On the Influence of the Feature Computation Budget on Per-Instance Algorithm Selection for Black-Box Optimization
Authors: Koen van der Blom, Diederick Vermetten
Organizations: Centrum Wiskunde & Informatica, Amsterdam, The Netherlands · Sorbonne Universit´e, CNRS, LIP6, Paris, France
Abstract
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.
In black-box optimization, a central question is which algorithm to use to solve a given, previously unseen, problem. Selecting a single algorithm, however, entails inherent risks: inaccuracies in the selector may lead to poor choices, and even well-performing algorithms with high variance can yield unsatisfactory results in a single run. A natural remedy is to split the evaluation budget across multiple runs of potentially different algorithms. Such sequential algorithm portfolios benefit from variance reduction and complementarities between algorithms, often outperforming approaches that allocate the entire budget to a single solver. While effective portfolios can be constructed post-hoc, transferring this idea to the algorithm selection setting is non-trivial. We show that a naive portfolio constructed over the full training set already outperforms the strongest traditional baseline, the virtual best solver. We then propose a simple yet effective k-nearest-neighbor-based finetuning approach to construct portfolios tailored to unseen instances, yielding further improvements and highlighting the effectiveness of portfolio selection in fixed-budget black-box optimization.
The present paper introduces a new representation-driven approach to per-instance algorithm selection, applied to black-box optimization, for automatically choosing the most promising solver from a fixed portfolio. Prior work in continuous optimization largely relies on numerical descriptors, including Exploratory Landscape Analysis features and learned embeddings such as Deep-ELA. This work studies a complementary representation: contour-map visualizations of probed landscapes. A CNN regressor takes multiple instance-specific contour views (stacked or encoded per view and aggregated) and predicts per-solver performance, enabling selection by the predicted best value. On the standard BBOB 2009 single-objective protocol, the resulting selectors significantly outperform the single best solver (SBS) and are competitive with feature-based baselines. A subsequent bi-objective evaluation under the DeepELA setting further indicates that the same image-based principle can be competitive when using windowed contour views. Overall, the results suggest that simple vision models can exploit spatial structure in probed landscapes for algorithm selection without handcrafted ELA features.
In typical black-box optimization applications, the available computational budget is often allocated to a single algorithm, typically chosen based on user preference with limited knowledge about the problem at hand or according to some expert knowledge. However, we show that splitting the budget across several algorithms yield significantly better results. This approach benefits from both algorithm complementarity across diverse problems and variance reduction within individual functions, and shows that algorithm portfolios do NOT require parallel evaluation capabilities. To demonstrate the advantage of sequential algorithm portfolios, we apply it to the COCO data archive, using over 200 algorithms evaluated on the BBOB test suite. The proposed sequential portfolios consistently outperform single-algorithm baselines, achieving relative performance gains of over 14%, and offering new insights into restart mechanisms and potential for warm-started execution strategies.