Constrained Control of Large Graph-Based MDPs Under Measurement Uncertainty

Abstract

We consider controlling a graph-based Markov decision process (GMDP) with a control capacity constraint given only uncertain measurements of the underlying state. We also consider two special structural properties of GMDPs, called Anonymous Influence and Symmetry. Large-scale spatial processes such as forest wildfires, disease epidemics, opinion dynamics, and robot swarms are well-modeled by GMDPs with these properties. We adopt a certainty-equivalence approach and derive efficient and scalable algorithms for estimating the GMDP state given uncertain measurements, and for computing approximately optimal control policies given a maximum-likelihood state estimate. We also derive sub-optimality bounds for our estimation and control algorithms. Unlike prior work, our methods scale to GMDPs with large state-spaces and explicitly enforce a control constraint. We demonstrate the effectiveness of our estimation and control approach in simulations of controlling a forest wildfire using a model with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{1192}$</tex-math></inline-formula> total states.