SCOBO: Sparsity-Aware Comparison Oracle Based Optimization
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We study derivative-free optimization for convex functions where we further assume that function evaluations are unavailable. Instead, one only has access to a comparison oracle, which, given two points x and y, and returns a single bit of information indicating which point has larger function value, f(x) or f(y), with some probability of being incorrect. This probability may be constant or it may depend on |f(x)-f(y)|. Previous algorithms for this problem have been hampered by a query complexity which is polynomially dependent on the problem dimension, d. We propose a novel algorithm that breaks this dependence: it has query complexity only logarithmically dependent on d if the function in addition has low dimensional structure that can be exploited. Numerical experiments on synthetic data and the MuJoCo dataset show that our algorithm outperforms state-of-the-art methods for comparison based optimization, and is even competitive with other derivative-free algorithms that require explicit function evaluations.
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