  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, we provide the first accelerated optimization
algorithm using the Order Oracle. And also, using an already different approach
we provide the asymptotic convergence of the first algorithm with the
stochastic Order Oracle concept. Finally, our theoretical results demonstrate
effectiveness of proposed algorithms through numerical experiments.
