Individualized treatment recommendation is a crucial task in evidence-based decision-making. In this study, we formulate this task as a fixed-budget best arm identification (BAI) problem with contextual information. In this setting, we consider an adaptive experiment given multiple treatment arms. At each round, a decision-maker observes a context (covariate) that characterizes an experimental unit and assigns the unit to one of the treatment arms. At the end of the experiment, the decision-maker recommends a treatment arm estimated to yield the highest expected outcome conditioned on a context (best treatment arm). The effectiveness of this decision is measured in terms of the worst-case expected simple regret (policy regret), which represents the largest difference between the conditional expected outcomes of the best and recommended treatment arms given a context. Our initial step is to derive asymptotic lower bounds for the worst-case expected simple regret, which also implies ideal treatment assignment rules. Following the lower bounds, we propose the Adaptive Sampling (AS)-Policy Learning recommendation (PL) strategy. Under this strategy, we randomly assign a treatment arm with a ratio of a target assignment ratio at each round. At the end of the experiment, we train a policy, a function that recommends a treatment arm given a context, by maximizing the counterfactual empirical policy value. Our results show that the AS-PL strategy is asymptotically minimax optimal, with its leading factor of expected simple regret converging with our established worst-case lower bound. This research has broad implications in various domains, and in light of existing literature, our method can be perceived as an adaptive experimental design tailored for policy learning, on-policy learning, or adaptive welfare maximization.

个性化治疗建议、最佳治疗方法鉴定、上下文信息、自适应实验以及策略学习是这篇研究论文的关键词，通过推荐最佳治疗方法的决策策略获得最小的预期简单后悔，同时为政策学习、实验设计和自适应福利最大化提供了新的方法。

上下文固定预算的最佳臂识别：具有策略学习的自适应实验设计