Per-instance algorithm selection (PIAS) takes advantage of complementarity between a set of algorithms by deciding which algorithm to run on a given instance. This decision is based on features of the instances, which, in the context of black-box optimization (BBO), require a part of the optimization budget to be computed. This raises two questions: (a) from which fraction of the budget spent on feature computation does PIAS become worth it for BBO, and (b) which fraction of the budget optimizes the tradeoff between feature accuracy and PIAS performance. To this end, we perform a broad study where PIAS with varying sampling budgets for feature computation is compared to the single best algorithm on a broad range of algorithm selection scenarios. These scenarios consist of two portfolio sizes, three problem sets, 4 dimensionalities, and 10 target budgets. We find that PIAS is viable for the majority of tested scenarios, even when as much as a quarter of the total budget is spent on feature computation. The tradeoff for the fraction of the budget spent on feature computation to maximize the benefit of PIAS is highly dependent on the specific AS scenario. Further, on average 20 percent of PIAS loss to the virtual best solver is explained by the budget spent on feature computation, highlighting the importance of properly accounting for the feature budget.

翻译：逐实例算法选择（PIAS）利用一组算法之间的互补性，通过决定在给定实例上运行哪个算法来提升性能。这一决策基于实例的特征，而在黑箱优化（BBO）的背景下，这些特征需要消耗部分优化预算进行计算。这引出了两个问题：（a）对于BBO，从特征计算所消耗的预算比例达到多少时，PIAS才变得值得；（b）哪个预算比例能在特征准确性与PIAS性能之间实现最优权衡。为此，我们进行了一项广泛研究，将采用不同采样预算进行特征计算的PIAS与单一最佳算法在多种算法选择场景中进行比较。这些场景包括两种组合规模、三组问题集、四种维度以及十种目标预算。我们发现，在大多数测试场景中，PIAS是可行的，即使特征计算消耗了总预算的四分之一。用于最大化PIAS收益的特征计算预算比例高度依赖于具体的算法选择场景。此外，平均而言，PIAS相对于虚拟最优求解器的性能损失中有20%可归因于特征计算所消耗的预算，这凸显了合理考虑特征预算的重要性。