  We consider expected risk minimization problems when the range of the
estimator is required to be nonnegative, motivated by the settings of maximum
likelihood estimation (MLE) and trajectory optimization. To facilitate
nonlinear interpolation, we hypothesize that the search space is a Reproducing
Kernel Hilbert Space (RKHS). We develop first and second-order variants of
stochastic mirror descent employing (i) \emph{pseudo-gradients} and (ii)
complexity-reducing projections. Compressive projection in the first-order
scheme is executed via kernel orthogonal matching pursuit (KOMP), which
overcomes the fact that the vanilla RKHS parameterization grows unbounded with
the iteration index in the stochastic setting. Moreover, pseudo-gradients are
needed when gradient estimates for cost are only computable up to some
numerical error, which arise in, e.g., integral approximations. Under constant
step-size and compression budget, we establish tradeoffs between the radius of
convergence of the expected sub-optimality and the projection budget parameter,
as well as non-asymptotic bounds on the model complexity. To refine the
solution's precision, we develop a second-order extension which employs
recursively averaged pseudo-gradient outer-products to approximate the Hessian
inverse, whose convergence in mean is established under an additional
eigenvalue decay condition on the Hessian of the optimal RKHS element, which is
unique to this work. Experiments demonstrate favorable performance on
inhomogeneous Poisson Process intensity estimation in practice.
