Solving Factored MDPs with Continuous and Discrete Variables
This addresses stochastic planning problems in real-world domains like robotics or control systems that require hybrid models, representing a novel method rather than an incremental improvement.
The authors tackled the problem of solving hybrid Markov decision processes with both continuous and discrete variables, which current methods cannot handle adequately, by developing a new framework that uses a factored discretization approach to avoid exponential blow-up and demonstrated its effectiveness on control problems with up to 28-dimensional continuous state spaces.
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 first framework that can exploit problem structure for modeling and solving hybrid problems efficiently. 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). This formulation also allows us to apply our methods to collaborative multiagent settings. We present a new linear program approximation method that exploits the structure of the hybrid MDP and lets us compute approximate value functions more efficiently. 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 scale-up 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.