Min Max Generalization for Two-stage Deterministic Batch Mode Reinforcement Learning: Relaxation Schemes

Raphael Fonteneau; Damien Ernst; Bernard Boigelot; Quentin Louveaux

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arXiv · 1202.5298

Min Max Generalization for Two-stage Deterministic Batch Mode Reinforcement Learning: Relaxation Schemes

Raphael Fonteneau·Damien Ernst·Bernard Boigelot·Quentin Louveaux

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Abstract

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].

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BibTeX RIS

Raphael Fonteneau, Damien Ernst, Bernard Boigelot, Quentin Louveaux. 2012-02-23. Min Max Generalization for Two-stage Deterministic Batch Mode Reinforcement Learning: Relaxation Schemes. https://arxiv.org/abs/1202.5298

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