Dynamic Programming for Structured Continuous Markov Decision Problems

Abstract

We describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the same throughout the region. We first describe the algorithm for piecewise constant representations. We then extend it to piecewise linear representations, using techniques from POMDPs to represent and reason about linear surfaces efficiently. We show that for complex, structured problems, our approach exploits the natural structure so that optimal solutions can be computed efficiently.

Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004)

References in corpus (3)

• SPUDD: Stochastic Planning using Decision Diagrams
• Incremental Pruning: A Simple, Fast, Exact Method for Partially Observable Markov Decision Processes
• Planning under Continuous Time and Resource Uncertainty: A Challenge for AI