Stochastic Zeroth-order Optimization in High Dimensions
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We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order query oracles. Such problems arise naturally in a variety of practical applications, including optimizing experimental or simulation parameters with many variables. Under sparsity assumptions on the gradients or function values, we present a successive component/feature selection algorithm and a noisy mirror descent algorithm with Lasso gradient estimates and show that both algorithms have convergence rates depending only logarithmically on the ambient problem dimension. Empirical results verify our theoretical findings and suggest that our designed algorithms outperform classical zeroth-order optimization methods in the high-dimensional setting.
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