  Many important challenges in science and technology can be cast as
optimization problems. When viewed in a statistical physics framework, these
can be tackled by simulated annealing, where a gradual cooling procedure helps
search for groundstate solutions of a target Hamiltonian. While powerful,
simulated annealing is known to have prohibitively slow sampling dynamics when
the optimization landscape is rough or glassy. Here we show that by
generalizing the target distribution with a parameterized model, an analogous
annealing framework based on the variational principle can be used to search
for groundstate solutions. Modern autoregressive models such as recurrent
neural networks provide ideal parameterizations since they can be exactly
sampled without slow dynamics even when the model encodes a rough landscape. We
implement this procedure in the classical and quantum settings on several
prototypical spin glass Hamiltonians, and find that it significantly
outperforms traditional simulated annealing in the asymptotic limit,
illustrating the potential power of this yet unexplored route to optimization.
