[Bug] Resume advances Megatron scheduler with rollout_id instead of train step

Bug Description

On resume, slime does:

iteration, _ = load_checkpoint(...)
opt_param_scheduler.step(increment=iteration * args.global_batch_size)

But in slime, the saved Megatron iteration is effectively used as rollout_id, not true train step:

• save path uses save(rollout_id, ...)
• load path uses loaded_rollout_id = iteration
• then start_rollout_id = loaded_rollout_id + 1

This is fine for rollout/data-order resume, but not for scheduler resume.

Steps to Reproduce

opt_param_scheduler is stepped per successful optimizer update:

opt_param_scheduler.step(increment=args.global_batch_size)

A rollout may contain multiple train steps (num_steps_per_rollout > 1), so rollout_id * global_batch_size is not the
correct scheduler position.

Also, Megatron checkpoints already save/load scheduler state, so this extra step(...) can double-advance the scheduler.

Expected Behavior

Resume can produce right LR/WD schedule.

Actual Behavior

Resume can produce wrong LR/WD schedule, especially when:

• num_steps_per_rollout > 1
• non-constant LR schedule is used

Current ckpt tests do not catch this because they use constant LR and num_steps_per_rollout == 1.

Environment

• slime version:
• Python version:
• PyTorch version:
• CUDA/ROCm version:
• GPU type and count:
• OS:
• SGLang version (if relevant):
• Megatron-LM version (if relevant):

Logs

Additional Context

No response

Pre-submission Checklist

• I have read the CONTRIBUTING.md and understand the collaboration scope.
• I have read the documentation and my issue is not addressed there.
• I have searched for existing issues and this is not a duplicate.
• I have provided a minimal, reproducible example.

Start at the resume path around load_checkpoint and opt_param_scheduler.step, then inspect the existing checkpoint tests. Add coverage for num_steps_per_rollout greater than 1 and a non-constant LR schedule; done means resume preserves the correct LR/WD schedule without advancing it twice.