation methodology which makes the estimation of the price-sensitivity parameters robust to biases in the estimators of the nuisance parameters of the model. In the first-stage we construct estimators of observed purchases and prices given the feature vector using sophisticated ML estimators such as deep neural networks. Utilizing the estimators from the first-stage, in the second-stage we leverage a Bayesian dynamic generalized linear model to estimate the price-sensitivity parameters. We test the performance of the proposed estimation schemes on simulated and real sales transaction data from the Airline industry. Our numerical studies demonstrate that our proposed two-stage approach reduces the estimation error in price-sensitivity parameters from 25\% to 4\% in realistic simulation settings. The two-stage estimation techniques proposed in this work allows practitioners to leverage modern ML techniques to robustly estimate price-sensitivities while still maintaining interpretability and allowing ease of validation of its various constituent parts.

使用历史观察数据的政策学习是发现广泛应用程序的重要问题。示例包括选择优惠，价格，要发送给客户的广告，以及选择要开出患者的药物。但是，现有的文献取决于这样一个关键假设，即将在未来部署学习策略的未来环境与生成数据的过去环境相同 - 这个假设通常是错误或太粗糙的近似值。在本文中，我们提高了这一假设，并旨在通过不完整的观察数据来学习一项稳健的策略。我们首先提出了一个政策评估程序，该程序使我们能够评估政策在最坏情况下的转变下的表现。然后，我们为此建议的政策评估计划建立了中心限制定理类型保证。利用这种评估方案，我们进一步提出了一种新颖的学习算法，该算法能够学习一项对对抗性扰动和未知协变量转移的策略，并根据统一收敛理论的性能保证进行了绩效保证。最后，我们从经验上测试了合成数据集中提出的算法的有效性，并证明它提供了使用标准策略学习算法缺失的鲁棒性。我们通过在现实世界投票数据集的背景下提供了我们方法的全面应用来结束本文。

Counterfactual reasoning from logged data has become increasingly important for many applications such as web advertising or healthcare. In this paper, we address the problem of learning stochastic policies with continuous actions from the viewpoint of counterfactual risk minimization (CRM). While the CRM framework is appealing and well studied for discrete actions, the continuous action case raises new challenges about modelization, optimization, and~offline model selection with real data which turns out to be particularly challenging. Our paper contributes to these three aspects of the CRM estimation pipeline. First, we introduce a modelling strategy based on a joint kernel embedding of contexts and actions, which overcomes the shortcomings of previous discretization approaches. Second, we empirically show that the optimization aspect of counterfactual learning is important, and we demonstrate the benefits of proximal point algorithms and differentiable estimators. Finally, we propose an evaluation protocol for offline policies in real-world logged systems, which is challenging since policies cannot be replayed on test data, and we release a new large-scale dataset along with multiple synthetic, yet realistic, evaluation setups.

高质量数据在确保政策评估的准确性方面起着核心作用。本文启动了针对强盗政策评估的高效和安全数据收集的研究。我们提出问题并研究其几种代表性变体。对于每个变体，我们分析其统计属性，得出相应的勘探策略，并设计用于计算它的有效算法。理论分析和实验都支持所提出方法的有用性。

Causal inference is the process of using assumptions, study designs, and estimation strategies to draw conclusions about the causal relationships between variables based on data. This allows researchers to better understand the underlying mechanisms at work in complex systems and make more informed decisions. In many settings, we may not fully observe all the confounders that affect both the treatment and outcome variables, complicating the estimation of causal effects. To address this problem, a growing literature in both causal inference and machine learning proposes to use Instrumental Variables (IV). This paper serves as the first effort to systematically and comprehensively introduce and discuss the IV methods and their applications in both causal inference and machine learning. First, we provide the formal definition of IVs and discuss the identification problem of IV regression methods under different assumptions. Second, we categorize the existing work on IV methods into three streams according to the focus on the proposed methods, including two-stage least squares with IVs, control function with IVs, and evaluation of IVs. For each stream, we present both the classical causal inference methods, and recent developments in the machine learning literature. Then, we introduce a variety of applications of IV methods in real-world scenarios and provide a summary of the available datasets and algorithms. Finally, we summarize the literature, discuss the open problems and suggest promising future research directions for IV methods and their applications. We also develop a toolkit of IVs methods reviewed in this survey at https://github.com/causal-machine-learning-lab/mliv.

