Mathematical Sciences: Sequential Experimentation and Adaptive Control

本研究将研究三个问题。 第一组 在顺序设计和调度中称为强盗问题。 一 多臂强盗问题在k个独立 随机序列在每个阶段n根据指定的 统治 “索引规则”选择具有最大“Gittins”的序列 index”。 这些指数不易计算。 的 研究人员将继续开发简单近似值， 最优停止问题 第二组问题使用边界穿越理论 对于样本平均值，可以找到某些贝叶斯的有用近似值 试验. 调查人员已经发现了这种近似 对于一般指数族。 现在他提议延长 结果超出了指数族和更高的维度。 第三组问题涉及随机回归 自适应控制。 经典随机自适应控制 是输出的最佳调节，当它被设计为 先前p个输出和q个输入的线性组合。 的 根据各种标准调节输出， 最小化平方和等。 调查员已经 这一领域取得了一些成果，他计划继续追求这些成果 问题进一步。

This research will study three problems. The first set is called bandit problems in sequential design and scheduling. A multi-armed bandit problem selects between k independent stochastic sequences at every stage n according to a specified rule. The "index rule" selects a sequence with maximum "Gittins index". These indices are not easily computable. The investigator will continue to develop simple approximations to the optimal stopping problems. The second set of problems uses the boundary crossing theory for sample means to find useful approximations to certain Bayes tests. The investigator has already found such approximations for general exponential families. Now he proposes to extend the results beyond the exponential families and to higher dimensions. The third set of problems deals with stochastic regression and adaptive control. The classical stochastic adaptive control is the optimal regulation of the output when it is designed as a linear combination of previous p outputs and q inputs. The output is regulated according to various criteria such as mimimizing the sum of squares etc.. The investigator already has several results in this area and he plans to pursue these problems further.