LITE: Efficiently Estimating Gaussian Probability of Maximality

Nicolas Menet, Jonas Hübotter, Parnian Kassraie, Andreas Krause

TL;DR: We propose a competitive method for estimating the probability of maximality, which attains linear time and memory complexity.

Abstract: We consider the problem of computing the *probability of maximality* (PoM) of a Gaussian random vector, i.e., the probability for each dimension to be maximal. This is a key challenge in applications ranging from Bayesian optimization to reinforcement learning, where the PoM not only helps with finding an optimal action, but yields a fine-grained analysis of the action domain, crucial in tasks such as drug discovery. Existing techniques are costly, scaling polynomially in computation and memory with the vector size. We introduce LITE, the first approach for estimating Gaussian PoM with *almost-linear time and memory* complexity. LITE achieves SOTA accuracy on a number of tasks, while being in practice several orders of magnitude faster than the baselines. This also translates to a better performance on downstream tasks such as entropy estimation and optimal control of bandits. Theoretically, we cast LITE as entropy-regularized UCB and connect it to prior PoM estimators.

Submission Number: 1981