# A variational formula for risk-sensitive reward

arXiv: https://arxiv.org/abs/1501.00676 · HTML: https://mlsanity.com/paper/1501.00676/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2015.

## Built on by (most cited first, 3 of 3)

- [Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control](https://mlsanity.com/paper/2109.08947/) (2021)
- [Policy Newton methods for Distortion Riskmetrics](https://mlsanity.com/paper/2508.07249/) (2025)
- [Sample Complexity of Policy Gradient for Log-Growth Control](https://mlsanity.com/paper/2605.26640/) (2026)

## Abstract (arXiv)

We derive a variational formula for the optimal growth rate of reward in the infinite horizon risk-sensitive control problem for discrete time Markov decision processes with compact metric state and action spaces, extending a formula of Donsker and Varadhan for the Perron-Frobenius eigenvalue of a positive operator. This leads to a concave maximization formulation of the problem of determining this optimal growth rate.