  We develop a non-parametric, data-driven, tractable approach for solving
multistage stochastic optimization problems in which decisions do not affect
the uncertainty. The proposed framework represents the decision variables as
elements of a reproducing kernel Hilbert space and performs functional
stochastic gradient descent to minimize the empirical regularized loss. By
incorporating sparsification techniques based on function subspace projections
we are able to overcome the computational complexity that standard kernel
methods introduce as the data size increases. We prove that the proposed
approach is asymptotically optimal for multistage stochastic optimization with
side information. Across various computational experiments on stochastic
inventory management problems, {our method performs well in multidimensional
settings} and remains tractable when the data size is large. Lastly, by
computing lower bounds for the optimal loss of the inventory control problem,
we show that the proposed method produces decision rules with near-optimal
average performance.
