  We consider the sequential decision optimization on the periodic environment,
that occurs in a wide variety of real-world applications when the data involves
seasonality, such as the daily demand of drivers in ride-sharing and dynamic
traffic patterns in transportation. In this work, we focus on learning the
stochastic periodic world by leveraging this seasonal law. To deal with the
general action space, we use the bandit based on Gaussian process (GP) as the
base model due to its flexibility and generality, and propose the Periodic-GP
method with a temporal periodic kernel based on the upper confidence bound.
Theoretically, we provide a new regret bound of the proposed method, by
explicitly characterizing the periodic kernel in the periodic stationary model.
Empirically, the proposed algorithm significantly outperforms the existing
methods in both synthetic data experiments and a real data application on
Madrid traffic pollution.
