Traditional multi-armed bandit (MAB) frameworks, predominantly examined under stochastic or adversarial settings, often overlook the temporal dynamics inherent in many real-world applications such as recommendation systems and online advertising. This paper introduces a novel non-stationary MAB framework that captures the temporal structure of these real-world dynamics through an auto-regressive (AR) reward structure. We propose an algorithm that integrates two key mechanisms: (i) an alternation mechanism adept at leveraging temporal dependencies to dynamically balance exploration and exploitation, and (ii) a restarting mechanism designed to discard out-of-date information. Our algorithm achieves a regret upper bound that nearly matches the lower bound, with regret measured against a robust dynamic benchmark. Finally, via a real-world case study on tourism demand prediction, we demonstrate both the efficacy of our algorithm and the broader applicability of our techniques to more complex, rapidly evolving time series.

Today's online platforms rely heavily on algorithmic recommendations to bolster user engagement and drive revenue. However, such algorithmic recommendations can impact diverse stakeholders involved, namely the platform, items (seller), and users (customers), each with their unique objectives. In such multi-sided platforms, finding an appropriate middle ground becomes a complex operational challenge. Motivated by this, we formulate a novel fair recommendation framework, called Problem (FAIR), that not only maximizes the platform's revenue, but also accommodates varying fairness considerations from the perspectives of items and users. Our framework's distinguishing trait lies in its flexibility -- it allows the platform to specify any definitions of item/user fairness that are deemed appropriate, as well as decide the "price of fairness" it is willing to pay to ensure fairness for other stakeholders. We further examine Problem (FAIR) in a dynamic online setting, where the platform needs to learn user data and generate fair recommendations simultaneously in real time, which are two tasks that are often at odds. In face of this additional challenge, we devise a low-regret online recommendation algorithm, called FORM, that effectively balances the act of learning and performing fair recommendation. Our theoretical analysis confirms that FORM proficiently maintains the platform's revenue, while ensuring desired levels of fairness for both items and users. Finally, we demonstrate the efficacy of our framework and method via several case studies on real-world data.