  We introduce a new framework that leverages machine learning models known as
generative models to solve optimization problems. Our Generator-Enhanced
Optimization (GEO) strategy is flexible to adopt any generative model, from
quantum to quantum-inspired or classical, such as Generative Adversarial
Networks, Variational Autoencoders, or Quantum Circuit Born Machines, to name a
few. Here, we focus on a quantum-inspired version of GEO relying on
tensor-network Born machines and referred to hereafter as TN-GEO. We present
two prominent strategies for using TN-GEO. The first uses data points
previously evaluated by any quantum or classical optimizer, and we show how
TN-GEO improves the performance of the classical solver as a standalone
strategy in hard-to-solve instances. The second strategy uses TN-GEO as a
standalone solver, i.e., when no previous observations are available. Here, we
show its superior performance when the goal is to find the best minimum given a
fixed budget for the number of function calls. This might be ideal in
situations where the cost function evaluation can be very expensive. To
illustrate our results, we run these benchmarks in the context of the portfolio
optimization problem by constructing instances from the S\&P 500 and several
other financial stock indexes. We also comprehensively compare state-of-the-art
algorithms in a generalized version of the portfolio optimization problem. The
results show that TN-GEO is among the best compared to these state-of-the-art
algorithms; a remarkable outcome given the solvers used in the comparison have
been fine-tuned for decades in this real-world industrial application. We see
this as an important step toward a practical advantage with quantum-inspired
models and, subsequently, with quantum generative models.
