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。该决策基于实例的特征，在黑箱优化（BBO）的背景下，这些特征需要消耗部分优化预算来计算。这引出了两个问题：（a）在BBO中，花费在特征计算上的预算占比达到多少时，PIAS才变得值得；（b）何种预算占比能优化特征准确性与PIAS性能之间的权衡。为此，我们进行了一项广泛研究，将不同特征计算采样预算下的PIAS与单一最佳算法在多种算法选择场景中进行比较。这些场景涵盖两种组合规模、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，即使将总预算的四分之一用于特征计算，PIAS仍然可行。用于最大化PIAS收益的特征计算预算占比权衡高度依赖于具体的算法选择场景。此外，平均而言，PIAS相对于虚拟最佳求解器的损失中有20%可由特征计算预算解释，这凸显了恰当考虑特征预算的重要性。