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In $\mathcal{X}$-armed bandit problem an agent sequentially interacts withenvironment which yields a reward based on the vector input the agent provides.The agent's goal is to maximise the sum of these rewards across some number oftime steps. The problem and its variations have been a subject of numerousstudies, suggesting sub-linear and some times optimal strategies. The givenpaper introduces a novel variation of the problem. We consider an environment,which can abruptly change its behaviour an unknown number of times. To that endwe propose a novel strategy and prove it attains sub-linear cumulative regret.Moreover, in case of highly smooth relation between an action and thecorresponding reward, the method is nearly optimal. The theoretical result aresupported by experimental study.

How to gamble with non-stationary $\mathcal{X}$-armed bandits and have no regrets