# Statistical Efficiency of Single- and Multi-step Models for Forecasting and Control

arXiv: https://arxiv.org/abs/2603.23465 · HTML: https://mlsanity.com/paper/2603.23465/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2026.

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

- [Parallel Predictive World Models for Accurate and Efficient Long-Horizon Planning](https://mlsanity.com/paper/2610.08627/) (2026)

## Abstract (arXiv)

Compounding error, where small prediction mistakes accumulate over time, presents a major challenge in learning-based control. A common remedy is to train multi-step predictors directly instead of rolling out single-step models. However, it is unclear when the benefits of multi-step predictors outweigh the difficulty of learning a more complex model. We provide the first quantitative analysis of this trade-off for linear dynamical systems. We study three predictor classes: (i) single step models, (ii) multi-step models, and (iii) single step models trained with multi-step losses. We show that when the model class is well-specified and accurately captures the system dynamics, single-step models achieve the lowest asymptotic prediction error. On the other hand, when the model class is misspecified due to partial observability, direct multi-step predictors can significantly reduce bias and improve accuracy. We provide theoretical and empirical evidence that these trade-offs persist when predictors are used in closed-loop control.