import math
import torch
[docs]
class SOPA(torch.optim.Optimizer):
r"""
Stochastic Optimization for One-way pAUC (SOPA) is used for optimizing :obj:`~libauc.losses.pAUC_CVaR_Loss`. The key update steps are summarized as follows:
1. Initialize :math:`\mathbf s^1=0, \mathbf w_0`
2. For :math:`t=1, \ldots, T`:
3. :math:`\hspace{5mm}` Sample two mini-batches :math:`\mathcal B_+\subset\mathcal S_+` and :math:`\mathcal B_-\subset\mathcal S_-`.
4. :math:`\hspace{5mm}` Compute :math:`p_{ij} =\mathbb I (\ell(h(\mathbf w_t, \mathbf x_i) - h(\mathbf w_t, \mathbf x_j)) - s^t_i> 0)` for each positive-negative pair (:math:`\mathbf x_i\in\mathcal B_+, \mathbf x_j\in\mathcal B_-`)
5. :math:`\hspace{5mm}` Update :math:`s^{t+1}_i =s^t_i - \frac{\eta_2}{n_+} (1 - \frac{\sum_j p_{ij}}{\beta |\mathcal B_-|} )` for each positive data.
6. :math:`\hspace{5mm}` Compute a gradient estimator:
.. math::
\nabla_t = \frac{1}{\beta |\mathcal B_+||\mathcal B_-|}\sum_{\mathbf x_i\in\mathcal B_+} \sum_{\mathbf x_j\in \mathcal B_-}p_{ij}\nabla_\mathbf w L(\mathbf w_t; \mathbf x_i, \mathbf x_j)
7. :math:`\hspace{5mm}` Update :math:`\mathbf w_{t+1} =\mathbf w_t - \eta_1 \nabla_t` (or Momentum/Adam style)
For more details, please refer to `When AUC meets DRO: Optimizing Partial AUC for Deep Learning with Non-Convex Convergence Guarantee <https://proceedings.mlr.press/v162/zhu22g.html>`__.
Args:
params (iterable): iterable of parameters to optimize
loss_fn (callable): loss function used for optimization (default: ``None``)
lr (float): learning rate (default: ``0.1``)
mode (str): optimization mode, 'sgd' or 'adam' (default: ``'sgd'``)
weight_decay (float, optional): weight decay (L2 penalty) (default: ``1e-5``)
epoch_decay (float, optional): epoch decay (epoch-wise l2 penalty) (default: ``0.0``)
momentum (float, optional): momentum factor for 'sgd' mode (default: ``0.9``)
betas (Tuple[float, float], optional): coefficients used for computing
running averages of gradient and its square for 'adam' mode (default: ``(0.9, 0.999)``)
eps (float, optional): term added to the denominator to improve
numerical stability for 'adam' mode (default: ``1e-8``)
amsgrad (bool, optional): whether to use the AMSGrad variant of 'adam' mode
from the paper `On the Convergence of Adam and Beyond` (default: ``False``)
verbose (bool, optional): whether to print optimization progress (default: ``True``)
device (torch.device, optional): the device used for optimization, e.g., 'cpu' or 'cuda' (default: ``None``)
Example:
>>> optimizer = libauc.optimizers.SOPA(model.parameters(), loss_fn=loss_fn, lr=0.1, momentum=0.9)
>>> optimizer.zero_grad()
>>> loss_fn(model(input), target).backward()
>>> optimizer.step()
Reference:
.. [1] Zhu, Dixian and Li, Gang and Wang, Bokun and Wu, Xiaodong and Yang, Tianbao.
"When AUC meets DRO: Optimizing Partial AUC for Deep Learning with Non-Convex Convergence Guarantee."
In International Conference on Machine Learning, pp. 27548-27573. PMLR, 2022.
https://proceedings.mlr.press/v162/zhu22g.html
"""
def __init__(self,
params,
mode='adam',
eta=1.0,
lr=1e-3,
clip_value=1.0,
weight_decay=0,
epoch_decay=0,
betas=(0.9, 0.999),
eps=1e-8,
amsgrad=False,
momentum=0.9,
nesterov=False,
dampening=0,
verbose=False,
device=None,
**kwargs):
if not device:
self.device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
else:
self.device = device
if not 0.0 <= lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <= eps:
raise ValueError("Invalid epsilon value: {}".format(eps))
if not 0.0 <= betas[0] < 1.0:
raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
if not 0.0 <= betas[1] < 1.0:
raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
if not 0.0 <= weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
if not 0.0 <= epoch_decay:
raise ValueError("Invalid epoch_decay value: {}".format(epoch_decay))
if not isinstance(mode, str):
raise ValueError("Invalid mode type: {}".format(mode))
self.params = list(params) # support optimizing partial parameters of models
self.lr = lr
self.mode = mode.lower()
self.model_ref = self.__init_model_ref__(self.params) if epoch_decay > 0 else None
self.model_acc = self.__init_model_acc__(self.params) if epoch_decay > 0 else None
self.T = 0 # for epoch_decay
self.steps = 0 # total optimization steps
self.verbose = verbose # print updates for lr/regularizer
self.epoch_decay = epoch_decay
assert self.mode in ['adam', 'sgd'], "Keyword is not found in [`adam`, `sgd`]!"
