def run_GN_iter(self, num_cg_iter):
"""Runs a single GN iteration."""
self.x.requires_grad(True)
# Evaluate function at current estimate
self.f0 = self.problem(self.x)
# Create copy with graph detached
self.g = self.f0.vdetach()
if self.debug and not self.analyze_convergence:
loss = self.problem.ip_output(self.g, self.g)
self.losses = torch.cat(
(self.losses, loss.detach().cpu().view(-1)))
self.g.requires_grad(True)
# Get df/dx^t @ f0
self.dfdxt_g = TensorList(
torch.autograd.grad(self.f0, self.x, self.g, create_graph=True))
# Get the right hand side
self.b = -self.dfdxt_g.vdetach()
# Run CG
delta_x, res = self.run_CG(num_cg_iter, eps=self.cg_eps)
self.x.vdetach_()
self.x.plus_(delta_x)
if self.debug:
self.residuals = torch.cat((self.residuals, res))
def run_newton_iter(self, num_cg_iter):
self.x.requires_grad(True)
# Evaluate function at current estimate
self.f0 = self.problem(self.x)
if self.debug and not self.analyze_convergence:
self.losses = torch.cat(
(self.losses, self.f0.detach().cpu().view(-1)))
# Gradient of loss
self.g = TensorList(
torch.autograd.grad(self.f0, self.x, create_graph=True))
# Get the right hand side
self.b = -self.g.vdetach()
# Run CG
delta_x, res = self.run_CG(num_cg_iter, eps=self.cg_eps)
self.x.vdetach_()
self.x.plus_(delta_x)
if self.debug:
self.residuals = torch.cat((self.residuals, res))
def run(self, num_cg_iter):
"""Run the oprimizer with the provided number of iterations."""
if num_cg_iter == 0:
return
lossvec = None
if self.debug:
lossvec = torch.zeros(2)
self.x.requires_grad(True)
# Evaluate function at current estimate
self.f0 = self.problem(self.x)
# Create copy with graph detached
self.g = self.f0.vdetach()
if self.debug:
lossvec[0] = self.problem.ip_output(self.g, self.g)
self.g.requires_grad(True)
# Get df/dx^t @ f0
self.dfdxt_g = TensorList(
torch.autograd.grad(self.f0, self.x, self.g, create_graph=True))
# Get the right hand side
self.b = -self.dfdxt_g.vdetach()
# Run CG
delta_x, res = self.run_CG(num_cg_iter, eps=self.cg_eps)
self.x.vdetach_()
self.x.plus_(delta_x)
if self.debug:
self.f0 = self.problem(self.x)
lossvec[-1] = self.problem.ip_output(self.f0, self.f0)
self.residuals = torch.cat((self.residuals, res))
self.losses = torch.cat((self.losses, lossvec))
if self.plotting:
plot_graph(self.losses, self.fig_num[0], title='Loss')
plot_graph(self.residuals,
self.fig_num[1],
title='CG residuals')
self.x.vdetach_()
self.clear_temp()
def evaluate_CG_iteration(self, delta_x):
if self.analyze_convergence:
x = (self.x + delta_x).detach()
x.requires_grad_(True)
# compute loss and gradient
loss = self.problem(x)
grad = TensorList(torch.autograd.grad(loss, x))
# store in the vectors
self.losses = torch.cat(
(self.losses, loss.detach().cpu().view(-1)))
self.gradient_mags = torch.cat(
(self.gradient_mags,
sum(grad.view(-1)
@ grad.view(-1)).cpu().sqrt().detach().view(-1)))
def A(self, x):
dfdx_x = torch.autograd.grad(self.dfdxt_g,
self.g,
x,
retain_graph=True)
return TensorList(
torch.autograd.grad(self.f0, self.x, dfdx_x, retain_graph=True))
def __init__(self,
problem: L2Problem,
variable: TensorList,
cg_eps=0.0,
fletcher_reeves=True,
standard_alpha=True,
direction_forget_factor=0,
debug=False,
plotting=False,
fig_num=(10, 11)):
super().__init__(fletcher_reeves, standard_alpha,
direction_forget_factor, debug or plotting)
self.problem = problem
self.x = variable.variable()
self.plotting = plotting
