Statistical Inference for Adaptive Data
Abstract
Approved for Public ReleaseAbstract Modern decision-making systems, whether they are computational or implemented by humans, need to be adaptive to their environments to be most effective. The research in this proposal will develop novel methods to address the pressing need for the analysis of data collected by such adaptive systems, including reinforcement learning systems. Navy use cases include decision-making during and after any missions encountering novel circumstances, such as inferring the best treatment regime from data on corpsmen treating sailors injured by a new enemy weapon, or ensuring safety of an autonomous reconnaissance drone navigating an unexplored environment. Analyzing such adaptive data to draw rigorous insights from it, i.e., statistical inference, is challenging because each data point depends heavily (and in a changing way) on all the data that came before it, precluding application of the vast majority of the existing statistics literature. Existing methods heavily constrain the forms of adaptivity allowed in thedata and hence cannot be used to conduct inference for data from the best-performing adaptive decision-making algorithms. The proposed research overcomes the limitations of existing work via a novel framework that is flexible enough to accommodate any adaptive decision-making algorithm, including state-of-the-art machine learning and artificial intelligence, yet provides powerful and exactly valid statistical inference. The proposed work will comprehensively explore the methodological, computational, and theoretical aspects of this framework to maximize its practical utility in Navy and civilian applications. In particular, the first thrust of the proposed research will develop new computational methods for efficient and accurate sampling from complex sequential conditional distributions to maximize the scalability and power of the proposed framework. The second thrust will provide methods within the frameworkthat answer especially subtle inferential questions arising particularly often in adaptive data, namely, questions that themselves (not just their answers) depend on the data. The final thrust will leverage problem structure common in systems with complex dynamics in order to maximize the computational and inferential power of the framework in such settings. The success of this research will lead to significant mathematical and methodological progress in the study of decision making under uncertainty, directly contributing to the Mathematical Data Science program and advancing Naval decision superiority.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 10, 2025
- Source ID
- N000142512269
Entities
People
- Lucas Janson
Organizations
- Office of Naval Research
- President and Fellows of Harvard College
- United States Navy