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We propose a fully backward representation of semilinear PDEs withapplication to stochastic control. Based on this, we develop a fully backwardMonte-Carlo scheme allowing to generate the regression grid, backwardly intime, as the value function is computed. This offers two key advantages interms of computational efficiency and memory. First, the grid is generatedadaptively in the areas of interest and second, there is no need to store theentire grid. The performances of this technique are compared in simulations tothe traditional Monte-Carlo forward-backward approach on a control problem ofthermostatic loads.

A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems