Constrained Control of Large Graph-Based MDPs Under Measurement Uncertainty

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 suboptimality 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
$10^{1192}$
total states.