An Error Bound for Aggregation in Approximate Dynamic Programming
Optimization and Control
2026-05-06 v2 Systems and Control
Systems and Control
Abstract
We consider a general aggregation framework for discounted finite-state infinite horizon dynamic programming (DP) problems. It defines an aggregate problem whose optimal cost function can be obtained off-line by exact DP and then used as a terminal cost approximation for an on-line reinforcement learning (RL) scheme. We derive a bound on the error between the optimal cost functions of the aggregate problem and the original problem. This bound was first derived by Tsitsiklis and van Roy [TvR96] for the special case of hard aggregation. Our bound is similar but applies far more broadly, including to soft aggregation and feature-based aggregation schemes.
Cite
@article{arxiv.2507.01324,
title = {An Error Bound for Aggregation in Approximate Dynamic Programming},
author = {Yuchao Li and Dimitri Bertsekas},
journal= {arXiv preprint arXiv:2507.01324},
year = {2026}
}