  We propose a fully backward representation of semilinear PDEs with
application to stochastic control. Based on this, we develop a fully backward
Monte-Carlo scheme allowing to generate the regression grid, backwardly in
time, as the value function is computed. This offers two key advantages in
terms of computational efficiency and memory. First, the grid is generated
adaptively in the areas of interest and second, there is no need to store the
entire grid. The performances of this technique are compared in simulations to
the traditional Monte-Carlo forward-backward approach on a control problem of
thermostatic loads.
