Three-Point Method with Zero-Order Oracle that Inexactly and Randomly Compares Function Values
Keywords: zero-order optimization, derivative-free optimization, stochastic optimization, stochastic three-point method, human feedback
Abstract: In this paper, we consider zero-order optimization setting, in which it is not possible to return the function values; instead, the oracle is only capable of comparing these values. In order to address this formulation, one can utilize the well-established stochastic three-point method, which is able to select the minimum from the three points under consideration at each iteration. Furthermore, in this setting, we assume that the oracle produces inaccurate and random results. In particular, we consider strategies in which the probability of selecting the correct value is either constant (determined by a coin flip) or dependent on the difference between the values of the function at the current point and the minimum of the three points selected at this iteration. In a further strategy, we consider the possibility that the difference value may be subject to noise, whether random or deterministic. These settings aim to obtain a more approximate description of the real-world problems that arise, for instance, in human feedback systems. We select parameters in the stochastic three-point method for all considered strategies in the different cases and evaluated the convergence rates for strongly convex, convex and non-convex optimization problems. The obtained results are verified on practical examples.
Submission Number: 32
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