  In this paper, we leverage an information-theoretic upper bound on the
maximum admissible level of noise (MALN) in convex Lipschitz-continuous
zeroth-order optimisation to establish corresponding upper bounds for classes
of strongly convex and smooth problems. We derive these bounds through
non-constructive proofs via optimal reductions. Furthermore, we demonstrate
that by employing a one-dimensional grid-search algorithm, one can devise an
algorithm for simplex-constrained optimisation that offers a superior upper
bound on the MALN compared to the case of ball-constrained optimisation and
estimates asymptotic in dimensionality.
