  We propose a new least-squares Monte Carlo algorithm for the approximation of
conditional expectations in the presence of stochastic derivative weights. The
algorithm can serve as a building block for solving dynamic programming
equations, which arise, e.g., in non-linear option pricing problems or in
probabilistic discretization schemes for fully non-linear parabolic partial
differential equations. Our algorithm can be generically applied when the
underlying dynamics stem from an Euler approximation to a stochastic
differential equation. A built-in variance reduction ensures that the
convergence in the number of samples to the true regression function takes
place at an arbitrarily fast polynomial rate, if the problem under
consideration is smooth enough.
