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import torch.nn as nn
from torch.optim import Optimizer
from torch import Tensor
from torch.autograd import Function
import numpy as np
import scipy
import time
import cvxpy
# import solvers
# from qpthlocal.solvers.pdipm import batch as pdipm_b
# from qpthlocal.solvers.pdipm import spbatch as pdipm_spb
# from qpthlocal.solvers.cvxpy import forward_single_np
from .utils import forward_single_np
from enum import Enum
from .utils import extract_nBatch, expandParam
from typing import cast, List, Optional, Union
# from cvxpylayers.torch import CvxpyLayer
# class QPSolvers(Enum):
# PDIPM_BATCHED = 1
# CVXPY = 2
# class ffoqp(torch.nn.Module):
# def __init__(self, eps=1e-12, verbose=0, notImprovedLim=3, maxiter=20, solver=None, lamb=100):
# super(ffoqp, self).__init__()
# self.eps = eps
# self.verbose = verbose
# self.notImprovedLim = notImprovedLim
# self.maxiter = maxiter
# self.solver = solver if solver is not None else QPSolvers.CVXPY
# self.lamb = lamb
def ffoqp(eps=1e-12, verbose=0, notImprovedLim=3, maxIter=20, lamb=100, check_Q_spd=True,
solver='GUROBI', solver_opts={"verbose": False}):
class QPFunctionFn(torch.autograd.Function):
@staticmethod
def forward(ctx, Q_, p_, G_, h_, A_, b_):
# p_ = p_ + 1/lamb * torch.randn_like(p_)
start_time = time.time()
nBatch = extract_nBatch(Q_, p_, G_, h_, A_, b_)
Q, _ = expandParam(Q_, nBatch, 3)
p, _ = expandParam(p_, nBatch, 2)
G, _ = expandParam(G_, nBatch, 3)
h, _ = expandParam(h_, nBatch, 2)
A, _ = expandParam(A_, nBatch, 3)
b, _ = expandParam(b_, nBatch, 2)
if check_Q_spd:
try:
torch.linalg.cholesky(Q)
except:
raise RuntimeError('Q is not SPD.')
_, nineq, nz = G.size()
neq = A.size(1) if A.nelement() > 0 else 0
assert(neq > 0 or nineq > 0)
ctx.neq, ctx.nineq, ctx.nz = neq, nineq, nz
# if solver == QPSolvers.PDIPM_BATCHED:
# ctx.Q_LU, ctx.S_LU, ctx.R = pdipm_b.pre_factor_kkt(Q, G, A)
# zhats, nus, lams, slacks = pdipm_b.forward(
# Q, p, G, h, A, b, ctx.Q_LU, ctx.S_LU, ctx.R,
# eps, verbose, notImprovedLim, maxIter)
# elif solver == QPSolvers.CVXPY:
vals = torch.Tensor(nBatch).type_as(Q)
zhats = torch.Tensor(nBatch, ctx.nz).type_as(Q)
lams = torch.Tensor(nBatch, ctx.nineq).type_as(Q)
nus = torch.Tensor(nBatch, ctx.neq).type_as(Q) \
if ctx.neq > 0 else torch.Tensor()
slacks = torch.Tensor(nBatch, ctx.nineq).type_as(Q)
for i in range(nBatch):
Ai, bi = (A[i], b[i]) if neq > 0 else (None, None)
vals[i], zhati, nui, lami, si = forward_single_np(
*[x.cpu().numpy() if x is not None else None
for x in (Q[i], p[i], G[i], h[i], Ai, bi)],
solver=solver, solver_opts=solver_opts)
# if zhati[0] is None:
# import IPython, sys; IPython.embed(); sys.exit(-1)
zhats[i] = torch.Tensor(zhati)
lams[i] = torch.Tensor(lami)
slacks[i] = torch.Tensor(si)
if neq > 0:
nus[i] = torch.Tensor(nui)
ctx.vals = vals
ctx.lams = lams
ctx.nus = nus
ctx.slacks = slacks
# else:
# raise NotImplementedError("Solver not implemented")
# ctx.vals = vals
ctx.lams = lams
ctx.nus = nus
ctx.slacks = slacks
ctx.save_for_backward(zhats, lams, nus, Q_, p_, G_, h_, A_, b_)
# print('value', vals)
# print('solution', zhats)
return zhats
@staticmethod
def backward(ctx, grad_output):
# Backward pass to compute gradients with respect to inputs
zhats, lams, nus, Q_, p_, G_, h_, A_, b_ = ctx.saved_tensors
lams = torch.clamp(lams, min=0)
nBatch = extract_nBatch(Q_, p_, G_, h_, A_, b_)
# Formulate a different QP to solve
# L = f + \lamb * (g + lams * h - g^*) + \lamb^2 * |h_+|^2
Q, Q_e = expandParam(Q_, nBatch, 3)
p, p_e = expandParam(p_, nBatch, 2)
G, G_e = expandParam(G_, nBatch, 3)
h, h_e = expandParam(h_, nBatch, 2)
A, A_e = expandParam(A_, nBatch, 3)
b, b_e = expandParam(b_, nBatch, 2)
Q, p, G, h, A, b = Q.to(zhats.device), p.to(zhats.device), G.to(zhats.device), h.to(zhats.device), A.to(zhats.device), b.to(zhats.device)
# Running gradient descent for a few iterations
_, nineq, nz = G.size()
neq = A.size(1) if A.nelement() > 0 else 0
delta_directions = grad_output.unsqueeze(-1)
zhats = zhats.unsqueeze(-1).detach()
# Iterative solution
# print('newzhat shape:', zhats.shape)
# print('Q shape:', Q.shape)
iterative = False
if iterative:
with torch.enable_grad():
newzhat = zhats.clone().detach().requires_grad_(True)
optimizer = torch.optim.Adam([newzhat], lr=1e-3)
gd_maxiter = 1 # int(np.sqrt(lamb) * 100)
# print('dual solutions', lams)
for i in range(gd_maxiter):
