Repository: pytorch
Issue: Restoring SequentialLR has undocumented side-effects on Optimizer
Labels: module: optimizer,triaged,actionable,module: LrScheduler,bug

### 🐛 Describe the bug

When saving and restoring optimizer and LRScheduler states, the order in which the state_dicts are restored determines whether or not the restored optimizer behaves correctly.


Consider the following example
```
import torch

model = torch.nn.Linear(10, 10)
optim = torch.optim.SGD(model.parameters(), lr=3e-5)
lr = torch.optim.lr_scheduler.LambdaLR(optim, lr_lambda=cosine_decay_linear_warmup)
lrs = []

for i in range(100):
    optim.step()
    lr.step()
    lrs.append(lr.get_last_lr())

model2 = torch.nn.Linear(10, 10)
optim2 = torch.optim.SGD(model2.parameters(), lr=3e-4)
scheduler2 = torch.optim.lr_scheduler.CosineAnnealingLR(optim2, T_max=80, eta_min=3e-5)
scheduler1 = torch.optim.lr_scheduler.LinearLR(optim2, start_factor=0.1, end_factor=1, total_iters=20)
lr2 = torch.optim.lr_scheduler.SequentialLR(optim2, schedulers=[scheduler1, scheduler2], milestones=[20])
lrs2 = []
lrs3 = []

for i in range(25):
    optim2.step()
    lr2.step()
    lrs2.append(lr2.get_last_lr())
    lrs3.append(lr2.get_last_lr())

torch.save(lr2.state_dict(), '/home/ubuntu/save_seq2.pt')
torch.save(optim2.state_dict(), '/home/ubuntu/save_optim2.pt')
    
# Correct Behavior
model2 = torch.nn.Linear(10, 10)
optim2 = torch.optim.SGD(model2.parameters(), lr=3e-4)
scheduler2 = torch.optim.lr_scheduler.CosineAnnealingLR(optim2, T_max=80, eta_min=3e-5)
scheduler1 = torch.optim.lr_scheduler.LinearLR(optim2, start_factor=0.1, end_factor=1, total_iters=20)
lr2 = torch.optim.lr_scheduler.SequentialLR(optim2, schedulers=[scheduler1, scheduler2], milestones=[20])
lr2.load_state_dict(torch.load('/home/ubuntu/save_seq2.pt'))
optim2.load_state_dict(torch.load('/home/ubuntu/save_optim2.pt'))

for i in range(25, 100):
    lr2.step()
    lrs2.append(lr2.get_last_lr())
    
# Incorrect Behavior
model2 = torch.nn.Linear(10, 10)
optim2 = torch.optim.SGD(model2.parameters(), lr=3e-4)
optim2.load_state_dict(torch.load('/home/ubuntu/save_optim2.pt'))
scheduler2 = torch.optim.lr_scheduler.CosineAnnealingLR(optim2, T_max=80, eta_min=3e-5)
scheduler1 = torch.optim.lr_scheduler.LinearLR(optim2, start_factor=0.1, end_factor=1, total_iters=20)
lr2 = torch.optim.lr_scheduler.SequentialLR(optim2, schedulers=[scheduler1, scheduler2], milestones=[20])
lr2.load_state_dict(torch.load('/home/ubuntu/save_seq2.pt'))

for i in range(25, 100):
    lr2.step()
    lrs3.append(lr2.get_last_lr())
```

The first example (with no restore) produces the following learning rate
![image](https://github.com/pytorch/pytorch/assets/1673186/bcf97286-8343-43f2-afcc-4275989699ca)


The second example where the optimizer is restored **last**, the behavior is also correct
![image](https://github.com/pytorch/pytorch/assets/1673186/b753fb87-1233-4ce0-be21-4e09cb6010db)

The third example, where the optimizer is restored **first**, the behavior is incorrect.
![image](https://github.com/pytorch/pytorch/assets/1673186/a3b1bc7b-56ad-49bb-a42a-2f2c2d19318e)

This is caused because the SequentialLR has side effects on the optimizer when it is initialized. Other LRSchedulers do not cause the same side-effects (ie order of restoring objects does not matter).







