Privacy Preserving Adaptive Experiment Design
CoRR(2024)
摘要
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.
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