DeepAI AI Chat
Log In Sign Up

Combinatorial Bayesian Optimization using Graph Representations

02/01/2019
by   ChangYong Oh, et al.
2

This paper focuses on Bayesian Optimization - typically considered with continuous inputs - for discrete search input spaces, including integer, categorical or graph structured input variables. In Gaussian process-based Bayesian Optimization a problem arises, as it is not straightforward to define a proper kernel on discrete input structures, where no natural notion of smoothness or similarity could be provided. We propose COMBO, a method that represents values of discrete variables as vertices of a graph and then use the diffusion kernel on that graph. As the graph size explodes with the number of categorical variables and categories, we propose the graph Cartesian product to decompose the graph into smaller sub-graphs, enabling kernel computation in linear time with respect to the number of input variables. Moreover, in our formulation we learn a scale parameter per subgraph. In empirical studies on four discrete optimization problems we demonstrate that our method is on par or outperforms the state-of-the-art in discrete Bayesian optimization.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/26/2020

Combinatorial Bayesian Optimization with Random Mapping Functions to Convex Polytope

Bayesian optimization is a popular method for solving the problem of glo...
11/03/2020

Bayesian Variational Optimization for Combinatorial Spaces

This paper focuses on Bayesian Optimization in combinatorial spaces. In ...
02/25/2021

Mixed Variable Bayesian Optimization with Frequency Modulated Kernels

The sample efficiency of Bayesian optimization(BO) is often boosted by G...
01/09/2013

Bayesian Optimization in a Billion Dimensions via Random Embeddings

Bayesian optimization techniques have been successfully applied to robot...
02/02/2022

Mold into a Graph: Efficient Bayesian Optimization over Mixed-Spaces

Real-world optimization problems are generally not just black-box proble...
11/22/2022

Kernelization of Discrete Optimization Problems on Parallel Architectures

There are existing standard solvers for tackling discrete optimization p...