LITE: Efficiently Estimating Gaussian Probability of Maximality
This addresses a key bottleneck in applications like Bayesian optimization and reinforcement learning, offering significant speed improvements for tasks such as drug discovery, though it is an incremental advancement in method efficiency.
The paper tackles the problem of efficiently computing the probability of maximality (PoM) for Gaussian random vectors, which is computationally expensive with existing methods, and introduces LITE, achieving state-of-the-art accuracy with almost-linear time and memory complexity, making it several orders of magnitude faster in practice.
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.