Finite-sample performance guarantees for one-dimensional stochastic root finding

We study the one-dimensional root finding problem for increasing convex functions. We give gradient-free algorithms for both exact and inexact (stochastic) function evaluations. For the stochastic case, we supply a probabilistic convergence guarantee in the spirit of selection-of-the-best methods. A worst-case bound on the work performed by the algorithm shows an improvement over naive stochastic bisection.