Stepsize anything: A unified learning rate schedule for budgeted-iteration training

The expanding computational costs and limited resources underscore the critical need for budgeted-iteration training, which aims to achieve optimal learning within predetermined iteration this http URL learning rate schedules fundamentally govern the performance of different networks and tasks, particularly in budgeted-iteration scenarios, their design remains largely heuristic, lacking theoretical this http URL addition, the optimal learning rate schedule requires extensive trial-and-error selection, making the training process this http URL this work, we propose the Unified Budget-Aware (UBA) schedule, a theoretically grounded learning rate schedule that consistently outperforms commonly-used schedules among diverse architectures and tasks under different constrained training this http URL, we bridge the gap by constructing a novel training budget-aware optimization framework, which explicitly accounts for the robustness to landscape curvature this http URL this framework, we derive the UBA schedule, controlled by a single hyper-parameter $\varphi$ that provides a trade-off between flexibility and simplicity, eliminating the need for per-network numerical optimization. Moreover, we establish a theoretical connection between $\varphi$ and the condition number, adding interpretation and justification to our approach. Besides, we prove the convergence for different values of $\varphi$.We offer practical guidelines for its selection via theoretical analysis and empirical this http URL experimental results show that UBA \textit{consistently surpasses} the commonly-used schedules across diverse vision and language tasks, spanning network architectures (e.g., ResNet, OLMo) and scales, under different training-iteration budgets.

@article{tang2025_2505.24452,
  title={ Stepsize anything: A unified learning rate schedule for budgeted-iteration training },
  author={ Anda Tang and Yiming Dong and Yutao Zeng and zhou Xun and Zhouchen Lin },
  journal={arXiv preprint arXiv:2505.24452},
  year={ 2025 }
}