GSAM Optimizer

Surrogate Gap Guided Sharpness-Aware Minimization

[Paper, ICLR 2022] [Webpate]

Official implementation in jax: https://github.com/google-research/big_vision/tree/main/big_vision/trainers/proj/gsam

Discussion on reproducing results with jax code: google-research/big_vision#8

Disclaimer: This repository is a re-implmentation in PyTorch tested only on a Cifar10 experiment, not tested by reproduction of results in the paper.

Acknowledgement: This repository is based on https://github.com/davda54/sam

(Potentially) Unresolved issues with PyTorch code on per-worker unsynchronized gradient and weight perturbation

Since the SAM family works best wheneach worker has its own (different) gradient and weight perturbation, but in DataParallel mode in PyTorch the gradient is synchronized across workers hence perturbation is also synchronized across workers.

In order to let each worker use its own gradient, I use model.no_sync() in the code, perform the gradient decomposition in GSAM for each worker separately, then synchronize the here before feeding it to the base optimizer. However, I'm not sure if model.no_sync() only works in DistributedDataParallel mode but not in DataParallel mode.

I suppose the training script needs to be set as DistributedDataParallel in order to replicate my experiments with Jax, but I have quite limited experimence with PyTorch distributed training. Please feel free to create a PR if you are an expert on this.

Algorithm and results on ImageNet in the paper

How to use GSAM in code

For readability the essential code is highlighted (at a cost of an extra "+" sign at the beginning of line). Please remove the beginning "+" when using GSAM in your project. Each step of code is marked with notes, please read before using.

# import GSAM class and scheduler
from gsam import GSAM, LinearScheduler

# Step 0): set up base optimizer, e.g. SGD, Adam, AdaBelief ...
+base_optimizer = torch.optim.SGD(model.parameters(), lr=args.learning_rate, momentum=args.momentum, weight_decay=args.weight_decay)

# Step 1): set up learning rate scheduler. See [below](https://github.com/juntang-zhuang/GSAM/edit/main/README.md#notes-on-rho_scheduler)
# If you pass base_optimizer to lr_scheduler, lr_scheduler.step() will update lr for all trainable parameters in base_optimizer. 
# Otherwise, it only returns the value, and you need to manually assign lr to parameters in base_optimizer.
# Currently LinearScheduler, CosineScheduler and PolyScheduler are re-implemented, all have support for warmup and user-specified min value.
# You can also use torch.optim.lr_scheduler to adjust learning rate, however, in this case, it's recommended to use ProportionScheduler for rho_t.

+lr_scheduler = LinearScheduler(T_max=args.epochs*len(dataset.train), max_value=args.learning_rate, min_value=args.learning_rate*0.01, optimizer=base_optimizer)

# Step 2): set up rho_t scheduler. 
# There are two ways to set up rho_t decays proportional to lr, e.g. (lr - lr_min) / (lr_max - lr_min) = (rho - rho_min) / (rho_max - rho_min)
#
# Method a), call same scheduler twice with different ```max_value``` and ```min_value```:
#            lr_scheduler = CosineScheduler(T_max=args.epochs*len(dataset.train), max_value=args.learning_rate, min_value=args.learning_rate*0.01, optimizer=base_optimizer)
#            rho_scheduler = CosineScheduler(T_max=args.epochs*len(dataset.train), max_value=args.rho_max, min_value=args.rho_min)
#
# Method b), call the ```ProportionScheduler``` class:
#            lr_scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(base_optimizer, T_max, eta_min=0, last_epoch=- 1, verbose=False)
#            rho_scheduler = ProportionScheduler(lr_scheduler, max_lr=args.learning_rate, min_lr=args.min_lr, max_value=args.rho_max, min_value=args.rho_min)
+rho_scheduler = LinearScheduler(T_max=args.epochs*len(dataset.train), max_value=args.rho_max, min_value=args.rho_min)

# Step 3): configure GSAM
+gsam_optimizer = GSAM(params=model.parameters(), base_optimizer=base_optimizer, model=model, gsam_alpha=args.alpha, rho_scheduler=rho_scheduler, adaptive=args.adaptive)

# ============================================================================================
# training loop

for batch in dataset.train:
    inputs, targets = (b.cuda() for b in batch)
        
    # Step 4): Define loss function, so that loss_fn only takes two inputs (predictions, targets), and outputs a scalar valued loss.
    # If you have auxialliary parameters e.g. arg1, arg2, arg3 ..., please define as:
    #           criterion = nn.CrossEntropyLoss()
    #           loss_fn = lambda predictions, targets: criterion(predictions, targets, arg1=arg1, arg2=arg2, arg3=arg3 ...)
    
