Safeguarded Accelerated Adaptive Search under Unreliable Gradient Oracles
From the probabilistic-model viewpoint, stochastic adaptive search can require any fraction $θ\in(0,1)$ of the predicted model reduction for acceptance. Classical backtracking with Nesterov acceleration pairs its momentum construction with a test certifying $1/2$ of this reduction. In stochastic search, however, rejection entails a fresh oracle query without updating the iterates. We therefore separate the fraction required by the search from that used to construct momentum, allowing smaller search fractions to ease acceptance and potentially reduce the oracle cost of reaching a target accuracy. Safeguarded Accelerated Adaptive Search (\texttt{SAAS}) addresses smooth convex optimization with unreliable gradients and inexact function value oracles. We establish high-probability trial bounds under finite-moment gradient errors allowing bias and infinite variance, or bounded corruption subject to relative-accuracy conditions. Numerical experiments demonstrate that the preferred balance between search and momentum varies with gradient reliability, and that decoupling the scales enables stable and rapid progress.