Risk-Aware Multi-Armed Bandits With Refined Upper Confidence Bounds

The classical multi-armed bandit (MAB) framework studies the exploration-exploitation dilemma of decisionmaking problem and always treats arm with highest expected reward as optimal choice. However, in some applications, an a high can be risky to play if variance is high. Hence, variation should considered make arm-selection process risk-aware. In this letter, mean-variance metric investigated measure uncertainty received rewards. We first study risk-aware MAB when follows Gaussian distribution, concentration inequality on developed design risk aware-upper confidence bound algorithm. Furthermore, we extend algorithm novel asymptotic by developing upper based distribution sample variance. Theoretical analysis proves that both proposed algorithms achieve O(log(T)) regret. Finally, numerical results demonstrate our outperform several algorithms.