aiqbench analysis
This paper addresses efficiency bottlenecks in Black-Box Optimization by introducing "algorithm-dependent learnability," a theoretical framework that shifts focus from general region coverage to accuracy along the optimizer's specific trajectory. The authors validate this approach with UGTL, a method using conditional diffusion to model search paths, which outperforms 24 other techniques on discrete submodular maximization and convex minimization tasks without requiring new online evaluations.
Rethinking Learnability in Offline Data-driven Optimization
arXiv:2609.01493v1 Announce Type: new Abstract: Black-Box Optimization (BBO) has found broad applications, but evolutionary algorithms and Bayesian optimization face efficiency challenges as real-world BBO problems grow increasingly complex. Data-driven optimization improves the efficiency of BBO algorithms by learning from data. Offline data-driven optimization seeks high-quality solutions using only a fixed set of previous evaluations, attracting substantial attention because it requires no additional online evaluations. Many offline optimization methods have been proposed, but a fundamental question remains unanswered: what learnability is sufficient for offline optimization? Prior theoretical studies show that Probably Approximately Correct (PAC) learnability is insufficient, as the optimal region may remain poorly learned even when most regions are well learned. In this paper, we propose algorithm-dependent learnability, which requires accuracy only on the optimizer's trajectory. We prove that its value-query form is sufficient for representative discrete settings, including greedy and local search for submodular maximization, while its first-order analogue is sufficient for projected gradient descent on convex minimization. Motivated by this notion, we formalize a trajectory-learning framework comprising trajectory construction, trajectory modeling, and candidate generation, and analyze existing trajectory-based methods under it. We further propose Uncertainty-aware Gradient-guided Trajectory Learning (UGTL), which constructs locally coherent improvement trajectories reflecting plausible search paths, models them with conditional diffusion, and selects a diverse candidate set. On five Design-Bench tasks, UGTL achieves the best aggregate mean rank, $3.1/25$, among 25 methods. Controlled trajectory analyses and cross-architecture replacements confirm that our trajectory construction plays a significant role in the improvement.
Abstract:Black-Box Optimization (BBO) has found broad applications, but evolutionary algorithms and Bayesian optimization face efficiency challenges as real-world BBO problems grow increasingly complex. Data-driven optimization improves the efficiency of BBO algorithms by learning from data. Offline data-driven optimization seeks high-quality solutions using only a fixed set of previous evaluations, attracting substantial attention because it requires no additional online evaluations. Many offline optimization methods have been proposed, but a fundamental question remains unanswered: what learnability is sufficient for offline optimization? Prior theoretical studies show that Probably Approximately Correct (PAC) learnability is insufficient, as the optimal region may remain poorly learned even when most regions are well learned. In this paper, we propose algorithm-dependent learnability, which requires accuracy only on the optimizer's trajectory. We prove that its value-query form is sufficient for representative discrete settings, including greedy and local search for submodular maximization, while its first-order analogue is sufficient for projected gradient descent on convex minimization. Motivated by this notion, we formalize a trajectory-learning framework comprising trajectory construction, trajectory modeling, and candidate generation, and analyze existing trajectory-based methods under it. We further propose Uncertainty-aware Gradient-guided Trajectory Learning (UGTL), which constructs locally coherent improvement trajectories reflecting plausible search paths, models them with conditional diffusion, and selects a diverse candidate set. On five Design-Bench tasks, UGTL achieves the best aggregate mean rank, $3.1/25$, among 25 methods. Controlled trajectory analyses and cross-architecture replacements confirm that our trajectory construction plays a significant role in the improvement.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Neural and Evolutionary Computing (cs.NE)
arXiv:2609.01493 [cs.LG]
(or arXiv:2609.01493v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.01493 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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