Incrementality Bidding via Reinforcement Learning under Mixed and Delayed Rewards Appendix AFormal Definition of Inhomogeneous Poisson Process

The inhomogeneous Poisson (point) process is a Poisson point process with a Poisson parameter set as some time-dependent function r(τ). Let N(a,b) represent the number of points of inhomogeneous Poisson process with intensity function r(t) occurring in the interval [a,b], then the probability of n points existing in the interval [a,b] is given by, P(N(a,b) = n) Λ(a,b)n n! In this paper, the points mean the conversions and the time-dependent intensity function r() is defined in Eq. (2) and it depends on the realization of the conversions and parameter θ. Suppose X1, Xn are independent, mean-zero, subexponential random variables, and a = (a1,,an) is an ndimensional constanst vector. We first introduce the main idea of the the PAMM algorithm.