Solving Optimization Problems with Continuous Variables within the Generator-Enhanced Optimization Framework

Recently, the Generator-Enhanced Optimization (GEO) framework [arXiv:2101.06250v2] has been proposed to solve combinatorial optimization problems, leveraging classical, quantum, quantum-inspired or hybrid generative models to generate solutions to such problems. In this work, we extend the domain of GEO to continuous variables (cGEO), broadening its application to a more general spectrum of optimization problems that arise in science and the industry. Crucially, cGEO excels at generating low-cost candidate solutions when the number of cost function evaluations is limited due to expensive computational cost. We show how our framework utilizes local optimization routines, including gradient-based optimizers, to exploit the cost function. In other words, cGEO acts as a cost landscape exploration mechanism that serves as a computationally cheap initialization strategy for minimizing a cost function through a local optimizer. We showcase cGEO in benchmark continuous optimization problems for different classical and quantum generative models including continuous variational autoencoders, Wasserstein generative adversarial networks (WGANs) and quantum circuit associative adversarial networks (QC-AANs).