self.fig_num = fig_num
self.cg_eps = cg_eps
self.f0 = None
self.g = None
self.dfdxt_g = None
self.residuals = torch.zeros(0)
self.losses = torch.zeros(0)
def run(self, num_iter, dummy=None):
if num_iter == 0:
return
lossvec = None
if self.debug:
lossvec = torch.zeros(num_iter + 1)
grad_mags = torch.zeros(num_iter + 1)
for i in range(num_iter):
self.x.requires_grad(True)
# Evaluate function at current estimate
self.f0 = self.problem(self.x)
# Compute loss
loss = self.problem.ip_output(self.f0, self.f0)
# Compute grad
grad = TensorList(torch.autograd.grad(loss, self.x))
# Update direction
if self.dir is None:
self.dir = grad
else:
self.dir = grad + self.momentum * self.dir
self.x.vdetach_()
self.x -= self.step_legnth * self.dir
if self.debug:
lossvec[i] = loss.item()
grad_mags[i] = sum(grad.view(-1) @ grad.view(-1)).sqrt().item()
if self.debug:
self.x.requires_grad_(True)
self.f0 = self.problem(self.x)
loss = self.problem.ip_output(self.f0, self.f0)
grad = TensorList(torch.autograd.grad(loss, self.x))
lossvec[-1] = self.problem.ip_output(self.f0, self.f0).item()
grad_mags[-1] = sum(
grad.view(-1) @ grad.view(-1)).cpu().sqrt().item()
self.losses = torch.cat((self.losses, lossvec))
self.gradient_mags = torch.cat((self.gradient_mags, grad_mags))
if self.plotting:
plot_graph(self.losses, self.fig_num[0], title='Loss')
plot_graph(self.gradient_mags,
self.fig_num[1],
title='Gradient magnitude')
self.x.vdetach_()
self.clear_temp()
def A(self, x):
return TensorList(
torch.autograd.grad(self.g, self.x, x,
retain_graph=True)) + self.hessian_reg * x
class NewtonCG(ConjugateGradientBase):
"""Newton with Conjugate Gradient. Handels general minimization problems."""
def __init__(self,
problem: MinimizationProblem,
variable: TensorList,
init_hessian_reg=0.0,
hessian_reg_factor=1.0,
cg_eps=0.0,
fletcher_reeves=True,
standard_alpha=True,
direction_forget_factor=0,
debug=False,
analyze=False,
plotting=False,
fig_num=(10, 11, 12)):
super().__init__(fletcher_reeves, standard_alpha,
direction_forget_factor, debug or analyze or plotting)
self.problem = problem
self.x = variable
self.analyze_convergence = analyze
self.plotting = plotting
self.fig_num = fig_num
self.hessian_reg = init_hessian_reg
self.hessian_reg_factor = hessian_reg_factor
self.cg_eps = cg_eps
self.f0 = None
self.g = None
self.residuals = torch.zeros(0)
self.losses = torch.zeros(0)
self.gradient_mags = torch.zeros(0)
def clear_temp(self):
self.f0 = None
self.g = None
def run(self, num_cg_iter, num_newton_iter=None):
if isinstance(num_cg_iter, int):
if num_cg_iter == 0:
return
if num_newton_iter is None:
num_newton_iter = 1
num_cg_iter = [num_cg_iter] * num_newton_iter
num_newton_iter = len(num_cg_iter)
if num_newton_iter == 0:
return
if self.analyze_convergence:
self.evaluate_CG_iteration(0)
for cg_iter in num_cg_iter:
self.run_newton_iter(cg_iter)
self.hessian_reg *= self.hessian_reg_factor
if self.debug:
if not self.analyze_convergence:
loss = self.problem(self.x)
self.losses = torch.cat(
(self.losses, loss.detach().cpu().view(-1)))
if self.plotting:
plot_graph(self.losses, self.fig_num[0], title='Loss')
plot_graph(self.residuals,
self.fig_num[1],
title='CG residuals')
if self.analyze_convergence:
plot_graph(self.gradient_mags, self.fig_num[2],
'Gradient magnitude')
self.x.vdetach_()
self.clear_temp()
return self.losses, self.residuals
def run_newton_iter(self, num_cg_iter):
self.x.requires_grad(True)
