Solving Factored MDPs with Hybrid State and Action Variables
  Efficient representations and solutions for large decision problems with
continuous and discrete variables are among the most important challenges faced
by the designers of automated decision support systems. In this paper, we
describe a novel hybrid factored Markov decision process (MDP) model that
allows for a compact representation of these problems, and a new hybrid
approximate linear programming (HALP) framework that permits their efficient
solutions. The central idea of HALP is to approximate the optimal value
function by a linear combination of basis functions and optimize its weights by
linear programming. We analyze both theoretical and computational aspects of
this approach, and demonstrate its scale-up potential on several hybrid
optimization problems.
