In the era of large-scale AI deployment and high-stakes clinical trials, adaptive experimentation faces a ``trilemma'' of conflicting objectives: minimizing cumulative regret (welfare loss during the experiment), maximizing the estimation accuracy of heterogeneous treatment effects (CATE), and ensuring differential privacy (DP) for participants. Existing literature typically optimizes these metrics in isolation or under restrictive parametric assumptions. In this work, we study the multi-objective design of adaptive experiments in a general non-parametric setting. First, we rigorously characterize the instance-dependent Pareto frontier between cumulative regret and estimation error, revealing the fundamental statistical limits of dual-objective optimization. We propose ConSE, a sequential segmentation and elimination algorithm that adaptively discretizes the covariate space to achieve the Pareto-optimal frontier. Second, we introduce DP-ConSE, a privacy-preserving extension that satisfies Joint Differential Privacy. We demonstrate that privacy comes ``for free'' in our framework, incurring only asymptotically negligible costs to regret and estimation accuracy. Finally, we establish a robust link between experimental design and long-term utility: we prove that any policy derived from our Pareto-optimal algorithms minimizes post-experiment simple regret, regardless of the specific exploration-exploitation trade-off chosen during the trial. Our results provide a theoretical foundation for designing ethical, private, and efficient adaptive experiments in sensitive domains.

翻译：在大规模人工智能部署与高风险临床试验的时代，自适应实验面临着一个相互冲突目标的“三元困境”：最小化累积遗憾（实验期间的福利损失）、最大化异质性处理效应（CATE）的估计精度，以及确保参与者的差分隐私（DP）。现有文献通常孤立地或在限制性参数假设下优化这些指标。本研究在一般非参数设定下探讨自适应实验的多目标设计。首先，我们严格刻画了累积遗憾与估计误差之间的实例依赖帕累托前沿，揭示了双目标优化的基本统计极限。我们提出ConSE算法——一种顺序分割与淘汰算法，能自适应地对协变量空间进行离散化以实现帕累托最优前沿。其次，我们引入DP-ConSE这一满足联合差分隐私的隐私保护扩展版本。我们证明隐私在我们的框架中可“免费”获得，仅对遗憾和估计精度产生渐近可忽略的成本。最后，我们在实验设计与长期效用之间建立了稳健联系：我们证明从帕累托最优算法导出的任何策略均能最小化实验后简单遗憾，且与试验期间选择的具体探索-利用权衡无关。我们的研究结果为在敏感领域设计符合伦理、隐私保护且高效的自适应实验提供了理论基础。