Function

Algorithm 2 details the pseudocode for the partition function used in LaMCTS, which we use in LaP3 as well. Algorithm 2 Partition Function 1: Input: Input Space Ω, Samples St, Node partition threshold Nthres, Partitioning Latent Model s(x) 2: Set V0 = {Ω} 3: Set Vqueue = {Ω} 4: while Vqueue 6= do 5: Ωp Vqueue.pop(0) It is clear that Fk(y) is a monotonically decreasing function with Fk(0) = 1 and limy + Fk(y) = 0. Here we assume it is strictly decreasing so that Fk(y) has a well-defined inverse function F 1k . In the following, we will omit the subscript k for brevity. P[f(xi) g y|xi Ωk] (4) = 1 Fntk (y) (5) Note that 1 is due to the fact that all samples x1,...,xnt are independently drawn within the region Ωk.