Adaptive Aggregation Methods for Infinite Horizon Dynamic Programming

We propose a class of iterative aggregation algorithms for solving infinite horizon dynamic programming problems. The idea is to interject aggregation iterations in the course of the usual successive approximation method. An important new feature that sets our method apart from earlier proposals is that the aggregate groups of states change adaptively from one aggregation iteration to the next, depending on the progress of the computation. This allows acceleration of convergence in difficult problems involving multiple ergodic classes for which methods using fixed groups of aggregate states are ineffective. No knowledge of special problem structure is utilized by the algorithms.