Joint tradeoff for stochastic certification

Characterize the joint tradeoff among trusted-sample size, statistical precision, and certification frequency when the certification module is a stochastic certification oracle for mixed-fidelity stochastic optimization.

Background

The paper analyzes exact trusted-gradient certification to isolate the tradeoff between the cost of obtaining trusted information and the frequency with which optimization progress is certified. In practical applications, however, the certification module may be constructed from a finite trusted sample, expert-reviewed observations, or repeated measurements rather than providing an exact gradient.

The unresolved problem is to analyze these statistical certification mechanisms jointly with the algorithmic certification schedule. Such an analysis would need to account simultaneously for the number of trusted samples, the accuracy or confidence of the resulting certificate, and the frequency of certification during optimization with biased stochastic oracles.