{"ID":2857258,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.08908","arxiv_id":"2510.08908","title":"A Frequency-Domain Analysis of the Multi-Armed Bandit Problem: A New Perspective on the Exploration-Exploitation Trade-off","abstract":"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.","short_abstract":"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 wel...","url_abs":"https://arxiv.org/abs/2510.08908","url_pdf":"https://arxiv.org/pdf/2510.08908v1","authors":"[\"Di Zhang\"]","published":"2025-10-10T01:45:14Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"cs.IT\",\"math.OC\",\"stat.ML\"]","methods":"[\"LoRA\"]","has_code":false}