A complementarity approach for solving Leontief substitution systems and (generalized) Markov decision processes

Solving Concurrent Markov Decision Processes

Typically, Markov decision problems (MDPs) assume a single action is executed per decision epoch, but in the real world one may frequently execute certain actions in parallel. This paper explores concurrent MDPs, MDPs which allow multiple non-conflicting actions to be executed simultaneously, and presents two new algorithms. Our first approach exploits two provably sound pruning rules, and thus...

Solving Hybrid Markov Decision Processes

Markov decision processes (MDPs) have developed as a standard for representing uncertainty in decision-theoretic planning. However, MDPs require an explicit representation of the state space and the probabilistic transition model which, in continuous or hybrid continuousdiscrete domains, are not always easy to define. Even when this representation is available, the size of the state space and t...

Solving Uncertain Markov Decision Processes

The authors consider the fundamental problem of nding good policies in uncertain models. It is demonstrated that although the general problem of nding the best policy with respect to the worst model is NP-hard, in the special case of a convex uncertainty set the problem is tractable. A stochastic dynamic game is proposed, and the security equilibrium solution of the game is shown to correspond ...

Solving Large Markov Decision Processes

Accelerated decomposition techniques for large discounted Markov decision processes

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorith...