  We provide an algorithm that uses Bayesian randomized benchmarking in concert
with a local optimizer, such as SPSA, to find a set of controls that optimizes
that average gate fidelity. We call this method Bayesian ACRONYM tuning as a
reference to the analogous ACRONYM tuning algorithm. Bayesian ACRONYM
distinguishes itself in its ability to retain prior information from
experiments that use nearby control parameters; whereas traditional ACRONYM
tuning does not use such information and can require many more measurements as
a result. We prove that such information reuse is possible under the relatively
weak assumption that the true model parameters are Lipshitz-continuous
functions of the control parameters. We also perform numerical experiments that
demonstrate that over-rotation errors in single qubit gates can be
automatically tuned from 88% to 99.95% average gate fidelity using less than
1kB of data and fewer than 20 steps of the optimizer.
