We develop a framework for convexifying a fairly general class of
optimization problems. Under additional assumptions, we analyze the
suboptimality of the solution to the convexified problem relative to the
original nonconvex problem and prove additive approximation guarantees. We then
develop algorithms based on stochastic gradient methods to solve the resulting
optimization problems and show bounds on convergence rates. %We show a simple
application of this framework to supervised learning, where one can perform
integration explicitly and can use standard (non-stochastic) optimization
algorithms with better convergence guarantees. We then extend this framework to
apply to a general class of discrete-time dynamical systems. In this context,
our convexification approach falls under the well-studied paradigm of
risk-sensitive Markov Decision Processes. We derive the first known model-based
and model-free policy gradient optimization algorithms with guaranteed
convergence to the optimal solution. Finally, we present numerical results
validating our formulation in different applications