LAMBDA: Covering the Solution Set of Black-Box Inequality by Search Space Quantization

TL;DR

This paper introduces LAMBDA, a novel search algorithm that efficiently covers the solution set of black-box inequalities by intelligently partitioning the search space, outperforming existing methods in speed and coverage.

Contribution

The paper formalizes the Black-Box Coverage problem and proposes LAMBDA, a new algorithm that enhances exploration and coverage efficiency using density-adaptive search strategies.

Findings

LAMBDA achieves up to 33x faster coverage than Random Search.

LAMBDA outperforms baseline methods in coverage accuracy.

Experiments show LAMBDA's potential in virtual autonomous system testing.

Abstract

Black-box functions are broadly used to model complex problems that provide no explicit information but the input and output. Despite existing studies of black-box function optimization, the solution set satisfying an inequality with a black-box function plays a more significant role than only one optimum in many practical situations. Covering as much as possible of the solution set through limited evaluations to the black-box objective function is defined as the Black-Box Coverage (BBC) problem in this paper. We formalized this problem in a sample-based search paradigm and constructed a coverage criterion with Confusion Matrix Analysis. Further, we propose LAMBDA (Latent-Action Monte-Carlo Beam Search with Density Adaption) to solve BBC problems. LAMBDA can focus around the solution set quickly by recursively partitioning the search space into accepted and rejected sub-spaces. Compared with La-MCTS, LAMBDA introduces density information to overcome the sampling bias of optimization and obtain more exploration. Benchmarking shows, LAMBDA achieved state-of-the-art performance among all baselines and was at most 33x faster to get 95% coverage than Random Search. Experiments also demonstrate that LAMBDA has a promising future in the verification of autonomous systems in virtual tests.