# Convergence of Dynamic Programming on the Semidefinite Cone

arXiv: https://arxiv.org/abs/2106.09391 · HTML: https://mlsanity.com/paper/2106.09391/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2021.

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

- [A Fully Data-Driven Value Iteration for Stochastic LQR: Convergence, Robustness and Stability](https://mlsanity.com/paper/2505.02970/) (2025)

## Abstract (arXiv)

The goal of this paper is to investigate new and simple convergence analysis of dynamic programming for linear quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of both matrix inequalities and matrix norm. Under a mild assumption on the initial parameter, we prove that the Q-value iteration exponentially converges to the optimal solution. Moreover, a global asymptotic convergence is also presented. These results are then extended to the policy iteration. We prove that in contrast to the Q-value iteration, the policy iteration always converges exponentially fast. An example is given to illustrate the results.