2024/02/27 by Jincheng Mei, Mei, Jincheng, Zixin Zhong +9
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2402.17235
openalex publication_date 2024/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the stochastic gradient bandit algorithm converges to a globally optimal policy at an O(1/t) rate, even with a constant step size. Remarkably, global convergence of the stochastic gradient bandit algorithm has not been previously established, even though it is an old algorithm known to be applicable to bandits. The new result is achieved by establishing two novel technical findings: first, the noise of the stochastic updates in the gradient bandit algorithm satisfies a strong ``growth condition'' property, where the variance diminishes whenever progress becomes small, implying that additional noise control via diminishing step sizes is unnecessary; second, a form of ``weak exploration'' is automatically achieved through the stochastic gradient updates, since they prevent the action probabilities from decaying faster than O(1/t), thus ensuring that every action is sampled infinitely often with probability 1. These two findings can be used to show that the stochastic gradient update is already ``sufficient'' for bandits in the sense that exploration versus exploitation is automatically balanced in a manner that ensures almost sure convergence to a global optimum. These novel theoretical findings are further verified by experimental results.