Adaptive sensor placement for continuous spaces

• DOI: 10.48550/arxiv.1905.06821
• Publication Date: 2019-01-01
• Authors: Grant, James; Boukouvalas, Alexis; Griffiths, Ryan-Rhys; Leslie, David; Vakili, Sattar; Munoz de Cote, En...
• Keywords: FOS: Computer and information sciences; Computer Science - Machine Learning; Statistics - Machine Learning; 0202 electrical engineering, electronic engineering, information engineering; Machine Learning (stat.ML); 02 engineering and technology; Machine Learning (cs.LG)

We consider the problem of adaptively placing sensors along an interval to detect stochastically-generated events. We present a new formulation of the problem as a continuum-armed bandit problem with feedback in the form of partial observations of realisations of an inhomogeneous Poisson process. We design a solution method by combining Thompson sampling with nonparametric inference via increasingly granular Bayesian histograms and derive an $\tilde{O}(T^{2/3})$ bound on the Bayesian regret in $T$ rounds. This is coupled with the design of an efficent optimisation approach to select actions in polynomial time. In simulations we demonstrate our approach to have substantially lower and less variable regret than competitor algorithms.<br/>13 pages, accepted to ICML 2019<br/>