  Efficient classical optimizers are crucial in practical implementations of
Variational Quantum Algorithms (VQAs). In particular, to make Stochastic
Gradient Descent (SGD) resource efficient, adaptive strategies have been
proposed to determine the number of measurement shots used to estimate the
gradient. However, existing strategies overlook the overhead that occurs in
each iteration. In terms of wall-clock runtime, significant circuit-switching
and communication latency can slow the optimization process when using a large
number of iterations. In terms of economic cost when using cloud services,
per-task prices can become significant. To address these issues, we present an
adaptive strategy that balances the number of shots in each iteration to
maximize expected gain per unit time or cost by explicitly taking into account
the overhead. Our approach can be applied to not only to the simple SGD but
also its variants, including Adam. Numerical simulations show that our adaptive
shot strategy is actually efficient for Adam, outperforming many existing
state-of-the-art adaptive shot optimizers. However, this is not the case for
the simple SGD. When focusing on the number of shots as the resource, our
adaptive-shots Adam with zero-overhead also outperforms existing optimizers.
