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

机器学习通常用于科学和工业领域，对无法直接观察到的现象进行推断，但可以通过一系列实验进行探索。例如，优化化学反应时的主要指标可能是所需输出的产率，但许多实验条件（如pH值和环境温度）可能会影响产率。自适应实验设计提供了一个框架，利用过去观察到的测量计划在未来的测量在一个闭环。与预先选择的任何固定计划相比，它需要更少的总体测量来实现相同的推理目标。然而，一个限制是隐含的假设，即每一个可能的测量在任何时候都是可用的。在实践中，这很少是真的-例如，化学试剂可以用完，并限制了可能的实验。这迫使从业者做出权衡：如果目前只有一个子集的测量是可能的，并且你有一个固定的实验预算，那么是否值得进行一个可用的实验，或者放弃希望将来有更好的机会？本研究的重点是形式化这些问题，并制定一个框架，解决在线自适应实验设计的顺序设置不可预测的测量可用性。该项目还包括一项计划，在整个大学垂直整合涵盖所有级别和学科的强大数据收集技术，以及从K-12学生开始延伸到整个社区的推广活动。该项目融合了自适应实验设计，多武装土匪和在线算法的见解。目前的自适应实验设计方法，例如在随机优化和最佳臂识别中，假设每次都可以访问固定的一批实验进行选择，并明确计划使用最优设计技术（如G-最优设计）来发展该批实验中的测量分配。然而，如果测量集每次都在变化，可能是相反的，这样的规划是非常困难的。该项目旨在为实验设计提供一个通用框架，包括在线设置中的优化和多重测试。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.