# Finite Model Approximations and Asymptotic Optimality of Quantized Policies in Decentralized Stochastic Control

arXiv: https://arxiv.org/abs/1511.04657 · HTML: https://mlsanity.com/paper/1511.04657/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2015.

## Built on by (most cited first, 1 of 1)

- [Decentralized Multi-Agent Reinforcement Learning for Continuous-Space Stochastic Games](https://mlsanity.com/paper/2303.13539/) (2023)

## Abstract (arXiv)

In this paper, we consider finite model approximations of a large class of static and dynamic team problems where these models are constructed through uniform quantization of the observation and action spaces of the agents. The strategies obtained from these finite models are shown to approximate the optimal cost with arbitrary precision under mild technical assumptions. In particular, quantized team policies are asymptotically optimal. This result is then applied to Witsenhausen's celebrated counterexample and the Gaussian relay channel problem. For the Witsenhausen's counterexample, our approximation approach provides, to our knowledge, the first rigorously established result that one can construct an varepsilon-optimal strategy for any varepsilon > 0 through a solution of a simpler problem.