Repository: pytorch
Issue: FSDP convergence issue with CPU offload
Labels: oncall: distributed,triaged,module: fsdp

### 🐛 Describe the bug

We have seen the convergence [issue](https://github.com/facebookresearch/llama-recipes/issues/360) when using FSDP with CPU offload, training loss/ acc looks better without CPU offload. Talked off line with @awgu and opening this issue to keep track of it.

<img width="573" alt="300444679-e0aa45c7-cbe8-404d-8e10-e0d96ad63e52" src="https://github.com/pytorch/pytorch/assets/9162336/2747d342-80b2-4502-8979-ddac2d93f0b9">


[CPU offload](https://gist.github.com/HamidShojanazeri/ede2f72d2f4caa1ce89b8016355f61c7)
avg_train_prep, Value: 1.0844144423802693
avg_train_loss, Value: 0.08095582574605942

[No CPU offload](https://gist.github.com/HamidShojanazeri/576cd5dd391a1c3a4d9458441e48a937)

avg_train_prep, Value: 1.0553292433420818
avg_train_loss, Value: 0.05351858213543892


### Versions

```
Collecting environment information...
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 3.27.7
Libc version: glibc-2.31

Python version: 3.10.13 (main, Sep 11 2023, 13:44:35) [GCC 11.2.0] (64-bit runtime)
Python platform: Linux-5.15.0-1048-aws-x86_64-with-glibc2.31
Is CUDA available: True
CUDA runtime version: 12.1.105
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: 535.104.12
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:                            2999.998
BogoMIPS:                           5999.99
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 Gather data sampling: Unknown: Dependent on hypervisor status
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 rstack overflow: Not affected
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] mypy-extensions==1.0.0
[pip3] numpy==1.26.3
[pip3] torch==2.2.0+cu118
[pip3] triton==2.2.0
[conda] numpy                     1.26.3                   pypi_0    pypi
[conda] torch                     2.2.0+cu118              pypi_0    pypi
[conda] triton                    2.2.0                    pypi_0    pypi
```

cc @mrshenli @pritamdamania87 @zhaojuanmao @satgera @rohan-varma @gqchen @aazzolini @osalpekar @jiayisuse @H-Huang @kwen2501 @awgu @penguinwu @fegin @XilunWu @wanchaol @fduwjj @wz337 @tianyu-l @wconstab @yf225