I also am curious about this statement. If a problem becomes too complex for linear programming solutions, how easy is it to know that a reinforcement learning solution is actually a global optima and not just local?
If the problem is too complex for LP then you're probably not going to get a global optimal from RL either.
However, unless there is some aspect of the problem which is not known (e.g., you don’t exactly know the objective or constraints), so you model it as a distribution over LPs, I really don’t know how RL will help you. Gradient-based methods can give you improvements if your problem is very large scale and doesn’t have, e.g., sparse structure, but the above claim is bold.