Adaptive experiment is widely adopted to estimate conditional average treatment effect (CATE) in clinical trials and many other scenarios. While the primary goal in experiment is to maximize estimation accuracy, due to the imperative of social welfare, it's also crucial to provide treatment with superior outcomes to patients, which is measured by regret in contextual bandit framework. These two objectives often lead to contrast optimal allocation mechanism. Furthermore, privacy concerns arise in clinical scenarios containing sensitive data like patients health records. Therefore, it's essential for the treatment allocation mechanism to incorporate robust privacy protection measures. In this paper, we investigate the tradeoff between loss of social welfare and statistical power in contextual bandit experiment. We propose a matched upper and lower bound for the multi-objective optimization problem, and then adopt the concept of Pareto optimality to mathematically characterize the optimality condition. Furthermore, we propose differentially private algorithms which still matches the lower bound, showing that privacy is "almost free". Additionally, we derive the asymptotic normality of the estimator, which is essential in statistical inference and hypothesis testing.

翻译：自适应实验被广泛应用于临床试验及许多其他场景中以估计条件平均处理效应（CATE）。虽然实验的首要目标是最大化估计精度，但由于社会福利的迫切需求，为患者提供疗效更优的治疗方案也至关重要，这通过情境强盗框架中的遗憾值来衡量。这两个目标往往导致对比最优分配机制。此外，包含患者健康记录等敏感数据的临床场景引发了隐私问题。因此，治疗分配机制必须融入稳健的隐私保护措施。本文研究了情境强盗实验中社会福利损失与统计效力之间的权衡。我们提出了多目标优化问题的匹配上下界，并采用帕累托最优概念从数学上刻画最优性条件。进一步地，我们提出了差分隐私算法，该算法仍能达到下界匹配，表明隐私是"几乎免费"的。此外，我们推导了估计量的渐近正态性，这对统计推断和假设检验至关重要。