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In this paper, we consider non-smooth stochastic convex optimization with twofunction evaluations per round under infinite noise variance. In the classicalsetting when noise has finite variance, an optimal algorithm, built upon thebatched accelerated gradient method, was proposed in (Gasnikov et. al., 2022).This optimality is defined in terms of iteration and oracle complexity, as wellas the maximal admissible level of adversarial noise. However, the assumptionof finite variance is burdensome and it might not hold in many practicalscenarios. To address this, we demonstrate how to adapt a refined clippedversion of the accelerated gradient (Stochastic Similar Triangles) method from(Sadiev et al., 2023) for a two-point zero-order oracle. This adaptationentails extending the batching technique to accommodate infinite variance -- anon-trivial task that stands as a distinct contribution of this paper.

Accelerated Zeroth-order Method for Non-Smooth Stochastic Convex Optimization Problem with Infinite Variance