Solving Very Large Weakly Coupled Markov Decision Processes

Nicolas Meuleau, Milos Hauskrecht, Kee-Eung Kim, Leonid Peshkin, Leslie Pack Kaelbling, Thomas Dean, Craig Boutilier

We present a technique for computing approximately optimal solutions to stochastic resource allocation problems modeled as Markov decision processes (MDPs). We exploit two key properties to avoid explicitly enumerating the very large state and action spaces associated with these problems. First, the problems are composed of multiple tasks whose utilities are independent. Second, the actions taken with respect to (or resources allocated to) a task do not influence the status of any other task. We can therefore view each task as an MDP. However, these MDPs are weakly coupled by resource constraints: actions selected for one MDP restrict the actions available to others. We describe heuristic techniques for dealing with several classes of constraints that use the solutions for individual MDPs to construct an approximate global solution. We demonstrate this technique on problems involving thousandsof tasks, approximating the solution to problems that are far beyond the reach of standard methods.

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