When using AutoFiniteDiff, one should be able to change the absstep and relstep parameters as described in the FiniteDiff.jl documentation. This seems to be impossible with the current DifferentiationInterface.jl API.
From this question on the Julia discourse: https://discourse.julialang.org/t/changing-the-relstep-of-autofinitediff-in-an-optimizationfunction/125004