Neural Predictor-Corrector (NPC) 🔄
Solving Homotopy Problems with Reinforcement Learning

ICLR 2026

Jiayao Mai^*   Bangyan Liao^*   Zhenjun Zhao^†   Yingping Zeng
Haoang Li   Javier Civera   Tailin Wu   Yi Zhou^✉   Peidong Liu^✉

^*Equal contribution  ·  ^†Project lead  ·  ^✉Corresponding authors

Official implementation of the ICLR 2026 paper: "Neural Predictor-Corrector: Solving Homotopy Problems with Reinforcement Learning"

NPC reveals that robust optimization, global optimization, polynomial root-finding, and sampling all share a common predictor-corrector structure, and learns efficient solver policies via reinforcement learning.

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🔍 Overview

Homotopy methods are ubiquitous across scientific computing, from Graduated Non-Convexity (GNC) in robust optimization to annealed Langevin dynamics in sampling. Despite their apparent diversity, these methods all follow a common predictor-corrector (PC) structure. Yet practical solvers rely on hand-crafted heuristics for step size selection and termination criteria, which are often suboptimal and require tedious per-task tuning.

NPC (Neural Predictor-Corrector) is the first unified framework that:

1. Reveals the shared predictor-corrector structure underlying these diverse homotopy problems
2. Replaces hand-crafted heuristics with learned policies trained via reinforcement learning (PPO)

At each homotopy level, NPC:

• Observes the current homotopy level, corrector statistics, and convergence velocity
• Decides the predictor step size and corrector tolerance
• Learns to optimally balance accuracy and efficiency across problem classes

✨ Highlights

• 🔗 First unified framework for homotopy methods spanning robust optimization, global optimization, polynomial root-finding, and sampling
• 🤖 RL-based policy learning via PPO replaces all hand-crafted predictor-corrector heuristics
• ✅ No per-instance tuning trains once on a problem class and generalizes to unseen instances
• 🚀 State-of-the-art efficiency with superior stability across all benchmarks

🎬 Video

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📦 Installation

Clone the repository and install dependencies:

git clone git@github.com:maijiayao1/NPC.git
cd NPC
pip install -r requirements.txt

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🚀 Usage

Training

Train a new NPC model on a target problem class:

python script/GNC_PPO_training.py --model-save-path="model/your_model_name"

Monitor training with TensorBoard:

tensorboard --logdir=./logs/ppo_gnc_tensorboard

Then open http://localhost:6006 in your browser.

Evaluation

Evaluate a trained model:

python script/GNC_PPO_inference.py --model-save-path="model/your_model_name"

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📊 Results

NPC achieves consistent speedups across all benchmark tasks. See the paper for the full evaluation.

Point Cloud Registration via Graduated Non-Convexity (GNC)

Rotation error (log E_R) and translation error (log E_t) are reported on a log₁₀ scale. NPC matches classical accuracy while reducing iterations and runtime by 4–10×.

Sequence	Method	log(E_R) ↓	log(E_t) ↓	Iter	Time (s)
bunny	Classic GNC	-0.85	-2.76	783	161.00
	IRLS GNC	-0.85	-2.75	309	61.59
	NPC + GNC	-0.85	-2.71	169	19.15
cube	Classic GNC	-1.12	-2.89	486	89.34
	IRLS GNC	-1.10	-2.90	141	26.13
	NPC + GNC	-1.11	-2.86	86	7.86
dragon	Classic GNC	-0.80	-2.82	859	177.11
	IRLS GNC	-0.80	-2.82	486	95.93
	NPC + GNC	-0.80	-2.80	201	26.42

NPC is trained on the Aquarius sequence and evaluated on unseen sequences (zero-shot generalization).

Efficiency vs. Precision Trade-off

NPC consistently achieves a better trade-off between efficiency (fewer iterations) and precision across all four task domains.

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🗃️ Code Structure

NPC/
├── assets/                     # Figures and teaser image
├── files/                      # Slides and poster (PDF)
├── Environment/
│   ├── GNC_CostFactor_PointCloudRegistration.py
│   ├── GNC_Env.py
│   └── point_cloud_registration_utils.py
├── script/
│   ├── GNC_PPO_training.py     # Training script
│   └── GNC_PPO_inference.py    # Evaluation script
├── model/                      # Saved model checkpoints
└── requirements.txt

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📝 Citation

If you find this work useful, please consider citing:

@article{mai2026neural,
  title={Neural Predictor-Corrector: Solving Homotopy Problems with Reinforcement Learning},
  author={Mai, Jiayao and Liao, Bangyan and Zhao, Zhenjun and Zeng, Yingping and Li, Haoang and Civera, Javier and Wu, Tailin and Zhou, Yi and Liu, Peidong},
  journal={arXiv preprint arXiv:2602.03086},
  year={2026}
}

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📬 Contact

For questions or feedback, feel free to reach out:

• Jiayao Mai
• Bangyan Liao
• Zhenjun Zhao