# Near Optimality of Quantized Policies in Stochastic Control Under Weak Continuity Conditions

arXiv: https://arxiv.org/abs/1410.6985 · HTML: https://mlsanity.com/paper/1410.6985/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2014.

## Built on by (most cited first, 4 of 4)

- [Q-Learning for MDPs with General Spaces: Convergence and Near Optimality via Quantization under Weak Continuity](https://mlsanity.com/paper/2111.06781/) (2021)
- [Quantizer Design for Finite Model Approximations, Model Learning, and Quantized Q-Learning for MDPs with Unbounded Spaces](https://mlsanity.com/paper/2510.04355/) (2025)
- [Model approximation in MDPs with unbounded per-step cost](https://mlsanity.com/paper/2402.08813/) (2024)
- [Kernel Mean Embedding Topology: Weak and Strong Forms for Stochastic Kernels and Implications for Model Learning](https://mlsanity.com/paper/2502.13486/) (2025)

## Abstract (arXiv)

This paper studies the approximation of optimal control policies by quantized (discretized) policies for a very general class of Markov decision processes (MDPs). The problem is motivated by applications in networked control systems, computational methods for MDPs, and learning algorithms for MDPs. We consider the finite-action approximation of stationary policies for a discrete-time Markov decision process with discounted and average costs under a weak continuity assumption on the transition probability, which is a significant relaxation of conditions required in earlier literature. The discretization is constructive, and quantized policies are shown to approximate optimal deterministic stationary policies with arbitrary precision. The results are applied to the fully observed reduction of a partially observed Markov decision process, where weak continuity is a much more reasonable assumption than more stringent conditions such as strong continuity or continuity in total variation.