# Risk Sensitive, Nonlinear Optimal Control: Iterative Linear Exponential-Quadratic Optimal Control with Gaussian Noise

arXiv: https://arxiv.org/abs/1512.07173 · HTML: https://mlsanity.com/paper/1512.07173/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2015.

## Built on by (most cited first, 2 of 2)

- [Efficient Stochastic Optimal Control through Approximate Bayesian Input Inference](https://mlsanity.com/paper/2105.07693/) (2021)
- [Keep it Simple: Data-efficient Learning for Controlling Complex Systems with Simple Models](https://mlsanity.com/paper/2102.02493/) (2021)

## Abstract (arXiv)

In this contribution, we derive ILEG, an iterative algorithm to find risk sensitive solutions to nonlinear, stochastic optimal control problems. The algorithm is based on a linear quadratic approximation of an exponential risk sensitive nonlinear control problem. ILEG allows to find risk sensitive policies and thus generalizes previous algorithms to solve nonlinear optimal control based on iterative linear-quadratic methods. Depending on the setting of the parameter controlling the risk sensitivity, two different strategies on how to cope with the risk emerge. For positive-value parameters, the control policy uses high feedback gains whereas for negative-value parameters, it uses a robust feedforward control strategy (a robust plan) with low gains. These results are illustrated with a simple example. This note should be considered as a preliminary report.