# Adjustment formulas for learning causal steady-state models from closed-loop operational data

arXiv: https://arxiv.org/abs/2211.05613 · HTML: https://mlsanity.com/paper/2211.05613/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 12 references that are in the map.
- First posted on arXiv 10 Nov 2022.

## Builds on (most cited first, 1 of 1)

- [Causal Modeling of Dynamical Systems](https://mlsanity.com/paper/1803.08784/) (2018)

## Abstract (arXiv)

Steady-state models which have been learned from historical operational data may be unfit for model-based optimization unless correlations in the training data which are introduced by control are accounted for. Using recent results from work on structural dynamical causal models, we derive a formula for adjusting for this control confounding, enabling the estimation of a causal steady-state model from closed-loop steady-state data. The formula assumes that the available data have been gathered under some fixed control law. It works by estimating and taking into account the disturbance which the controller is trying to counteract, and enables learning from data gathered under both feedforward and feedback control.