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We propose a hybrid algorithmic strategy for complex stochastic optimizationproblems, which combines the use of scenario trees from multistage stochasticprogramming with machine learning techniques for learning a policy in the formof a statistical model, in the context of constrained vector-valued decisions.Such a policy allows one to run out-of-sample simulations over a large numberof independent scenarios, and obtain a signal on the quality of theapproximation scheme used to solve the multistage stochastic program. Wepropose to apply this fast simulation technique to choose the best tree from aset of scenario trees. A solution scheme is introduced, where several scenariotrees with random branching structure are solved in parallel, and where thetree from which the best policy for the true problem could be learned isultimately retained. Numerical tests show that excellent trade-offs can beachieved between run times and solution quality.

Scenario trees and policy selection for multistage stochastic programming using machine learning