  In the algorithm selection research, the discussion surrounding algorithm
features has been significantly overshadowed by the emphasis on problem
features. Although a few empirical studies have yielded evidence regarding the
effectiveness of algorithm features, the potential benefits of incorporating
algorithm features into algorithm selection models and their suitability for
different scenarios remain unclear. In this paper, we address this gap by
proposing the first provable guarantee for algorithm selection based on
algorithm features, taking a generalization perspective. We analyze the
benefits and costs associated with algorithm features and investigate how the
generalization error is affected by different factors. Specifically, we examine
adaptive and predefined algorithm features under transductive and inductive
learning paradigms, respectively, and derive upper bounds for the
generalization error based on their model's Rademacher complexity. Our
theoretical findings not only provide tight upper bounds, but also offer
analytical insights into the impact of various factors, such as the training
scale of problem instances and candidate algorithms, model parameters, feature
values, and distributional differences between the training and test data.
Notably, we demonstrate how models will benefit from algorithm features in
complex scenarios involving many algorithms, and proves the positive
correlation between generalization error bound and $\chi^2$-divergence of
distributions.
