  Bi-fidelity stochastic optimization is increasingly favored for streamlining
optimization processes by employing a cost-effective low-fidelity (LF)
function, with the goal of optimizing a more expensive high-fidelity (HF)
function. In this paper, we introduce ASTRO-BFDF, a new adaptive sampling trust
region method specifically designed for solving unconstrained bi-fidelity
stochastic derivative-free optimization problems. Within ASTRO-BFDF, the LF
function serves two purposes: first, to identify better iterates for the HF
function when a high correlation between them is indicated by the optimization
process, and second, to reduce the variance of the HF function estimates by
Bi-fidelity Monte Carlo (BFMC). In particular, the sample sizes are dynamically
determined with the option of employing either crude Monte Carlo or BFMC, while
balancing optimization error and sampling error. We demonstrate that the
iterates generated by ASTRO-BFDF converge to the first-order stationary point
almost surely. Additionally, we numerically demonstrate the superiority of our
proposed algorithm by testing it on synthetic problems and simulation
optimization problems with discrete event simulations.
