A Near-Optimal Algorithm for Univariate Zeroth-Order Budget Convex Optimization. (arXiv:2208.06720v1 [math.OC])

This paper studies a natural generalization of the problem of minimizing a
univariate convex function $f$ by querying its values sequentially. At each
time-step $t$, the optimizer can invest a budget $b_t$ in a query point $X_t$
of their choice to obtain a fuzzy evaluation of $f$ at $X_t$ whose accuracy
depends on the amount of budget invested in $X_t$ across times. This setting is
motivated by the minimization of objectives whose values can only be determined
approximately through lengthy …

algorithm arxiv budget math near optimization