I'm looking for a proof of convergence of stochastic gradient descent applied to a non-convex smooth function. I'm generally interested in just asymptotic convergence, preferably to a critical point, but not necessary to a (local) minimizer. 


I have found many relevant results but they all have some additional assumptions such as convexity.


Given that I also don't care much about speed of convergence how can I obtain the proof?



Stochastic gradient descent convergence for non-convex smooth functions
There is also a more recent literature on convergence of a randomized SGD for non-convex functions: <http://arxiv.org/pdf/1309.5549v1.pdf>


