Constrained Feedback Learning for Non-Stationary Multi-Armed Bandits

Non-stationary multi-armed bandits (nsMAB) enable agents to adapt to changing environments by incorporating mechanisms to detect and respond to shifts in reward distributions, making them well-suited for dynamic settings. However, existing approaches typically assume that reward feedback is available at every round—an assumption that overlooks many real-world scenarios where feedback is limited.

In this paper, we take a significant step forward by introducing a new model of constrained feedback in non-stationary multi-armed bandits (ConFee-nsMAB), where the availability of reward feedback is restricted. We propose the first prior-free algorithm—that is, one that does not require prior knowledge of the degree of non-stationarity—that achieves near-optimal dynamic regret in this setting.

Specifically, our algorithm attains a dynamic regret of $\tilde{\mathcal{O}}(K^{1/3}{V}_T^{1/3}T/B^{1/3})$, where $T$ is the number of rounds, $K$ is the number of arms, $B$ is the query budget, and $V_T$ is the variation budget capturing the degree of non-stationarity.