defaults = dict(lr=lr, betas=betas, eps=eps, momentum=momentum, nesterov=nesterov, dampening=dampening,
epoch_decay=epoch_decay, weight_decay=weight_decay, amsgrad=amsgrad,
clip_value=clip_value, model_ref=self.model_ref, model_acc=self.model_acc)
super(SOPA, self).__init__(self.params, defaults)
def __setstate__(self, state):
r"""
# Set default options for sgd mode and adam mode
"""
super(SOPA, self).__setstate__(state)
for group in self.param_groups:
if self.mode == 'sgd':
group.setdefault('nesterov', False)
elif self.mode == 'adam':
group.setdefault('amsgrad', False)
else:
NotImplementedError
def __init_model_ref__(self, params):
model_ref = []
if not isinstance(params, list):
params = list(params)
for var in params:
if var is not None:
model_ref.append(torch.empty(var.shape).normal_(mean=0, std=0.01).to(self.device))
return model_ref
def __init_model_acc__(self, params):
model_acc = []
if not isinstance(params, list):
params = list(params)
for var in params:
if var is not None:
model_acc.append(torch.zeros(var.shape, dtype=torch.float32, device=self.device, requires_grad=False).to(self.device))
return model_acc
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@torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss = None
if closure is not None:
with torch.enable_grad():
loss = closure()
for group in self.param_groups:
self.lr = group['lr']
momentum = group['momentum']
dampening = group['dampening']
nesterov = group['nesterov']
model_ref = group['model_ref']
model_acc = group['model_acc']
clip_value = group['clip_value']
weight_decay = group['weight_decay']
epoch_decay = group['epoch_decay']
if self.mode == 'adam':
for i, p in enumerate(group['params']):
if p.grad is None:
continue
#grad = p.grad
if epoch_decay > 0:
grad = torch.clamp(p.grad.data , -clip_value, clip_value) + epoch_decay*(p.data - model_ref[i].data) + weight_decay*p.data
else:
grad = torch.clamp(p.grad.data , -clip_value, clip_value) + weight_decay*p.data
if grad.is_sparse:
raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
amsgrad = group['amsgrad']
state = self.state[p]
# State initialization
if len(state) == 0:
state['step'] = 0
# Exponential moving average of gradient values
state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
# Exponential moving average of squared gradient values
state['exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)
if amsgrad:
# Maintains max of all exp. moving avg. of sq. grad. values
state['max_exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)
exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
if amsgrad:
max_exp_avg_sq = state['max_exp_avg_sq']
beta1, beta2 = group['betas']
state['step'] += 1
bias_correction1 = 1 - beta1 ** state['step']
bias_correction2 = 1 - beta2 ** state['step']
#if group['weight_decay'] != 0:
# grad = grad.add(p, alpha=group['weight_decay'])
exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
# Use the max. for normalizing running avg. of gradient
denom = (max_exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
else:
denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
step_size = group['lr'] / bias_correction1
p.addcdiv_(exp_avg, denom, value=-step_size)
if epoch_decay > 0:
model_acc[i].data = model_acc[i].data + p.data
elif self.mode == 'sgd':
for i, p in enumerate(group['params']):
if p.grad is None:
continue
#d_p = p.grad
if epoch_decay > 0:
d_p = torch.clamp(p.grad.data , -clip_value, clip_value) + epoch_decay*(p.data - model_ref[i].data) + weight_decay*p.data
else:
d_p = torch.clamp(p.grad.data , -clip_value, clip_value) + weight_decay*p.data
if momentum != 0:
param_state = self.state[p]
if 'momentum_buffer' not in param_state:
buf = param_state['momentum_buffer'] = torch.clone(d_p).detach()
else:
buf = param_state['momentum_buffer']
buf.mul_(momentum).add_(d_p, alpha=1 - dampening)
if nesterov:
d_p = d_p.add(buf, alpha=momentum)
else:
d_p = buf
p.add_(d_p, alpha=-group['lr'])
if epoch_decay > 0:
model_acc[i].data = model_acc[i].data + p.data
self.steps += 1
self.T += 1
return loss
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def update_lr(self, decay_factor=None):
if decay_factor != None:
self.param_groups[0]['lr'] = self.param_groups[0]['lr']/decay_factor # for learning rate
print ('Reducing lr to %.5f @ T=%s!'%(self.param_groups[0]['lr'], self.steps))
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def update_regularizer(self, decay_factor=None):
r"""Updates learning rate given a decay factor and resets epoch-level regularizer."""
if decay_factor != None:
self.param_groups[0]['lr'] = self.param_groups[0]['lr']/decay_factor
if self.verbose:
print ('Reducing learning rate to %.5f @ T=%s!'%(self.param_groups[0]['lr'], self.steps))
if self.verbose:
print ('Updating regularizer @ T=%s!'%(self.steps))
for i, param in enumerate(self.model_ref):
self.model_ref[i].data = self.model_acc[i].data/self.T
for i, param in enumerate(self.model_acc):
self.model_acc[i].data = torch.zeros(param.shape, dtype=torch.float32, device=self.device, requires_grad=False).to(self.device)
self.T = 0