+   def loss_fn(predictions, targets):
+       return smooth_crossentropy(predictions, targets, smoothing=args.label_smoothing).mean()
    
    # Step 5): Set closure, GSAM automatically sets the closure as
    #            predictions = model(inputs), loss = loss_fn(predictions, targets), loss.backward()
    # Note: need to set_closure for each (inputs, targets) pair
    
+   gsam_optimizer.set_closure(loss_fn, inputs, targets)
    
    # Step 6): Update model parameters. 
    # optimizer.step() internally does the following: 
    #            (a) zero grad (b) get gradients (c) get rho_t from rho_scheduler (d) perturb weights (e) zero grad (f) get gradients at perturbed location
    #            (g) decompose gradients and update gradients (h) apply new gradients with base_optimizer
    # Note: zero_grad is called internally for every step of GSAM.step(), gradient accumulation is currently not supported
    
+   predictions, loss = gsam_optimizer.step()

    # Step 7): Upate lr and rho_t
+   lr_scheduler.step()
+   gsam_optimizer.update_rho_t()
# ============================================================================================

Notes on rho_scheduler

Case 1 (same as in paper for ImageNet experiments):

If you use the same type for lr_scheduler and rho_scheduler, it's equivalent to let rho_t evolves proportionally with learning rate, (lr - lr_min) / (lr_max - lr_min) = (rho - rho_min) / (rho_max - rho_min)

Example to use the same type of scheduler for rho and lr:

Method 1.1) Call the same Scheduler class twice for lr_scheduler and rho_scheduler

from gsam.scheduler import LinearScheduler
lr_scheduler = LinearScheduler(T_max=args.epochs*len(dataset.train), max_value=args.learning_rate, min_value=args.learning_rate*0.01, optimizer=base_optimizer, warmup_step=2000)
rho_scheduler = LinearScheduler(T_max=args.epochs*len(dataset.train), max_value=args.rho_max, min_value=args.rho_min, warmup_step=2000)

from gsam.scheduler import CosineScheduler
lr_scheduler = CosineScheduler(T_max=args.epochs*len(dataset.train), max_value=args.learning_rate, min_value=args.learning_rate*0.01, optimizer=base_optimizer, warmup_step=2000)
rho_scheduler = CosineScheduler(T_max=args.epochs*len(dataset.train), max_value=args.rho_max, min_value=args.rho_min, warmup_step=2000)

Method 1.2) Create an lr_scheduler from torch.optim.lr_scheduler, then call gsam.scheduler.ProportionScheduler

from torch.optim.lr_scheduler import CosineAnnealingLR
from gsam.scheduler import ProportionScheduler
base_optimizer = torch.optim.SGD(model.parameters(), lr=args.learning_rate)
lr_scheduler = CosineAnnealingLR(optimizer=base_optimizer, T_max=args.epochs*len(dataset.train), eta_min=args.learning_rate*0.01)
rho_scheduler = ProportionScheduler(pytorch_lr_scheduler=lr_scheduler, max_lr=args.learning_rate, min_lr=args.learning_rate*0.01, max_value=args.rho_max, min_value=args.rho_min)

Case 2 (write your own scheduler)

1. You can also write your own shceduler by inherit gsam.scheduler.SchedulerBase class and define step_func.
2. You can write your own lr scheduler by inheriting torch.optim.lr_scheduler._LRScheduler, or combining several schedulers using torch.optim.lr_scheduler.SequentialLR. After creating your own lr_scheduler, call gsam.ProportionScheduler to create rho_scheduler.

Citation

@inproceedings{
zhuang2022surrogate,
title={Surrogate Gap Minimization Improves Sharpness-Aware Training},
author={Juntang Zhuang and Boqing Gong and Liangzhe Yuan and Yin Cui and Hartwig Adam and Nicha C Dvornek and sekhar tatikonda and James s Duncan and Ting Liu},
booktitle={International Conference on Learning Representations},
year={2022},
url={https://openreview.net/forum?id=edONMAnhLu-}
}