The intersection of causal inference and machine learning for decision-making is rapidly expanding, but the default decision criterion remains an \textit{average} of individual causal outcomes across a population. In practice, various operational restrictions ensure that a decision-maker's utility is not realized as an \textit{average} but rather as an \textit{output} of a downstream decision-making problem (such as matching, assignment, network flow, minimizing predictive risk). In this work, we develop a new framework for off-policy evaluation with \textit{policy-dependent} linear optimization responses: causal outcomes introduce stochasticity in objective function coefficients. Under this framework, a decision-maker's utility depends on the policy-dependent optimization, which introduces a fundamental challenge of \textit{optimization} bias even for the case of policy evaluation. We construct unbiased estimators for the policy-dependent estimand by a perturbation method, and discuss asymptotic variance properties for a set of adjusted plug-in estimators. Lastly, attaining unbiased policy evaluation allows for policy optimization: we provide a general algorithm for optimizing causal interventions. We corroborate our theoretical results with numerical simulations.

各种研究中的主要研究目标是使用观察数据集，并提供一种可以产生因果改进的新的反事准则。人动态治疗制度（DTRS）被广泛研究以正规化此过程。然而，在寻找最佳DTR中的可用方法通常依赖于现实世界应用（例如，医学决策或公共政策）违反的假设，特别是当（a）不可忽视未观察到的混乱时，并且（b）未观察到的混乱是时变（例如，受前一个行动的影响）。当违反这种假设时，人们经常面临关于所需的潜在因果模型来获得最佳DTR的歧视。这种歧义是不可避免的，因为无法从观察到的数据中理解未观察到的混血者的动态及其对观察到的数据的因果影响。通过案例研究，为在移植后接受伴随医院移植的患者的患者寻找卓越的治疗方案，并在移植后遇到称为新的发病糖尿病（NODAT），我们将DTR扩展到一个新阶级，被称为暧昧的动态治疗制度（ADTR） ，其中根据潜在因果模型的“云”评估治疗方案的随意影响。然后，我们将Adtrs连接到Saghafian（2018）提出的暧昧部分可观察标记决策过程（APOMDPS），并开发了两种加强学习方法，称为直接增强V-Learning（DAV-Learning）和安全增强V-Learning（SAV-Learning），其中使用观察到的数据能够有效地学习最佳治疗方案。我们为这些学习方法制定理论结果，包括（弱）一致性和渐近正常性。我们进一步评估了这些学习方法在案例研究和仿真实验中的性能。

This work shows how to leverage causal inference to understand the behavior of complex learning systems interacting with their environment and predict the consequences of changes to the system. Such predictions allow both humans and algorithms to select the changes that would have improved the system performance. This work is illustrated by experiments on the ad placement system associated with the Bing search engine.

Statistical risk assessments inform consequential decisions such as pretrial release in criminal justice, and loan approvals in consumer finance. Such risk assessments make counterfactual predictions, predicting the likelihood of an outcome under a proposed decision (e.g., what would happen if we approved this loan?). A central challenge, however, is that there may have been unmeasured confounders that jointly affected past decisions and outcomes in the historical data. This paper proposes a tractable mean outcome sensitivity model that bounds the extent to which unmeasured confounders could affect outcomes on average. The mean outcome sensitivity model partially identifies the conditional likelihood of the outcome under the proposed decision, popular predictive performance metrics (e.g., accuracy, calibration, TPR, FPR), and commonly-used predictive disparities. We derive their sharp identified sets, and we then solve three tasks that are essential to deploying statistical risk assessments in high-stakes settings. First, we propose a doubly-robust learning procedure for the bounds on the conditional likelihood of the outcome under the proposed decision. Second, we translate our estimated bounds on the conditional likelihood of the outcome under the proposed decision into a robust, plug-in decision-making policy. Third, we develop doubly-robust estimators of the bounds on the predictive performance of an existing risk assessment.

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.

现代纵向研究在许多时间点收集特征数据，通常是相同的样本大小顺序。这些研究通常受到{辍学}和积极违规的影响。我们通过概括近期增量干预的效果（转换倾向分数而不是设置治疗价值）来解决这些问题，以适应多种结果和主题辍学。当条件忽略（不需要治疗阳性）时，我们给出了识别表达式的增量干预效果，并导出估计这些效果的非参数效率。然后我们提出了高效的非参数估计器，表明它们以快速参数速率收敛并产生均匀的推理保证，即使在较慢的速率下灵活估计滋扰函数。我们还研究了新型无限时间范围设置中的更传统的确定性效果的增量干预效应的方差比，其中时间点的数量可以随着样本大小而生长，并显示增量干预效果在统计精度下产生近乎指数的收益这个设置。最后，我们通过模拟得出结论，并在研究低剂量阿司匹林对妊娠结果的研究中进行了方法。

