# Factoring Exogenous State for Model-Free Monte Carlo

## TL;DR

This paper introduces MFMCi, a method that factors out exogenous state variables to enable Model-Free Monte Carlo to efficiently generate trajectories in high-dimensional MDPs, demonstrated on wildfire management.

## Contribution

MFMCi extends Model-Free Monte Carlo by factoring out exogenous variables, allowing off-policy simulation in high-dimensional MDPs.

## Key findings

- MFMCi successfully applied to wildfire management MDP.
- Factoring out exogenous variables improves MFMC scalability.
- Enhanced off-policy trajectory generation in complex environments.

## Abstract

Policy analysts wish to visualize a range of policies for large simulator-defined Markov Decision Processes (MDPs). One visualization approach is to invoke the simulator to generate on-policy trajectories and then visualize those trajectories. When the simulator is expensive, this is not practical, and some method is required for generating trajectories for new policies without invoking the simulator. The method of Model-Free Monte Carlo (MFMC) can do this by stitching together state transitions for a new policy based on previously-sampled trajectories from other policies. This "off-policy Monte Carlo simulation" method works well when the state space has low dimension but fails as the dimension grows. This paper describes a method for factoring out some of the state and action variables so that MFMC can work in high-dimensional MDPs. The new method, MFMCi, is evaluated on a very challenging wildfire management MDP.