objectives = (0.5 * newzhat.transpose(-1,-2) @ Q.detach() @ newzhat + (p.detach().unsqueeze(1) + delta_directions.transpose(-1,-2) / lamb) @ newzhat).squeeze(-1,-2)
violations = G.detach() @ newzhat - h.unsqueeze(-1)
active_constraints = (lams > 1e-5).unsqueeze(-1).float()
ineq_penalties = lams.unsqueeze(1) @ violations + 0.5 * lamb * torch.sum((violations * active_constraints) ** 2, dim=(-1,-2))
if neq > 0:
eq_penalties = nus.unsqueeze(1) @ (A.detach() @ newzhat.unsqueeze(-1) - b.detach().unsqueeze(-1))
else:
eq_penalties = 0
# print('obj, vio, active_constraints, lamb, ineq_penality shape:', objectives.shape, violations.shape, active_constraints.shape, lamb, ineq_penalties.shape)
lagrangians = objectives + ineq_penalties + eq_penalties
loss = torch.sum(lagrangians)
# print('Iteration {}: loss: {}, obj: {}, violation: {}'.format(i, loss, objectives.mean(), violations.mean()))
loss.backward()
optimizer.step()
optimizer.zero_grad()
# print('new zhat', newzhats.detach())
# Clampping the dual solutions
# lams = torch.clamp(lams, max=100)
else:
# Deterministic solution by solving a new QP
temperature = 10
start_time = time.time()
active_constraints = torch.tanh(lams * temperature).unsqueeze(-1)
# active_constraints = (lams > 1e-3).unsqueeze(-1).float()
G_active = G * active_constraints
h_active = h.unsqueeze(-1) * active_constraints
newQ = Q + lamb * G_active.transpose(-1,-2) @ G_active # + torch.eye(nz).repeat(nBatch, 1, 1).to(Q.device)
newp = p.unsqueeze(-1) + delta_directions / lamb - lamb * G_active.transpose(-1,-2) @ h_active + G.transpose(-1,-2) @ lams.unsqueeze(-1) # - zhats
# print('newQ, newp shape:', newQ.shape, newp.shape)
# print('A, b shape:', A.shape, b.shape)
if neq > 0:
newQ = torch.cat((newQ, lamb * A), dim=1)
newp = torch.cat((newp, - lamb * b.unsqueeze(-1)), dim=1)
# print('condition number:', torch.linalg.cond(newQ))
# newzhat = torch.linalg.solve(newQ, -newp)
newzhat = torch.linalg.lstsq(newQ, -newp, driver='gels').solution
# newzhat = - newQ.pinverse() @ newp
# print('prediction', p)
# print('solution distance:', torch.linalg.norm(newzhat - zhats))
# print(lams)
# print(zhats)
# print(newzhat)
# print('solution shape:', newzhat.shape, zhats.shape)
# print('solution max distance:', torch.max(torch.abs(newzhat - zhats)))
# assert False
# print('newQ, p, newp, z shape:', newQ.shape, p.shape, newp.shape, newzhats.shape)
# Computing the gradients of the Lagrangians
start_time = time.time()
with torch.enable_grad():
Q_torch = Q.detach().clone().requires_grad_(True)
p_torch = p.detach().clone().requires_grad_(True)
G_torch = G.detach().clone().requires_grad_(True)
h_torch = h.detach().clone().requires_grad_(True)
A_torch = A.detach().clone().requires_grad_(True)
b_torch = b.detach().clone().requires_grad_(True)
upper_level_objectives = (delta_directions.transpose(-1,-2) @ newzhat).squeeze(-1,-2)
objectives = (0.5 * newzhat.transpose(-1,-2) @ Q_torch @ newzhat + p_torch.unsqueeze(1) @ newzhat).squeeze(-1,-2) # 1/2 * z^T Q z + p^T z
optimal_objectives = (0.5 * zhats.transpose(-1,-2) @ Q_torch @ zhats + p_torch.unsqueeze(1) @ zhats).squeeze(-1,-2) # 1/2 * z*^T Q z* + p^T z*
violations = G_torch @ newzhat - h.unsqueeze(-1) # G z - h
active_constraints = torch.tanh(lams * temperature).unsqueeze(-1).float()
ineq_penalties = lams.unsqueeze(1) @ violations + 0.5 * lamb * torch.sum((violations * active_constraints) ** 2, dim=(-1,-2))
if neq > 0:
eq_violations = A_torch @ newzhat - b_torch.unsqueeze(-1)
eq_penalties = nus.unsqueeze(1) @ eq_violations # + 0.5 * lamb * torch.sum(eq_violations ** 2, dim=(-1,-2))
# print(eq_violations)
else:
eq_penalties = 0
# print('obj, vio, active_constraints, lamb, ineq_penality shape:', objectives.shape, violations.shape, active_constraints.shape, lamb, ineq_penalties.shape)
lagrangians = upper_level_objectives / lamb + objectives - optimal_objectives + ineq_penalties # + eq_penalties
loss = torch.sum(lagrangians) * lamb
loss.backward()
Q_grad = Q_torch.grad
p_grad = p_torch.grad
G_grad = G_torch.grad
h_grad = h_torch.grad
A_grad = A_torch.grad
b_grad = b_torch.grad
return (Q_grad, p_grad, G_grad, h_grad, A_grad, b_grad) # (None,) * len(ctx.saved_tensors)
return QPFunctionFn.apply
def to_numpy(x):
# convert torch tensor to numpy array
return x.cpu().detach().double().numpy()
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