Research Initiation: Stochastic Optimization and Search Algorithms

在这项研究中，采用了贝叶斯公式的优化和搜索问题，以非常宽松的假设区分开来。算法的最优性准则是条件概率相对于观测值的离散度最小。这项研究解决了最优近视算法的一致性、算法的特征以及对概率假设不敏感的高效算法的开发等理论问题。带有部分信息的优化和搜索问题比比皆是。一种常见的情况是，从关于要优化的函数或要找到的对象的最少信息开始，然后进行观察以改进我们的信息。有效的观测选择是一个困难而重要的问题，因为一些选择可能比另一些选择提供更多的信息。虽然符合这种描述的问题很常见，但在规划合理的战略时，很少有理论指导，因为大多数优化或搜索方法所需的强有力的假设通常不能被证明是合理的。

A Bayesian formulation of optimization and search problems that are distinguished by very lax assumptions is adopted in this research. The optimality criterion for algorithms is the minimization of dispersion of the conditional probabilities with respect to the observations. The research addresses the theoretical issues of consistency of optimal myopic algorithms, characterizations of algorithms, and the development of efficient algorithms that are not sensitive to probabilistic assumptions. Problems of optimization and search with partial information abound. A common situation is to start with minimal information about the function to be optimized or the object to be found and then make observations that improve our information. An efficient choice of observations is a difficult and important problem since some choices may be much more informative than others. While problems that fit this description are commonplace, there is very little theory to guide in planning sensible strategies since the strong assumptions needed for most optimization or search methods can not typically be justified.