RI: Small: Scalable Online Learning with Gaussian Processes

现代世界充满了高度复杂的系统，它们相互作用，运输货物和原材料，制造为手机和笔记本电脑供电的微小部件，协助外科医生进行精密的医疗程序。每天，这些系统的操作员都必须做出一般性的决定，比如如何安排工人和交货，以及具体的决定，比如装配线上的某个机器人应该如何工作。在每种情况下，一个好的决策不仅要考虑环境的已知情况，还要考虑未知情况。有时需要收集更多的信息，有时必须采取行动来避免不太可能发生但代价高昂的错误。此外，每一个决定都会影响下一个决定，每一步判断中的错误和延迟都可能被传播和放大。科学家们在做决定时严重依赖计算机模型来控制未知因素，但在许多情况下，这些模型速度太慢，无法发挥作用。这项研究将大大减少对不确定性的鲁棒表示所需的计算需求，这意味着计算机模型可以以更低的成本更快、更可靠地量化不确定性的影响。在一个未知被仔细建模的世界里，自动驾驶汽车更安全，基础设施更高效，科学实验更有信息量。高斯过程是不确定性表示的黄金标准。然而，训练后进行预测的高计算成本限制了它们在贝叶斯优化和强化学习的顺序决策框架中的适用性，在这些框架中，不确定性估计的质量可能会产生巨大的影响。本研究开发了代数方法，利用这些设置中可扩展高斯过程的硬件设计的进步。这项工作将扩大贝叶斯优化方法对一般目标的适用性，具有重要的科学影响，如自动化核磁共振波谱。这项研究还将在基于模型的强化学习中实现更现实的假设，以捕获工程系统的许多可能的未来状态，有效地探索可能的状态，以及高维状态空间的表示。这些特性是向复杂工程系统（如无人驾驶车辆）自动控制迈出的重要一步，在这些系统中，获取数据成本高昂，安全保证至关重要。总的来说，这项工作将有助于释放概率方法在连续在线决策中的潜力，同时在教育环境中提供交互式工程演示。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。

The modern world is filled with highly complex systems interacting to transport goods and raw materials, to manufacture the tiny components that power phones and laptops, and to assist surgeons in delicate medical procedures. Every day, the operators of these systems must make general decisions like how to schedule workers and deliveries, and specific decisions like how a certain robot in an assembly line should function. In each case, a good decision must account not only for what is known about the environment, but also what is unknown. Sometimes more information should be gathered, and sometimes action must be taken to avoid unlikely but costly mistakes. Moreover, every decision affects the next, and errors and delays in judgement at each step can be propagated and amplified. Scientists rely heavily on computer models to control for unknowns when making decisions, but in many situations the models are simply too slow to be useful. This research will greatly reduce the computational requirements needed for a robust representation of uncertainty, meaning computer models can quantify the effect of uncertainty more quickly and reliably, at a lower cost. In a world where unknowns are carefully modeled, autonomous vehicles are safer, infrastructure is more efficient, and scientific experiments are more informative.Gaussian processes are a gold standard for uncertainty representation. However, the high computational cost of making predictions, after training, has limited their applicability in the sequential decision making frameworks for Bayesian optimization and reinforcement learning, where the quality of uncertainty estimates can have enormous impact. This research develops algebraic methods that exploit advances in hardware design for scalable Gaussian processes in these settings. This work will broaden the applicability of Bayesian optimization methods to general purpose objectives, with crucial scientific impacts such as automating NMR spectroscopy. This research will also enable more realistic assumptions in model-based reinforcement learning, to capture many possible future states of an engineering system, efficient exploration of possible states, and representation of high dimensional state spaces. These features are an important step towards automatic control in complicated engineering systems, such as unmanned vehicles, where data is costly to acquire and safety guarantees are critical. Overall this work will help unlock the potential of probabilistic methods for sequential online decision making, while providing interactive engineering demonstrations in educational 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.