learning rate schedule

Learning rate schedules adjust learning rate during training to improve convergence and final performance. **Why schedule**: High LR early for fast progress, lower LR later for fine-grained optimization. Fixed LR may oscillate or plateau. **Common schedules**: **Step decay**: Reduce LR by factor at specific epochs. Simple but discontinuous. **Cosine annealing**: Smooth cosine decay to near-zero. Popular for vision and LLMs. **Linear decay**: Constant decrease. Often used after warmup. **Exponential decay**: Multiply by constant each step. **Inverse sqrt**: LR proportional to 1/sqrt(step). Common for transformers. **Warmup + decay**: Warmup to peak, then decay. Standard for LLM training. **Choosing schedule**: Cosine is safe default. Experiment if training plateaus or diverges. **One-cycle**: Peak in middle, aggressive decay at end. Can improve convergence. **Implementation**: PyTorch schedulers (CosineAnnealingLR, OneCycleLR), TensorFlow schedules. **Interaction with optimizer**: Adaptive optimizers (Adam) already adjust effectively, but schedule still helps. **Tuning**: LR is most important hyperparameter. Schedule is second-order but impactful.