# Contractivity of Bellman Operator in Risk Averse Dynamic Programming with Infinite Horizon

arXiv: https://arxiv.org/abs/2208.01990 · HTML: https://mlsanity.com/paper/2208.01990/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2022.

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

- [Distributional Inverse Reinforcement Learning](https://mlsanity.com/paper/2510.03013/) (2025)

## Abstract (arXiv)

The paper deals with a risk averse dynamic programming problem with infinite horizon. First, the required assumptions are formulated to have the problem well defined. Then the Bellman equation is derived, which may be also seen as a standalone reinforcement learning problem. The fact that the Bellman operator is contraction is proved, guaranteeing convergence of various solution algorithms used for dynamic programming as well as reinforcement learning problems, which we demonstrate on the value iteration algorithm.