Convergence results on projected stochastic approximation?

Question

For general projection-free stochastic approximation(SA) $x_{n+1}=x_n+\alpha_n (f(x_n)+M_n)$, there has been many convergence results rely on $sup\|x_n\|<\infty, a.s.$. This condition is however hard to verify in practice. So it should be natural to consider the projected SA $x_{n+1}=\prod_C (x_n+\alpha_n (f(x_n)+M_n))$ for some campact set $C$. However I couldn't find much references on its convergence. The only one I found in this paper but this paper assume the regularity of the function which is pretty strong. So I am wondering if there is any more reference on the convergence of projected SA.