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

机器学习通常用于科学和工业中，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期望输出的产率，但许多实验条件，如pH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，在闭环中计划未来的测量。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，限制是隐含的假设，即所有可能的测量在任何时候都是可用的。在实践中，这很少是正确的-例如，化学试剂可能会耗尽并限制可能的实验。这迫使从业者权衡：如果当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，那么选择一个可用的实验是值得的，还是放弃希望在未来有更好的机会？本研究的重点是将这些问题形式化，并开发一个框架，用于在不可预测的测量可用性的顺序设置中解决在线自适应实验设计。该项目还包括一项计划，旨在垂直整合整个大学的强大数据收集技术，涉及所有级别和学科，以及从K-12学生开始扩展到整个社区的推广。这个项目融合了自适应实验设计、多臂盗匪和在线算法的见解。当前的自适应实验设计方法，例如随机优化和最佳臂识别，假设每次都有固定批次的实验可供选择，并明确计划使用g -最优设计等优化设计技术在此批次上进化测量分配。然而，如果度量集每次都在变化，那么这样的计划是非常困难的。在凸面优化技术的推动下，该项目旨在为实验设计提供一个通用框架，包括优化和在线多次测试。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识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.