A new two-phase UCB algorithm, Safe-LUCB, achieves Õ(√T) regret with a known positive safety gap and Õ(T^{2/3}) regret in the worst case, while keeping every action safe with high probability.
Parametric bandits: The generalized linear case
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Linear Stochastic Bandits Under Safety Constraints
A new two-phase UCB algorithm, Safe-LUCB, achieves Õ(√T) regret with a known positive safety gap and Õ(T^{2/3}) regret in the worst case, while keeping every action safe with high probability.