# Evaluate function at current estimate
self.f0 = self.problem(self.x)
if self.debug and not self.analyze_convergence:
self.losses = torch.cat(
(self.losses, self.f0.detach().cpu().view(-1)))
# Gradient of loss
self.g = TensorList(
torch.autograd.grad(self.f0, self.x, create_graph=True))
# Get the right hand side
self.b = -self.g.vdetach()
# Run CG
delta_x, res = self.run_CG(num_cg_iter, eps=self.cg_eps)
self.x.vdetach_()
self.x.plus_(delta_x)
if self.debug:
self.residuals = torch.cat((self.residuals, res))
def A(self, x):
return TensorList(
torch.autograd.grad(self.g, self.x, x,
retain_graph=True)) + self.hessian_reg * x
def ip(self, a, b):
# Implements the inner product
return self.problem.ip_input(a, b)
def M1(self, x):
return self.problem.M1(x)
def M2(self, x):
return self.problem.M2(x)
def evaluate_CG_iteration(self, delta_x):
if self.analyze_convergence:
x = (self.x + delta_x).detach()
x.requires_grad_(True)
# compute loss and gradient
loss = self.problem(x)
grad = TensorList(torch.autograd.grad(loss, x))
# store in the vectors
self.losses = torch.cat(
(self.losses, loss.detach().cpu().view(-1)))
self.gradient_mags = torch.cat(
(self.gradient_mags,
sum(grad.view(-1)
@ grad.view(-1)).cpu().sqrt().detach().view(-1)))
class GaussNewtonCG(ConjugateGradientBase):
"""Gauss-Newton with Conjugate Gradient optimizer."""
def __init__(self,
problem: L2Problem,
variable: TensorList,
cg_eps=0.0,
fletcher_reeves=True,
standard_alpha=True,
direction_forget_factor=0,
debug=False,
analyze=False,
plotting=False,
fig_num=(10, 11, 12)):
super().__init__(fletcher_reeves, standard_alpha,
direction_forget_factor, debug or analyze or plotting)
self.problem = problem
self.x = variable
self.analyze_convergence = analyze
self.plotting = plotting
self.fig_num = fig_num
self.cg_eps = cg_eps
self.f0 = None
self.g = None
self.dfdxt_g = None
self.residuals = torch.zeros(0)
self.losses = torch.zeros(0)
self.gradient_mags = torch.zeros(0)
def clear_temp(self):
self.f0 = None
self.g = None
self.dfdxt_g = None
def run_GN(self, *args, **kwargs):
return self.run(*args, **kwargs)
def run(self, num_cg_iter, num_gn_iter=None):
"""Run the optimizer.
args:
num_cg_iter: Number of CG iterations per GN iter. If list, then each entry specifies number of CG iterations
and number of GN iterations is given by the length of the list.
num_gn_iter: Number of GN iterations. Shall only be given if num_cg_iter is an integer.
"""
if isinstance(num_cg_iter, int):
if num_gn_iter is None:
raise ValueError(
'Must specify number of GN iter if CG iter is constant')
num_cg_iter = [num_cg_iter] * num_gn_iter
num_gn_iter = len(num_cg_iter)
if num_gn_iter == 0:
return
if self.analyze_convergence:
self.evaluate_CG_iteration(0)
# Outer loop for running the GN iterations.
for cg_iter in num_cg_iter:
self.run_GN_iter(cg_iter)
if self.debug:
if not self.analyze_convergence:
self.f0 = self.problem(self.x)
loss = self.problem.ip_output(self.f0, self.f0)
self.losses = torch.cat(
(self.losses, loss.detach().cpu().view(-1)))
if self.plotting:
plot_graph(self.losses, self.fig_num[0], title='Loss')
plot_graph(self.residuals,
self.fig_num[1],
title='CG residuals')
if self.analyze_convergence:
plot_graph(self.gradient_mags, self.fig_num[2],
'Gradient magnitude')
self.x.vdetach_()
self.clear_temp()
return self.losses, self.residuals
def run_GN_iter(self, num_cg_iter):
"""Runs a single GN iteration."""
