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The multi-armed bandits' framework is the most common platform to studystrategies for sequential decision-making problems. Recently, the notion offairness has attracted a lot of attention in the machine learning community.One can impose the fairness condition that at any given point of time, evenduring the learning phase, a poorly performing candidate should not bepreferred over a better candidate. This fairness constraint is known to be oneof the most stringent and has been studied in the stochastic multi-armedbandits' framework in a stationary setting for which regret bounds have beenestablished. The main aim of this paper is to study this problem in anon-stationary setting. We present a new algorithm called Fair Upper ConfidenceBound with Exploration Fair-UCBe algorithm for solving a slowly varyingstochastic $k$-armed bandit problem. With this we present two results: (i)Fair-UCBe indeed satisfies the above mentioned fairness condition, and (ii) itachieves a regret bound of $O\left(k^{\frac{3}{2}} T^{1 - \frac{\alpha}{2}}\sqrt{\log T}\right)$, for some suitable $\alpha \in (0, 1)$, where $T$ is thetime horizon. This is the first fair algorithm with a sublinear regret boundapplicable to non-stationary bandits to the best of our knowledge. We show thatthe performance of our algorithm in the non-stationary case approaches that ofits stationary counterpart as the variation in the environment tends to zero.

A Regret bound for Non-stationary Multi-Armed Bandits with Fairness Constraints