2025/10/10 by Di Zhang, Zhang, Di
Computer Science · Decision Sciences · #62L05 #68T05 #94A12 #Advanced Bandit Algorithms Research #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #G.3 #I.2.6 #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Optimization and Search Problems #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.2510.08908
openalex publication_date 2025/10/10 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
The stochastic multi-armed bandit (MAB) problem is one of the most fundamental models in sequential decision-making, with the core challenge being the trade-off between exploration and exploitation. Although algorithms such as Upper Confidence Bound (UCB) and Thompson Sampling, along with their regret theories, are well-established, existing analyses primarily operate from a time-domain and cumulative regret perspective, struggling to characterize the dynamic nature of the learning process. This paper proposes a novel frequency-domain analysis framework, reformulating the bandit process as a signal processing problem. Within this framework, the reward estimate of each arm is viewed as a spectral component, with its uncertainty corresponding to the component's frequency, and the bandit algorithm is interpreted as an adaptive filter. We construct a formal Frequency-Domain Bandit Model and prove the main theorem: the confidence bound term in the UCB algorithm is equivalent in the frequency domain to a time-varying gain applied to uncertain spectral components, a gain inversely proportional to the square root of the visit count. Based on this, we further derive finite-time dynamic bounds concerning the exploration rate decay. This theory not only provides a novel and intuitive physical interpretation for classical algorithms but also lays a rigorous theoretical foundation for designing next-generation algorithms with adaptive parameter adjustment.