In “Optimistic Optimization of a Deterministic Function without the Knowledge of its Smoothness“, Remi Munos (2011) develops an optimization algorithm similar to hierarchical optimistic optimization, Lipschitz optimization, the Zooming algorithm (Klienberg, Slivkins, & Upfal 2008), branch and bound, and the upper confidence bound algorithm. The algorithm does not minimize regret, rather it attempts to maximize $\max_n f(x_n)$ over all the samples $x_n$. Munos’s first algorithm, Deterministic Optimistic Optimization, requires that the function be smooth with respect to a known semi-metric. His second algorithm, Simultaneous Optimistic Optimization, does not require knowledge of the smoothness semi-metric. He proves performance bounds, gives examples for both algorithms, and finishes the paper by comparing the algorithm to the well known DIRECT (DIviding RECTangles) algorithm (Jones, Perttunen, Stuckman 1993).

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