结构化Pfaffian设置的算法配置
Algorithm Configuration for Structured Pfaffian Settings
AI总结：
本文提出Pfaffian GJ框架，为涉及Pfaffian函数的参数化数据驱动算法设计提供分布和在线学习保证，扩展了经典GJ框架的适用范围。
摘要：
数据驱动的算法设计自动将算法适应于特定应用领域，从而实现更好的性能。在参数化算法的背景下，这种方法涉及使用从目标应用领域的问题分布中抽取的问题实例来调整算法的超参数。这可以通过最大化衡量算法性能作为其超参数函数的经验效用来实现，使用问题实例。虽然经验证据支持数据驱动算法设计的有效性，但为几个参数化家族提供理论保证仍然具有挑战性。这是由于它们相应的效用函数的复杂行为，这些函数通常具有分段不连续结构。在这项工作中，我们提出了精细的框架，用于在分布学习和在线学习设置中为参数化数据驱动算法设计问题提供学习保证。对于分布学习设置，我们引入了\ extit{Pfaffian GJ框架}，这是经典\ extit{GJ框架}的扩展，能够为计算涉及Pfaffian函数的函数类提供学习保证。与仅限于计算由有理函数表征的函数类的GJ框架不同，我们提出的框架可以处理涉及Pfaffian函数的函数类，这些函数更加通用且应用广泛。然后我们表明，对于许多感兴趣的参数化算法，其效用函数具有\ extit{精细的分段结构}，这自动转化为使用我们提出的框架的学习保证。
英文摘要：
Data-driven algorithm design automatically adapts algorithms to specific application domains, achieving better performance. In the context of parameterized algorithms, this approach involves tuning the algorithm's hyperparameters using problem instances drawn from the problem distribution of the target application domain. This can be achieved by maximizing empirical utilities that measure the algorithms' performance as a function of their hyperparameters, using problem instances. While empirical evidence supports the effectiveness of data-driven algorithm design, providing theoretical guarantees for several parameterized families remains challenging. This is due to the intricate behaviors of their corresponding utility functions, which typically admit piecewise discontinuous structures. In this work, we present refined frameworks for providing learning guarantees for parameterized data-driven algorithm design problems in both distributional and online learning settings. For the distributional learning setting, we introduce the \textit{Pfaffian GJ framework}, an extension of the classical \textit{GJ framework}, that is capable of providing learning guarantees for function classes for which the computation involves Pfaffian functions. Unlike the GJ framework, which is limited to function classes with computation characterized by rational functions, our proposed framework can deal with function classes involving Pfaffian functions, which are much more general and widely applicable. We then show that for many parameterized algorithms of interest, their utility function possesses a \textit{refined piecewise structure}, which automatically translates to learning guarantees using our proposed framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
