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In this paper, we propose an alternative technique to dynamic programming forsolving stochastic control problems. We consider a weak formulation that iswritten as an optimization (minimization) problem on the space ofprobabilities. We then propose a regularized version of this problem obtainedby splitting the minimization variables and penalizing the entropy between thetwo probabilities to be optimized. We show that the regularized problemprovides a good approximation of the original problem when the weight of theentropy regularization term is large enough. Moreover, the regularized problemhas the advantage of giving rise to optimization problems that are easy tosolve in each of the two optimization variables when the other is fixed. Wetake advantage of this property to propose an alternating optimizationalgorithm whose convergence to the infimum of the regularized problem is shown.The relevance of this approach is illustrated by solving a high-dimensionalstochastic control problem aimed at controlling consumption in electricalsystems.

An entropy penalized approach for stochastic control problems. Complete version