通常使用参数模型进行经验领域的参数估计，并且此类模型很容易促进统计推断。不幸的是，它们不太可能足够灵活，无法充分建模现实现象，并可能产生偏见的估计。相反，非参数方法是灵活的，但不容易促进统计推断，并且仍然可能表现出残留的偏见。我们探索了影响功能（IFS）的潜力（a）改善初始估计器而无需更多数据（b）增加模型的鲁棒性和（c）促进统计推断。我们首先对IFS进行广泛的介绍，并提出了一种神经网络方法“ Multinet”，该方法使用单个体系结构寻求合奏的多样性。我们还介绍了我们称为“ Multistep”的IF更新步骤的变体，并对不同方法提供了全面的评估。发现这些改进是依赖数据集的，这表明所使用的方法与数据生成过程的性质之间存在相互作用。我们的实验强调了从业人员需要通过不同的估计器组合进行多次分析来检查其发现的一致性。我们还表明，可以改善“自由”的现有神经网络，而无需更多数据，而无需重新训练。

使用始终有效的在线统计学习程序设计动态定价政策是一个重要且尚未解决的问题。最现有的动态定价政策，重点关注所采用的客户选择模型的忠诚度，展示了在定价过程中调整学习统计模型的在线不确定性的有限能力。在本文中，我们提出了一种新颖的方法，可以使用理论担保设计基于动态定价策略的正规化在线统计学习。新方法克服了在线套索程序持续监测的挑战，并具有多种吸引人的财产。特别是，我们做出了决定性观察，即定价决策的始终有效性构建和茁壮成长在线正规方案。我们所提出的在线正则化计划将建议的乐观在线正常化最高似然定价（Oormlp）定价政策具有三大优势：将市场噪声知识编码为定价过程乐观;在线统计学习，以所有决策点的始终有效期以时间均匀的非渐近Oracle不等式信封预测误差过程。这种类型的非渐近推理结果允许我们在实践中设计更具样品有效和强大的动态定价算法。理论上，所提出的OormLP算法利用高维模型的稀疏结构，并在决策范围内确保对数后悔。通过提出一种乐观的在线套索程序，可以根据非渐近鞅浓度的新颖，提出解决过程级别的动态定价问题的乐观在线套索程序来实现这些理论前进。在实验中，我们在不同的合成和实际定价问题设置中评估OormLP，并证明OormLP推进了最先进的方法。

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.

大型观察数据越来越多地提供健康，经济和社会科学等学科，研究人员对因果问题而不是预测感兴趣。在本文中，从旨在调查参与学校膳食计划对健康指标的实证研究，研究了使用非参数回归的方法估算异质治疗效果的问题。首先，我们介绍了与观察或非完全随机数据进行因果推断相关的设置和相关的问题，以及如何在统计学习工具的帮助下解决这些问题。然后，我们审查并制定现有最先进的框架的统一分类，允许通过非参数回归模型来估算单个治疗效果。在介绍模型选择问题的简要概述后，我们说明了一些关于三种不同模拟研究的方法的性能。我们通过展示一些关于学校膳食计划数据的实证分析的一些方法的使用来结束。

有许多可用于选择优先考虑治疗的可用方法，包括基于治疗效果估计，风险评分和手工制作规则的遵循申请。我们将秩加权平均治疗效应（RATY）指标作为一种简单常见的指标系列，用于比较水平竞争范围的治疗优先级规则。对于如何获得优先级规则，率是不可知的，并且仅根据他们在识别受益于治疗中受益的单位的方式进行评估。我们定义了一系列速率估算器，并证明了一个中央限位定理，可以在各种随机和观测研究环境中实现渐近精确的推断。我们为使用自主置信区间的使用提供了理由，以及用于测试关于治疗效果中的异质性的假设的框架，与优先级规则相关。我们对速率的定义嵌套了许多现有度量，包括QINI系数，以及我们的分析直接产生了这些指标的推论方法。我们展示了我们从个性化医学和营销的示例中的方法。在医疗环境中，使用来自Sprint和Accor-BP随机对照试验的数据，我们发现没有明显的证据证明异质治疗效果。另一方面，在大量的营销审判中，我们在一些数字广告活动的治疗效果中发现了具有的强大证据，并证明了如何使用率如何比较优先考虑估计风险的目标规则与估计治疗效益优先考虑的目标规则。