Multi-Armed Bandit (MAB) techniques have been successfully applied to many classes of sequential decision problems in the past decades. However, non-stationary settings -- very common in real-world applications -- received little attention so far, and theoretical guarantees on the regret are known only for some frequentist algorithms. In this paper, we propose an algorithm, namely Sliding-Window Thompson Sampling (SW-TS), for nonstationary stochastic MAB settings. Our algorithm is based on Thompson Sampling and exploits a sliding-window approach to tackle, in a unified fashion, two different forms of non-stationarity studied separately so far: abruptly changing and smoothly changing. In the former, the reward distributions are constant during sequences of rounds, and their change may be arbitrary and happen at unknown rounds, while, in the latter, the reward distributions smoothly evolve over rounds according to unknown dynamics. Under mild assumptions, we provide regret upper bounds on the dynamic pseudo-regret of SW-TS for the abruptly changing environment, for the smoothly changing one, and for the setting in which both the non-stationarity forms are present. Furthermore, we empirically show that SW-TS dramatically outperforms state-of-the-art algorithms even when the forms of non-stationarity are taken separately, as previously studied in the literature.

(1) Background: In advanced non-small cell lung cancer (aNSCLC), programmed death ligand 1 (PD-L1) remains the only biomarker for candidate patients to immunotherapy (IO). This study aimed at using artificial intelligence (AI) and machine learning (ML) tools to improve response and efficacy predictions in aNSCLC patients treated with IO. (2) Methods: Real world data and the blood microRNA signature classifier (MSC) were used. Patients were divided into responders (R) and non-responders (NR) to determine if the overall survival of the patients was likely to be shorter or longer than 24 months from baseline IO. (3) Results: One-hundred sixty-four out of 200 patients (i.e., only those ones with PD-L1 data available) were considered in the model, 73 (44.5%) were R and 91 (55.5%) NR. Overall, the best model was the linear regression (RL) and included 5 features. The model predicting R/NR of patients achieved accuracy ACC = 0.756, F1 score F1 = 0.722, and area under the ROC curve AUC = 0.82. LR was also the best-performing model in predicting patients with long survival (24 months OS), achieving ACC = 0.839, F1 = 0.908, and AUC = 0.87. (4) Conclusions: The results suggest that the integration of multifactorial data provided by ML techniques is a useful tool to select NSCLC patients as candidates for IO.