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 al...

We show that the direct image of the filtered logarithmic de Rham complex is a direct sum of filtered logarithmic complexes with coefficients in variations of Hodge structures, using a generalization of the decomposition theorem of Beilinson, Bernstein and Deligne to the case of filtered D-modules. As a corollary, we get the total infinitesimal invariant of a (higher) cycle in a direct sum of t...