迈向自动化置信界证明器和搜索器
Towards Automated Confidence Bound Provers and Searchers
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中文总结 AI 辅助
该研究为自动化寻找和证明均值下置信界有效性奠定基础，基于优化问题找到置信界与优化问题的关系，定义由阶函数参数化的松弛族，可近似其他目标松弛，线性阶函数时是线性规模混合整数线性规划。
中文摘要 AI 辅助
在这项工作中，我们为自动化寻找和证明均值的下置信界有效性的过程奠定基础。关键发现是在特定条件下找到最优置信界可表述为优化问题。我们据此表明任何有效置信界（如霍夫丁的）必定是某个优化问题的松弛。为自动找到并证明置信界，需自动化定义和找到这种松弛的过程。我们定义了一族由阶函数参数化的松弛。该族松弛通过将目标用作阶函数可近似任何其他目标松弛，如霍夫丁的。当阶函数是线性的（如霍夫丁情形下的样本均值），我们的松弛是线性规模的混合整数线性规划。
英文摘要
In this work we lay the groundwork for automating the process of finding and proving the validity of lower confidence bounds of the mean. Our key finding is based on the observation that finding an optimal confidence bound under certain conditions can be formulated as an optimization problem. We use this observation to show that any valid confidence bound (such as Hoeffding's) must be a relaxation of a certain optimization problem. To automatically find and prove confidence bounds, we need to automate the process of defining and finding such a relaxation. We define a family of relaxations parameterized by a function called the order function. This family of relaxations can approximate any other target relaxation such as Hoeffding's by using the target as the order function. When the order function is linear (such as the sample mean in the case of Hoeffding's), our relaxation is a linear-size mixed-integer linear program.