### Versions

PyTorch version: 2.2.0+cu118
Is debug build: False
CUDA used to build PyTorch: 11.8
ROCM used to build PyTorch: N/A

OS: Ubuntu 20.04.6 LTS (x86_64)
GCC version: (Ubuntu 9.4.0-1ubuntu1~20.04.2) 9.4.0
Clang version: Could not collect
CMake version: version 3.16.3
Libc version: glibc-2.31

Python version: 3.8.18 | packaged by conda-forge | (default, Dec 23 2023, 17:21:28)  [GCC 12.3.0] (64-bit runtime)
Python platform: Linux-5.15.0-1026-aws-x86_64-with-glibc2.10
Is CUDA available: True
CUDA runtime version: 11.7.99
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: 
GPU 0: NVIDIA A100-SXM4-40GB
GPU 1: NVIDIA A100-SXM4-40GB
GPU 2: NVIDIA A100-SXM4-40GB
GPU 3: NVIDIA A100-SXM4-40GB
GPU 4: NVIDIA A100-SXM4-40GB
GPU 5: NVIDIA A100-SXM4-40GB
GPU 6: NVIDIA A100-SXM4-40GB
GPU 7: NVIDIA A100-SXM4-40GB

Nvidia driver version: 515.65.01
cuDNN version: Could not collect
HIP runtime version: N/A
MIOpen runtime version: N/A
Is XNNPACK available: True

CPU:
Architecture:                    x86_64
CPU op-mode(s):                  32-bit, 64-bit
Byte Order:                      Little Endian
Address sizes:                   46 bits physical, 48 bits virtual
CPU(s):                          96
On-line CPU(s) list:             0-95
Thread(s) per core:              2
Core(s) per socket:              24
Socket(s):                       2
NUMA node(s):                    2
Vendor ID:                       GenuineIntel
CPU family:                      6
Model:                           85
Model name:                      Intel(R) Xeon(R) Platinum 8275CL CPU @ 3.00GHz
Stepping:                        7
CPU MHz:                         3000.000
BogoMIPS:                        6000.00
Hypervisor vendor:               KVM
Virtualization type:             full
L1d cache:                       1.5 MiB
L1i cache:                       1.5 MiB
L2 cache:                        48 MiB
L3 cache:                        71.5 MiB
NUMA node0 CPU(s):               0-23,48-71
NUMA node1 CPU(s):               24-47,72-95
Vulnerability Itlb multihit:     KVM: Mitigation: VMX unsupported
Vulnerability L1tf:              Mitigation; PTE Inversion
Vulnerability Mds:               Vulnerable: Clear CPU buffers attempted, no microcode; SMT Host state unknown
Vulnerability Meltdown:          Mitigation; PTI
Vulnerability Mmio stale data:   Vulnerable: Clear CPU buffers attempted, no microcode; SMT Host state unknown
Vulnerability Retbleed:          Vulnerable
Vulnerability Spec store bypass: Vulnerable
Vulnerability Spectre v1:        Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2:        Mitigation; Retpolines, STIBP disabled, RSB filling, PBRSB-eIBRS Not affected
Vulnerability Srbds:             Not affected
Vulnerability Tsx async abort:   Not affected
Flags:                           fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ss ht syscall nx pdpe1gb rdtscp lm constant_tsc arch_perfmon rep_good nopl xtopology nonstop_tsc cpuid aperfmperf tsc_known_freq pni pclmulqdq monitor ssse3 fma cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand hypervisor lahf_lm abm 3dnowprefetch invpcid_single pti fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid mpx avx512f avx512dq rdseed adx smap clflushopt clwb avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves ida arat pku ospke

Versions of relevant libraries:
[pip3] numpy==1.24.1
[pip3] torch==2.2.0+cu118
[pip3] torchaudio==2.2.0+cu118
[pip3] torchvision==0.17.0+cu118
[pip3] triton==2.2.0
[conda] numpy                     1.24.1                   pypi_0    pypi
[conda] torch                     2.2.0+cu118              pypi_0    pypi
[conda] torchaudio                2.2.0+cu118              pypi_0    pypi
[conda] torchvision               0.17.0+cu118             pypi_0    pypi
[conda] triton                    2.2.0                    pypi_0    pypi


cc @vincentqb @jbschlosser @albanD @janeyx99 @crcrpar