Bayesian Optimization of Functions over Node Subsets in Graphs
Keywords: Bayesian Optimization, Graphs
TL;DR: This paper extends Bayesian optimization to a novel graph setting, where the search space consists of node subsets in a generic graph.
Abstract: We address the problem of optimizing over functions defined on node subsets in a graph. The optimization of such functions is often a non-trivial task given their combinatorial, black-box and expensive-to-evaluate nature. Although various algorithms have been introduced in the literature, most are either task-specific or computationally inefficient and only utilize information about the graph structure without considering the characteristics of the function. To address these limitations, we utilize Bayesian Optimization (BO), a sample-efficient black-box solver, and propose a novel framework for combinatorial optimization on graphs. More specifically, we map each $k$-node subset in the original graph to a node in a new combinatorial graph and adopt a local modeling approach to efficiently traverse the latter graph by progressively sampling its subgraphs using a recursive algorithm. Extensive experiments under both synthetic and real-world setups demonstrate the effectiveness of the proposed BO framework on various types of graphs and optimization tasks, where its behavior is analyzed in detail with ablation studies.
Primary Area: Optimization (convex and non-convex, discrete, stochastic, robust)
Submission Number: 4018
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