[matrix72c]

Stacked on #2186 (stack/rl-ppo).

Root cause

Role workers build a LambdaLR from the role's LRConfig, but RoleWorker.save() / resume() only go through DCP. The scheduler step is never written, so a resumed actor or critic restarts its LR curve from step 0, warmup included. When load_optimizer_args=True, the restored optimizer LR is also overwritten by the fresh schedule on the first step.

Fix

• save_lr_scheduler() writes lr_scheduler.json into each role's DCP directory on rank 0, also when no_save_optimizer=True.
• resume_lr_scheduler() loads it when load_checkpoint_cfg.load_scheduler is set (the default), matching the SFT trainer. A missing file raises with a hint to set load_scheduler=False, which restarts the schedule.
• In both cases the optimizer LR is set from the scheduler, so it no longer depends on whether optimizer arguments were restored.

Test plan

tests/rl/test_scheduler_checkpoint.py checks constant/linear/cosine resumes against an uninterrupted run, actor and critic wiring through TrainingWorker.save/resume with and without optimizer arguments, saving with no_save_optimizer=True, and the missing-file / restart paths. Together with test_ppo_role_wiring.py, test_routed_experts_dtype.py and test_training_worker_rank.py: 65 passed on CPU.