Path-aware optimistic optimization for a mobile robot

We consider problems in which a mobile robot samples an unknown function defined over its operating space, so as to find a global optimum of this function. The path traveled by the robot matters, since it influences energy and time requirements. We consider a branch-and-bound algorithm called deterministic optimistic optimization, and extend it to the path-aware setting, obtaining path-aware optimistic optimization (OOPA). In this new algorithm, the robot decides how to move next via an optimal control problem that maximizes the long-term impact of the robot trajectory on lowering the upper bound, weighted by bound and function values to focus the search on the optima. An online version of value iteration is used to solve an approximate version of this optimal control problem. OOPA is evaluated in extensive experiments in two dimensions, where it does better than path-unaware and local-optimization baselines.