- Abstract: This paper presents a generalization of Bayesian Optimization (BO) that can cope with objective functions defined over discrete spaces. Typically, BO assumes a latent model represented by a Gaussian Process (GP) prior under Gaussian likeli- hood assumptions. This works well for continuous real valued objective functions that are Lipschitz continuous. However, discontinuous objective functions, which are a consequence of discrete inputs and outputs, present important challenges. The contribution in this paper is to address these challenges by making use of Generalized Gaussian Processes Models (GGPM), which have a Gaussian Process as an argument of the link function, and Monte Carlo Tree Search (MCTS) to deal with discrete inputs. We evaluate the proposed algorithms over a synthetic objective function and a real world process, both of which have integer output values as counts and discrete input locations.
- Keywords: bayesian optimisation, police patrolling, predictive policing, decision making, spatial temporal