UTA: Universal Training Adaptive Learning Rate Decay

Learning rate decay (LRD) is critical for training high-performance models, yet most designs remain empirically driven. Although the Universal Budget Aware (UBA) LRD offers a theoretical framework, its reliance on SGD dynamics limits its applicability to modern Adam-type optimizers and leaves its key `optimization difficulty parameter' opaque. To bridge this gap, we propose the Universal Training Adaptive (UTA) LRD. Unlike UBA's fixed offline trajectory anchored solely to iterations, UTA treats LRD as a closed-loop shape-and-scale problem. By continuous-time formulation, UTA is training-state adaptive with segment-wise optimal shape. This adaptivity links external iterations with internal training states, enabling a near-optimal path in both progression shape and learning rate (LR) scale, a property unattainable by other LRDs, including UBA. Empirically, we demonstrate consistent improvements across language models (LLaMA 60M to 1B) and vision models (ResNet50, ViT-B) on ImageNet with plug-and-play ease and negligible overhead. Extensive ablation studies further confirm UTA's robustness across dimensions, including peak LR, final decay ratio, its parameter $φ_0$, component efficacy and generalization to fine-tuning scenarios, underscoring its practical implementability.