[Feature] auto-cast optimizers to distributed version (#5746)

* auto-cast optimizers to distributed

* fix galore casting

* logger

---------

Co-authored-by: Edenzzzz <wtan45@wisc.edu>

docs/source/en/features/distributed_optimizers.md

@@ -9,7 +9,8 @@ Author: [Wenxuan Tan](https://github.com/Edenzzzz), [Junwen Duan](https://github
 - [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes] (https://arxiv.org/pdf/1904.00962)
 
 ## Introduction
-Apart from the widely adopted Adam and SGD, many modern optimizers require layer-wise statistics to efficiently update parameters, and are thus not directly applicable to parallel settings where model layers are sharded across multiple devices. We provide optimized distributed implementations with minimal extra communications, and seamless integrations with Tensor Parallel, DDP and ZeRO using plugins.
+Apart from the widely adopted Adam and SGD, many modern optimizers require layer-wise statistics to update parameters, and thus aren't directly applicable to settings where model layers are sharded across multiple devices. We provide optimized distributed implementations with minimal extra communications, and seamless integrations with Tensor Parallel, DDP and ZeRO plugins, which automatically uses distributed optimizers with 0 code change.
+
 ## Optimizers
 Adafactor is a first-order Adam variant using Non-negative Matrix Factorization(NMF) to reduce memory footprint. CAME improves by introducting a confidence matrix to correct NMF. GaLore further reduces memory by projecting gradients into a low-rank space and 8-bit block-wise quantization. Lamb allows huge batch sizes without lossing accuracy via layer-wise adaptive update bounded by the inverse of its Lipschiz constant.
 
@@ -21,7 +22,7 @@ Adafactor is a first-order Adam variant using Non-negative Matrix Factorization(
 {{ autodoc:colossalai.nn.optimizer.distributed_came.DistributedCAME }}
 
 ## Hands-On Practice
-We now demonstrate how to use Distributed Adafactor with booster API combining Tensor Parallel and ZeRO 2 with 4 GPUs.
+We now demonstrate how to use Distributed Adafactor with booster API combining Tensor Parallel and ZeRO 2 with 4 GPUs. **Note that even if you're not aware of distributed optimizers, the plugins automatically casts yours to the distributed version for convenience.**
 ### step 1. Import libraries
 
 ```python