Acceleration Exists! Optimization Problems When Oracle Can Only Compare Objective Function Values

Frequently, the burgeoning field of black-box optimization encounters challenges due to a limited understanding of the mechanisms of the objective function. To address such problems, in this work we focus on the deterministic concept of Order Oracle, which only utilizes order access between function values (possibly with some bounded noise), but without assuming access to their values. As theoretical results, we propose a new approach to create non-accelerated optimization algorithms (obtained by integrating Order Oracle into existing optimization "tools") in non-convex, convex, and strongly convex settings that are as good as both SOTA coordinate algorithms with first-order oracle and SOTA algorithms with Order Oracle up to logarithm factor. Moreover, using the proposed approach, . And also, using an already different approach we provide the asymptotic convergence of . Finally, our theoretical results demonstrate effectiveness of proposed algorithms through numerical experiments.