Speaker: Karun Adusumilli, University of Pennsylvania,
Title: Continuous Time Asymptotic Representations for Adaptive Experiments
Abstract: This article develops a continuous-time asymptotic framework for analyzing adaptive experiments—settings in which data collection and treatment assignment evolve dynamically in response to incoming information. Akey challenge in analyzing fully adaptive experiments, where the assignment policy is updated after each observation, is that the sequence of policy rules often lack a well-defined asymptotic limit. To address this, we focus instead on the empirical allocation process, which captures the (normalized) number of observations assigned to each treatment over time. We show that, under general conditions, any adaptive experiment and its associated empirical allocation process can be approximated by a limit experiment defined by Gaussian diffusions with unknown drifts and a corresponding continuous-time allocation process. This limit representation facilitates the analysis of optimal decision rules by reducing the dimensionality of the state-space and exploiting the tractability of Gaussian diffusions. We apply the framework to derive optimal estimators, analyze in-sample regret for adaptive experiments, and construct e-processes for anytime-valid inference. Notably, we introduce the first definition of any-time and any-experiment valid inference for multi-treatment settings.

Speaker: Toru Kitagawa, Brown University,
Title: TBA

Speaker: Chen Qiu, Cornell University,
Title: Local Asymptotics for Treatment Choice with Partial Identification
Abstract: We provide a new asymptotic framework to derive approximately optimal treatment assignments when sampling noise from data is compounded by fundamental uncertainty due to partial identification. We recenter the reduced-form parameter around its least-favorable configuration and consider drifting parameter sequences that yield both diminishing levels of sampling uncertainty and of partial identification. We characterize the limiting decision problem as a normal location shift model with a suitable limiting identified set. We apply our results to treatment choice problems with contaminated outcomes, to robust welfare analyses with partially identified consumer surplus, and to the problem of aggregating experimental estimates for policy adoption.