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We propose an algorithm for estimating the finite-horizon expected return of a closed loop control policy from an a priori given (off-policy) sample of one-step transitions. This algorithm, named Model-free Monte Carlo (MFMC) estimator, averages cumulated rewards along a set of "broken trajectories" made of one-step transitions selected from the sample on the basis of the control policy. Under some Lipschitz continuity assumptions on the system dynamics, reward function and control policy, we provide bounds on the bias and variance of the estimator that depend only on the Lipschitz constants, on the number of broken trajectories used in the estimator, and on the sparsity of the sample of one-step transitions.

Estimation Monte Carlo sans modèle de politiques de décision