Adaptive Sensor Placement for Continuous Spaces
This addresses sensor placement optimization for applications like environmental monitoring, though it is incremental as it builds on existing bandit and inference methods.
The paper tackles the problem of adaptively placing sensors in continuous spaces to detect stochastic events, achieving an $ ilde{O}(T^{2/3})$ Bayesian regret bound and demonstrating lower regret than competitors in simulations.
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.