Solving Factored MDPs with Continuous and Discrete Variables

Carlos Guestrin, Milos Hauskrecht, and Branislav Kveton

Although many real-world stochastic planning problems are more naturally formulated by hybrid models with both discrete and continuous variables, current state-of-the-art methods cannot adequately address these problems. We present the rst framework that can exploit problem structure for modeling and solving hybrid problems ef ciently. We formulate these problems as hybrid Markov decision processes (MDPs with continuous and discrete state and action variables), which we assume can be represented in a factored way using a hybrid dynamic Bayesian network (hybrid DBN). We present a new linear program approximation method that exploits the structure of the hybrid MDP and lets us compute approximate value functions more ef ciently. In particular, we describe a new factored discretization of continuous variables that avoids the exponential blow-up of traditional approaches. We provide theoretical bounds on the quality of such an approximation and on its scaleup potential. We support our theoretical arguments with experiments on a set of control problems with up to 28-dimensional continuous state space and 22-dimensional action space.

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