Filtered poisson process bandit on a continuum

We consider a version of the continuum armed bandit where an action induces filtered realisation non-homogeneous Poisson process. Point data in sample are then revealed to decision-maker, whose reward is total number points. Using knowledge function governing filtering, but without intensity function, decision-maker seeks maximise expected points over T rounds. propose upper confidence bound algorithm for this problem utilising data-adaptive discretisation space. This approach enjoys O˜(T2/3) regret under Lipschitz assumption on function. provide lower bounds any problem, via new related finite-armed bandits, and show that orders match up logarithmic factor.