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arXiv 2202.12958cs.LG
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具有策略依赖优化响应的非策略评估

Off-Policy Evaluation with Policy-Dependent Optimization Response

University of California, Berkeley(加州大学伯克利分校);University of Southern California(南加州大学)

Wenshuo Guo, Michael I. Jordan, Angela Zhou

摘要:

因果推理和机器学习决策的交叉点正在迅速扩大,但默认的决策标准仍然是整个人群中个体因果结果的\textit{average}。在实践中,各种操作限制确保决策者的效用不是作为\textit{average}实现的,而是作为下游决策问题(例如匹配、分配、网络流、最小化预测风险)的\textit{output}实现的。在这项工作中,我们开发了一个新的框架外政策评估与\textit{policy-dependent}线性优化响应:因果结果引入随机性的目标函数系数。在此框架下,决策者的效用取决于政策相关的优化,这引入了一个根本的挑战,即使是政策评估的情况下,\textit{optimization}偏见。我们构造了无偏估计的政策依赖估计的扰动方法,并讨论了一组调整插件估计的渐近方差性质。最后,实现无偏的政策评估允许政策优化:我们提供了一个通用的算法优化因果干预。我们证实了我们的理论结果与数值模拟。

英文摘要:

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.

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