  We consider risk-averse convex stochastic programs expressed in terms of
extended polyhedral risk measures. We derive computable confidence intervals on
the optimal value of such stochastic programs using the Robust Stochastic
Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the
objective functions are uniformly convex, we also propose a multistep extension
of the Stochastic Mirror Descent algorithm and obtain confidence intervals on
both the optimal values and optimal solutions. Numerical simulations show that
our confidence intervals are much less conservative and are quicker to compute
than previously obtained confidence intervals for SMD and that the multistep
Stochastic Mirror Descent algorithm can obtain a good approximate solution much
quicker than its nonmultistep counterpart. Our confidence intervals are also
more reliable than asymptotic confidence intervals when the sample size is not
much larger than the problem size.
