CIF: Small: Online Learning and Optimal Experiment Design with a Budget

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Machine learning is routinely used in science and industry to make inferences about a phenomenon that cannot be observed directly, but can be probed through a series of experiments. For instance, the chief metric when optimizing a chemical reaction may be the yield of the desired output, but many experimental conditions such as pH and ambient temperature may affect the yield. Adaptive experimental design provides a framework to exploit observed measurements of the past to plan measurements in the future in a closed loop. It has been shown to require far fewer overall measurements to achieve the same inference goals compared to any fixed plan chosen in advance. However, a limitation is the implicit assumption that every possible measurement is available at all times. In practice this is rarely true - for example chemical reagents can run out and restrict the possible experiments. This forces a tradeoff on practitioners: if only a subset of measurements are possible at the current time and you have a fixed budget of experiments, is it worth it to take one of the available experiments, or abstain in the hope of better opportunities in the future? The focus of this research is to formalize such questions and develop a framework for addressing online adaptive experimental design in the sequential setting of unpredictable measurement availability. The project also includes a plan to vertically integrate robust data collection techniques across the university touching all levels and disciplines, as well as outreach that starts with K-12 students and extends to the community at large.This project amalgamates insights from adaptive experimental design, multi-armed bandits, and online algorithms. Current adaptive experimental design methods, for instance in stochastic optimization and best-arm identification, assume access to a fixed batch of experiments to choose from at each time, and explicitly plan to evolve the allocation of measurements over this batch using optimal design techniques such as G-optimal design. However, if the measurement set is changing at each time, potentially adversarially, such planning is extremely difficult. Motivated by progress in specific cases that leverage advances in convex optimization, the project seeks to provide a general framework for experimental design including optimization and multiple testing in online settings.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.