无需标签即可自动选优化算法,用多核聚类提升泛化能力。
Unsupervised Multi-kernel Learning for Automated Algorithm Selection

- 基于多核聚类对问题特征分组,不依赖性能标签。
- 在DE算法上表现最优,PSO上接近领先方法。
- 能自适应筛选有效特征表示,适合黑箱优化场景。
黑箱优化中的自动算法选择通常依赖于监督模型,将景观特征映射到算法性能标签。这类模型训练成本高、依赖基准测试,且难以推广至未见问题类别。本文研究了一种无监督替代方案:基于异构景观表征的多核聚类,在聚类阶段不使用性能标签,再通过独立三阶段评估协议将聚类结果映射为求解器推荐。基于二十年来多核学习的发展,采用多核k-means框架,联合学习簇分配与四个异构景观视图(ELA、DeepELA、DoE2Vec、TransOptAS)的核权重。在固定评估预算下,针对差分进化(DE)和粒子群优化(PSO)的仿射BBOB衍生选择任务,报告了50次独立随机种子的均值±标准差选择器性能。多核聚类在DE组合中取得最强平均表现,于更紧凑的PSO组合中保持竞争力且略优于领先基线,各方法间差异相对于随机波动较小。代表性中位种子运行中,学习到的核权重保留了ELA和TransOptAS,对DeepELA和DoE2Vec赋零权重,揭示了该多核模型在面向选择的分组中保留的有效表征。
原文摘要 · Abstract (English)
Automated algorithm selection in black-box optimization typically relies on supervised models that map landscape features to algorithm performance labels. Such models are costly to train, benchmark-dependent, and often fail to generalize to unseen problem classes. We study an unsupervised alternative: multi-kernel clustering over heterogeneous landscape representations, in which problem instances are grouped without using performance labels in the clustering stage, and the resulting clusters are mapped post hoc to solver recommendations through a strictly separated three-stage evaluation protocol. Drawing on two decades of advances in multiple kernel learning, we adopt a multi-kernel k-means formulation that jointly learns cluster assignments and kernel weights over four heterogeneous landscape views: ELA, DeepELA, DoE2Vec, and TransOptAS. On affine BBOB-derived selector tasks for Differential Evolution (DE) and Particle Swarm Optimization (PSO) at a fixed evaluation budget, we report mean plus or minus standard deviation selector profiles over 50 independent random seeds for stochastic configurations. Multi-kernel clustering obtains the strongest mean profile on the DE portfolio and remains competitive with, and nominally ahead of, the leading baselines on the more compressed PSO portfolio, where differences among the best methods are small relative to stochastic variation. In representative median-seed runs used for visualization, the learned kernel weights retain ELA and TransOptAS while assigning zero weight to DeepELA and DoE2Vec, providing a task-specific interpretation of which representations are retained by the multi-kernel model for selector-oriented grouping.
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