Min Max Generalization for Two-stage Deterministic Batch Mode   Reinforcement Learning: Relaxation Schemes
  We study the minmax optimization problem introduced in [22] for computing policies for batch mode reinforcement learning in a deterministic setting. First, we show that this problem is NP-hard. In the two-stage case, we provide two relaxation schemes. The first relaxation scheme works by dropping some constraints in order to obtain a problem that is solvable in polynomial time. The second relaxation scheme, based on a Lagrangian relaxation where all constraints are dualized, leads to a conic quadratic programming problem. We also theoretically prove and empirically illustrate that both relaxation schemes provide better results than those given in [22]. 
Raphael Fonteneau, Damien Ernst, Bernard Boigelot and Quentin Louveaux
cs.SY cs.LG