Bayesian Optimisation of Functions on Graphs
This work addresses the need for efficient black-box optimization on large-scale or unknown graphs, which is incremental as it adapts existing Bayesian optimization to a novel graph-based setup.
The paper tackles the problem of optimizing functions defined on graph nodes by introducing a Bayesian optimization framework that learns suitable graph kernels, achieving superior sample efficiency compared to traditional graph search methods.
The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and do not make use of information about the function values; on the other hand, Bayesian optimisation is a class of promising black-box solvers with superior sample efficiency, but it has been scarcely been applied to such novel setups. To fill this gap, we propose a novel Bayesian optimisation framework that optimises over functions defined on generic, large-scale and potentially unknown graphs. Through the learning of suitable kernels on graphs, our framework has the advantage of adapting to the behaviour of the target function. The local modelling approach further guarantees the efficiency of our method. Extensive experiments on both synthetic and real-world graphs demonstrate the effectiveness of the proposed optimisation framework.