Analogical-based Bayesian Optimization
This addresses optimization challenges in domains like distribution spaces, but it appears incremental as it extends existing Bayesian Optimization frameworks.
The paper tackles the problem of optimizing black-box functions over domains where only a similarity score is defined, such as non-vectorial objects like distributions, by proposing Analogical-based Bayesian Optimization, which generalizes Gaussian Processes to use generic similarity scores and includes strategies for batch querying in high-dimensional data.
Some real-world problems revolve to solve the optimization problem \max_{x\in\mathcal{X}}f\left(x\right) where f\left(.\right) is a black-box function and X might be the set of non-vectorial objects (e.g., distributions) where we can only define a symmetric and non-negative similarity score on it. This setting requires a novel view for the standard framework of Bayesian Optimization that generalizes the core insightful spirit of this framework. With this spirit, in this paper, we propose Analogical-based Bayesian Optimization that can maximize black-box function over a domain where only a similarity score can be defined. Our pathway is as follows: we first base on the geometric view of Gaussian Processes (GP) to define the concept of influence level that allows us to analytically represent predictive means and variances of GP posteriors and base on that view to enable replacing kernel similarity by a more genetic similarity score. Furthermore, we also propose two strategies to find a batch of query points that can efficiently handle high dimensional data.