Reviews: A Latent Variational Framework for Stochastic Optimization

This paper studies a variational theoretical framework for stochastic optimization. In particular, the authors showed that finding the minimizer of stochastic optimization is equivalent to finding the solution of a variational problem over a latent function space and also equivalent to finding the solution of a forward backward SDE. They also showed how to recover some popular stochastic optimization algorithms through discretizing the optimality equations defined by the SDE. However, this part is not so clear in clarity and still requires more discussion on the theoretical behavior of these discretized algorithms. Overall, this paper is well written and has strong results.