  The exponential run time of quantum simulators on classical machines and long
queue times and high costs of real quantum devices present significant
challenges in the efficient optimization of Variational Quantum Algorithms
(VQAs) like Variational Quantum Eigensolver (VQE), Quantum Approximate
Optimization Algorithm (QAOA) and Quantum Neural Networks (QNNs). To address
these limitations, we propose a new approach, DyPP (Dynamic Parameter
Prediction), which accelerates the convergence of VQAs by exploiting regular
trends in the parameter weights to update parameters. We introduce two
techniques for optimal prediction performance namely, Naive Prediction (NaP)
and Adaptive Prediction (AdaP). Through extensive experimentation and training
of multiple QNN models on various datasets, we demonstrate that DyPP offers a
speedup of approximately $2.25\times$ compared to standard training methods,
while also providing improved accuracy (up to $2.3\%$ higher) and loss (up to
$6.1\%$ lower) with low storage and computational overheads. We also evaluate
DyPP's effectiveness in VQE for molecular ground-state energy estimation and in
QAOA for graph MaxCut. Our results show that on average, DyPP leads to speedup
of up to $3.1\times$ for VQE and $2.91\times$ for QAOA, compared to traditional
optimization techniques, while using up to $3.3\times$ lesser shots (i.e.,
repeated circuit executions). Even under hardware noise, DyPP outperforms
existing optimization techniques, delivering upto $3.33\times$ speedup and
$2.5\times$ fewer shots, thereby enhancing efficiency of VQAs.
