提出高效估算高斯向量最大值概率的新方法，速度远超现有技术。
LITE: Efficiently Estimating Gaussian Probability of Maximality
- 基于熵正则化UCB思想设计近线性复杂度算法
- 在多项任务上达到最优精度且速度提升数个数量级
- 适合需要快速决策的强化学习与贝叶斯优化场景
本文研究高斯随机向量各维度为最大值的概率（PoM）计算问题，该问题在贝叶斯优化、强化学习等场景中至关重要，尤其在药物发现等任务中可提供细粒度动作域分析。现有方法计算与内存开销随向量长度呈多项式增长，效率低下。本文提出LITE，首个实现几乎线性时间与内存复杂度的高斯PoM估计方法。LITE在多个任务中达到当前最优精度，实际运行速度比基线快数个数量级，同时提升了下游任务如熵估计和老虎机最优控制的表现。理论上，我们将LITE建模为熵正则化UCB，并揭示其与已有PoM估计器的联系。
原文摘要 · Abstract (English)
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.
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