Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies -- i.e., accepting the first reward larger than a certain threshold -- can achieve tight

In reinforcement learning (RL), agents sequentially interact with changing environments while aiming to maximize the obtained rewards.

A unifying theme in the design of intelligent agents is to efficiently optimize a policy based on what prior knowledge of the problem is available and what actions can be taken to learn more about it.

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Weprovideatightregretanalysis forExpTS, whichsimultaneously yields both the finite-timeregret bound as well as the asymptotic regret bound.