Cox Bayesian Optimization for Police Patrolling

Roman Marchant, Di Lu and Sally Cripps,

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