Computationally Aggressive Approaches to Adaptive Design

摘要本项目涉及跨学科研究，开发算法方法来设计和分析自适应实验。非适应（顺序）设计是一种其特征根据正在进行的实验中产生的信息而变化的设计，与传统的统计设计相反，这些特征是事先设定的，并且在整个过程中保持固定。适应性设计在临床试验、破坏性测试、行为生态学、计算机性能预测、自适应控制等方面有广泛的应用，它们有可能减少实验“资源”（如时间、金钱或生活质量）的支出。不幸的是，自适应设计很难分析和优化。精确的解析解很少可用，因此，从历史上看，这种设计主要是通过渐近方法和近似方法来实现的。在计算上，自适应设计需要大量的时间和空间，这往往使精确的计算变得不可行。该项目将通过开发新的计算方法来创建和评估设计以及利用最先进的计算设施，扩大可解决问题的规模和范围。关注在应用中重要的问题，主要强调为研究人员提供更大的灵活性，以建模他们的统计和成本目标。对于许多这样的问题，精确的最优性是不可能达到的，因此产生接近最优设计的技术也将被追求。其中一些技术是基于优化较小或更简单的问题，并将其解决方案结构外推到更大或更复杂的问题。这补充了分析的、渐近的工作，并为解的结构提供了新的见解。在其他情况下，从串行算法到并行算法的转换将用于解决额外的复杂性。

AbstractThis project involves interdisciplinary research in which algorithmicapproaches are developed to design and analyze adaptive experiments. Anadaptive (sequential) design is one whose characteristics change inaccordance with information arising from the ongoing experiment, as opposed to classical statistical designs where such characteristics areset in advance and remain fixed throughout. Adaptive designs have a widerange of application in clinical trials, destructive testing, behavioralecology, computer performance prediction, adaptive control, etc., wherethey have the potential to reduce the expenditure of experimental ``resources'' such as time, money, or quality of life. Unfortunately,adaptive designs are difficult to analyze and optimize. Exact analyticsolutions are rarely available, and thus, historically, such designs havebeen predominantly approached via asymptotic methods and ad hocapproximations. Computationally, adaptive designs require significanttime and space that has often made exact calculations infeasible.This project will expand the size and scope of solvable problems bydeveloping new computational approaches for creating and evaluatingdesigns and utilizing state of the art computational facilities.Attention is directed to problems that are important in applications,with a major emphasis on supplying researchers greater flexibility inmodeling their statistical and cost objectives. For many of theseproblems, exact optimality will be unattainable, and thus techniques forproducing near-optimal designs will also be pursued. Several of thesetechniques are based on optimizing smaller or simpler problems andextrapolating their solution structure to larger or more complexproblems. This compliments analytical, asymptotic work and provides newinsights into the structure of solutions. In other cases, a shift fromserial algorithms to parallel ones will be used to address theadditional complexity.