Nicolas Menet

Nicolas Menet, Jonas Hübotter, Parnian Kassraie et al.

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.

Nicolas Menet, Aleksandar Terzić, Michael Hersche et al.

Bayesian optimization in large unstructured discrete spaces is often hindered by the computational cost of maximizing acquisition functions due to the absence of gradients. We propose a scalable alternative based on Thompson sampling that eliminates the need for acquisition function maximization by directly parameterizing the probability that a candidate yields the maximum reward. Our approach, Thompson Sampling via Fine-Tuning (ToSFiT) leverages the prior knowledge embedded in prompt-conditioned large language models, and incrementally adapts them toward the posterior. Theoretically, we derive a novel regret bound for a variational formulation of Thompson Sampling that matches the strong guarantees of its standard counterpart. Our analysis reveals the critical role of careful adaptation to the posterior probability of maximality--a principle that underpins our ToSFiT algorithm. Empirically, we validate our method on three diverse tasks: FAQ response refinement, thermally stable protein search, and quantum circuit design. We demonstrate that online fine-tuning significantly improves sample efficiency, with negligible impact on computational efficiency.