self.x.requires_grad(True)
# Evaluate function at current estimate
self.f0 = self.problem(self.x)
# Create copy with graph detached
self.g = self.f0.vdetach()
if self.debug and not self.analyze_convergence:
loss = self.problem.ip_output(self.g, self.g)
self.losses = torch.cat(
(self.losses, loss.detach().cpu().view(-1)))
self.g.requires_grad(True)
# Get df/dx^t @ f0
self.dfdxt_g = TensorList(
torch.autograd.grad(self.f0, self.x, self.g, create_graph=True))
# Get the right hand side
self.b = -self.dfdxt_g.vdetach()
# Run CG
delta_x, res = self.run_CG(num_cg_iter, eps=self.cg_eps)
self.x.vdetach_()
self.x.plus_(delta_x)
if self.debug:
self.residuals = torch.cat((self.residuals, res))
def A(self, x):
dfdx_x = torch.autograd.grad(self.dfdxt_g,
self.g,
x,
retain_graph=True)
return TensorList(
torch.autograd.grad(self.f0, self.x, dfdx_x, retain_graph=True))
def ip(self, a, b):
return self.problem.ip_input(a, b)
def M1(self, x):
return self.problem.M1(x)
def M2(self, x):
return self.problem.M2(x)
def evaluate_CG_iteration(self, delta_x):
if self.analyze_convergence:
x = (self.x + delta_x).detach()
x.requires_grad_(True)
# compute loss and gradient
f = self.problem(x)
loss = self.problem.ip_output(f, f)
grad = TensorList(torch.autograd.grad(loss, x))
# store in the vectors
self.losses = torch.cat(
(self.losses, loss.detach().cpu().view(-1)))
self.gradient_mags = torch.cat(
(self.gradient_mags,
sum(grad.view(-1)
@ grad.view(-1)).cpu().sqrt().detach().view(-1)))
class ConjugateGradient(ConjugateGradientBase):
"""Conjugate Gradient optimizer, performing single linearization of the residuals in the start."""
def __init__(self,
problem: L2Problem,
variable: TensorList,
cg_eps=0.0,
fletcher_reeves=True,
standard_alpha=True,
direction_forget_factor=0,
debug=False,
plotting=False,
fig_num=(10, 11)):
super().__init__(fletcher_reeves, standard_alpha,
direction_forget_factor, debug or plotting)
self.problem = problem
self.x = variable.variable()
self.plotting = plotting
self.fig_num = fig_num
self.cg_eps = cg_eps
self.f0 = None
self.g = None
self.dfdxt_g = None
self.residuals = torch.zeros(0)
self.losses = torch.zeros(0)
def clear_temp(self):
self.f0 = None
self.g = None
self.dfdxt_g = None
def run(self, num_cg_iter):
"""Run the oprimizer with the provided number of iterations."""
if num_cg_iter == 0:
return
lossvec = None
if self.debug:
lossvec = torch.zeros(2)
self.x.requires_grad(True)
# Evaluate function at current estimate
self.f0 = self.problem(self.x)
# Create copy with graph detached
self.g = self.f0.vdetach()
if self.debug:
lossvec[0] = self.problem.ip_output(self.g, self.g)
self.g.requires_grad(True)
# Get df/dx^t @ f0
self.dfdxt_g = TensorList(
torch.autograd.grad(self.f0, self.x, self.g, create_graph=True))
# Get the right hand side
self.b = -self.dfdxt_g.vdetach()
# Run CG
delta_x, res = self.run_CG(num_cg_iter, eps=self.cg_eps)
self.x.vdetach_()
self.x.plus_(delta_x)
if self.debug:
self.f0 = self.problem(self.x)
lossvec[-1] = self.problem.ip_output(self.f0, self.f0)
self.residuals = torch.cat((self.residuals, res))
self.losses = torch.cat((self.losses, lossvec))
if self.plotting:
plot_graph(self.losses, self.fig_num[0], title='Loss')
plot_graph(self.residuals,
self.fig_num[1],
title='CG residuals')
self.x.vdetach_()
self.clear_temp()
def A(self, x):
dfdx_x = torch.autograd.grad(self.dfdxt_g,
self.g,
x,
retain_graph=True)
return TensorList(
torch.autograd.grad(self.f0, self.x, dfdx_x, retain_graph=True))
def ip(self, a, b):
return self.problem.ip_input(a, b)
def M1(self, x):
return self.problem.M1(x)
def M2(self, x):
return self.problem.M2(x)