We present the first nontrivial procedure for configuring heuristic algorithms to maximize the utility provided to their end users while also offering theoretical guarantees about performance. Existing procedures seek configurations that minimize expected runtime. However, very recent theoretical work argues that expected runtime minimization fails to capture algorithm designers' preferences. Here we show that the utilitarian objective also confers significant algorithmic benefits. Intuitively, this is because mean runtime is dominated by extremely long runs even when they are incredibly rare; indeed, even when an algorithm never gives rise to such long runs, configuration procedures that provably minimize mean runtime must perform a huge number of experiments to demonstrate this fact. In contrast, utility is bounded and monotonically decreasing in runtime, allowing for meaningful empirical bounds on a configuration's performance. This paper builds on this idea to describe effective and theoretically sound configuration procedures. We prove upper bounds on the runtime of these procedures that are similar to theoretical lower bounds, while also demonstrating their performance empirically.

翻译：我们提出了首个具有理论性能保证、且能最大化最终用户效用的启发式算法配置流程。现有配置方法旨在最小化期望运行时间。然而，最新理论研究表明，期望运行时间最小化无法捕捉算法设计者的偏好。本文证明功利主义目标同样能带来显著的算法优势。直观而言，这是由于均值运行时间受极端罕见的长时运行支配——即便算法从未产生此类长时运行，可证地最小化均值运行时间的配置流程仍需执行海量实验来证明这一事实。相比之下，效用具有有界性且随运行时间单调递减，这使得对配置性能进行有意义的经验性约束成为可能。本文基于这一思想，描述了有效且理论完备的配置流程。我们证明了这些流程运行时间的理论下界相关的上界，并通过实验验证了其性能表现。