  A key component of variational quantum algorithms (VQAs) is the choice of
classical optimizer employed to update the parameterization of an ansatz. It is
well recognized that quantum algorithms will, for the foreseeable future,
necessarily be run on noisy devices with limited fidelities. Thus, the
evaluation of an objective function (e.g., the guiding function in the quantum
approximate optimization algorithm (QAOA) or the expectation of the electronic
Hamiltonian in variational quantum eigensolver (VQE)) required by a classical
optimizer is subject not only to stochastic error from estimating an expected
value but also to error resulting from intermittent hardware noise. Model-based
derivative-free optimization methods have emerged as popular choices of a
classical optimizer in the noisy VQA setting, based on empirical studies.
However, these optimization methods were not explicitly designed with the
consideration of noise. In this work we adapt recent developments from the
``noise-aware numerical optimization'' literature to these commonly used
derivative-free model-based methods. We introduce the key defining
characteristics of these novel noise-aware derivative-free model-based methods
that separate them from standard model-based methods. We study an
implementation of such noise-aware derivative-free model-based methods and
compare its performance on demonstrative VQA simulations to classical solvers
packaged in \texttt{scikit-quant}.
