Arthur Gretton

Zikai Shen, Houssam Zenati, Nathan Kallus et al.

We study inference on scalar-valued pathwise differentiable targets after adaptive data collection, such as a bandit algorithm. We introduce a novel target-specific condition, directional stability, which is strictly weaker than previously imposed target-agnostic stability conditions. Under directional stability, we show that estimators that would have been efficient under i.i.d. data remain asymptotically normal and semiparametrically efficient when computed from adaptively collected trajectories. The canonical gradient has a martingale form, and directional stability guarantees stabilization of its predictable quadratic variation, enabling high-dimensional asymptotic normality. We characterize efficiency using a convolution theorem for the adaptive-data setting, and give a condition under which the one-step estimator attains the efficiency bound. We verify directional stability for LinUCB, yielding the first semiparametric efficiency guarantee for a regular scalar target under LinUCB sampling.

Taedong Yun, Eric Yang, Mustafa Safdari et al. · berkeley

We present an end-to-end framework for generating synthetic users for evaluating interactive agents designed to encourage positive behavior changes, such as in health and lifestyle coaching. The synthetic users are grounded in health and lifestyle conditions, specifically sleep and diabetes management in this study, to ensure realistic interactions with the health coaching agent. Synthetic users are created in two stages: first, structured data are generated grounded in real-world health and lifestyle factors in addition to basic demographics and behavioral attributes; second, full profiles of the synthetic users are developed conditioned on the structured data. Interactions between synthetic users and the coaching agent are simulated using generative agent-based models such as Concordia, or directly by prompting a language model. Using two independently-developed agents for sleep and diabetes coaching as case studies, the validity of this framework is demonstrated by analyzing the coaching agent's understanding of the synthetic users' needs and challenges. Finally, through multiple blinded evaluations of user-coach interactions by human experts, we demonstrate that our synthetic users with health and behavioral attributes more accurately portray real human users with the same attributes, compared to generic synthetic users not grounded in such attributes. The proposed framework lays the foundation for efficient development of conversational agents through extensive, realistic, and grounded simulated interactions.

Mónica Ribero, Antonin Schrab, Arthur Gretton

We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we estimate using kernel methods. The proposed test is adaptive over hyperparameters such as the kernel bandwidth and the regularization parameter. We provide theoretical guarantees for statistical test power across our family of $f$-divergence estimates. While our test covers a variety of $f$-divergences, we bring particular focus to the Hockey-Stick divergence, motivated by its applications to differential privacy auditing and machine unlearning evaluation. For two-sample testing, experiments demonstrate that different $f$-divergences are sensitive to different localized differences, illustrating the importance of leveraging diverse statistics. For machine unlearning, we propose a relative test that distinguishes true unlearning failures from safe distributional variations.