# Newton's Lantern: A Reinforcement Learning Framework for Finetuning AC Power Flow Warm Start Models

arXiv: https://arxiv.org/abs/2605.11102 · HTML: https://mlsanity.com/paper/2605.11102/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for energy, networks and operations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- Deep reinforcement learning methods / [RL for energy, networks and operations](https://mlsanity.com/deeprl/rl-for-energy-networks-and-operations/)

## Builds on (most cited first, 8 of 8)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations](https://mlsanity.com/paper/2403.17660/) (2024)
- [PFDelta: A Benchmark Dataset for Power Flow under Load, Generation, and Topology Variations](https://mlsanity.com/paper/2510.22048/) (2025)
- [Proximal Policy Optimization with Graph Neural Networks for Optimal Power Flow](https://mlsanity.com/paper/2212.12470/) (2022)
- [Resilience Analysis and Cascading FailureModeling of Power Systems under Extreme Temperatures](https://mlsanity.com/paper/2009.14155/) (2020)
- [Data driven approach towards more efficient Newton-Raphson power flow calculation for distribution grids](https://mlsanity.com/paper/2504.11650/) (2025)
- [Reinforcement Learning to Initialize Newton-Raphson for AC Power Flow with Quantum Annealing-Based Environment Updates](https://mlsanity.com/paper/2511.20237/) (2025)

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

- [Physics-Informed but Not Physics-Consistent: Error Geometry and Subspace Projection for Neural AC Power Flow](https://mlsanity.com/paper/2610.05959/) (2026)

## Abstract (arXiv)

Neural warm starts can sharply reduce the number of Newton-Raphson iterations required to solve the AC power flow problem, but existing supervised approaches generalize poorly on heavily loaded instances near voltage collapse. We prove a lower bound on the Newton-Raphson iteration count that depends on the direction of the warm start error rather than on its magnitude, and show as a corollary that the bound becomes vacuous as the smallest singular value of the power-flow Jacobian shrinks, identifying the failure mode of supervised regression near the saddle-node bifurcation. Motivated by this analysis, we introduce Newton's Lantern, a finetuning pipeline that combines group relative policy optimization with a learned reward model trained on perturbations of the base model's predictions, using the iteration count itself as the supervisory signal. Across IEEE 118-bus, GOC 500-bus, and GOC 2000-bus benchmarks, Newton's Lantern is the only method that converges on every test snapshot while attaining the smallest mean iteration count.