# Multilevel Optimization for Inverse Problems

arXiv: https://arxiv.org/abs/2204.13732 · HTML: https://mlsanity.com/paper/2204.13732/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2022.

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

- [Structure Matters: Dynamic Policy Gradient](https://mlsanity.com/paper/2411.04913/) (2024)
- [Adaptive Kernel Selection for Stein Variational Gradient Descent](https://mlsanity.com/paper/2510.02067/) (2025)
- [The Role of Target Update Frequencies in Q-Learning](https://mlsanity.com/paper/2602.03911/) (2026)

## Abstract (arXiv)

Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying framework of multilevel optimization that can be applied to a wide range of optimization-based solvers. Our framework provably reduces the computational cost associated with evaluating the expensive forward maps stemming from various physical models. To demonstrate the versatility of our analysis, we discuss its implications for various methodologies including multilevel (accelerated, stochastic) gradient descent, a multilevel ensemble Kalman inversion and a multilevel Langevin sampler. We also provide numerical experiments to verify our theoretical findings.