# SOLAR: A State-Driven Online Learning Rate Scheduler for LLM Pretraining

arXiv: https://arxiv.org/abs/2609.34681 · HTML: https://mlsanity.com/paper/2609.34681/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 53 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 38)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Population Based Training of Neural Networks](https://mlsanity.com/paper/1711.09846/) (2017)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [An Empirical Model of Large-Batch Training](https://mlsanity.com/paper/1812.06162/) (2018)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [The Road Less Scheduled](https://mlsanity.com/paper/2405.15682/) (2024)
- [Prodigy: An Expeditiously Adaptive Parameter-Free Learner](https://mlsanity.com/paper/2306.06101/) (2023)
- [Online Learning Rate Adaptation with Hypergradient Descent](https://mlsanity.com/paper/1703.04782/) (2017)
- [Learning-Rate-Free Learning by D-Adaptation](https://mlsanity.com/paper/2301.07733/) (2023)
- [Learned Optimizers that Scale and Generalize](https://mlsanity.com/paper/1703.04813/) (2017)
- [Spike No More: Stabilizing the Pre-training of Large Language Models](https://mlsanity.com/paper/2312.16903/) (2023)
- [The Sharpness Disparity Principle in Transformers for Accelerating Language Model Pre-Training](https://mlsanity.com/paper/2502.19002/) (2025)
- [Learning an Adaptive Learning Rate Schedule](https://mlsanity.com/paper/1909.09712/) (2019)
- [SPAM: Spike-Aware Adam with Momentum Reset for Stable LLM Training](https://mlsanity.com/paper/2501.06842/) (2025)

## Abstract (arXiv)

Learning-rate (LR) scheduling plays a central role in large language model (LLM) pretraining, yet current practice still relies heavily on hand-crafted heuristics such as Warmup-Cosine-Decay and Warmup-Stable-Decay. Because these schedules are fixed in advance, they cannot adapt to evolving optimization dynamics. Online learned scheduling within the Learning to Optimize (L2O) framework offers a dynamic alternative, but remains brittle at LLM scale due to noisy signals, delayed feedback, and the risk of catastrophic divergence. We propose SOLAR (State-driven Online Learning rAte scheduleR), a stabilized framework for reliable online LR adaptation. SOLAR uses a base schedule as a reference and learns bounded, state-dependent residual corrections for individual parameter groups. Each correction re-anchors to the base at every step, allowing the policy to adapt the LR without relearning the warmup-decay profile. A lightweight state representation and progress-aware reward guide online learning, while a Circuit-Breaker restores training after rare unsafe actions. Across autoregressive language-model pretraining, SOLAR improves final perplexity over tuned static schedules and automatic LR tuners for dense models from 60M to 1B, AdamW and Muon, and two MoE settings up to 3B. Matched 130M controls show that adding base anchoring and action bounds improves a global PPO controller from 27.09 to 23.74 final PPL, while group-wise control reaches 22.87 on the same two seeds. A residual policy trained on a 60M proxy can also be frozen and reused at larger dense scales without target PPO updates, remaining effective across a fourfold base-LR range. These results establish SOLAR as a practical learned LR controller for LLM pretraining.