def solve(self, step, stop):
# solves using gradient descent
self.init_solver()
for i in range(self.max_iters):
g = self.gradient()
nu = simplex_projection(self.nu - step() * g, self.b)
obj, a = self.objective(nu)
self.update(nu, obj, a)
if stop(): break
print 'iter: ', i
print 'obj: ', obj
return {'attack_rates': self.nu, 'obj_values': self.obj_values}
def solve(self, step, stop):
# solves using gradient descent
self.init_solver()
for i in range(self.max_iters):
g = self.gradient()
nu = simplex_projection(self.nu - step() * g, self.b)
obj, a = self.objective(nu)
self.update(nu, obj, a)
if stop(): break
print 'iter: ', i
print 'obj: ', obj
return {'attack_rates': self.nu, 'obj_values': self.obj_values}
def online_gradient_descent(batch_data, T, init, G, D):
'''
:param batch_data: ratios data of size (n_ratios, T)
:param T: Horizon of repeated game
:param init: Initial point x_1
:param G: Lipschitz coeeficient
:param D: Diameter
:return:
'''
xs = [init]
eta = D / (G * np.sqrt(T)) # fixed step size
rt = batch_data[:, 0] # initial ratios
for t in range(T-1):
# adapting step size
# eta = D / (G * np.sqrt(t+1))
# compute online gradient
grad = utl.get_grad(xs[-1], rt)
# perform OGD update (with projection)
xs.append(utl.simplex_projection(xs[-1] - eta * grad))
# observe next data point
rt = batch_data[:, t + 1]
return xs
def test_simplex_projection(self):
v = np.array([1, 0, 0, 0, 0, 0])
self.assertTrue(is_equal(simplex_projection(v), v))
v = np.array([0.1, 0.2, 0.3, 0.4])
self.assertTrue(is_equal(simplex_projection(v), v))
v = np.array([10, 10])
w = np.array([0.5, 0.5])
self.assertTrue(is_equal(simplex_projection(v), w))
v = np.array([-10, -10])
w = np.array([0.5, 0.5])
self.assertTrue(is_equal(simplex_projection(v), w))
v = np.array([-10, 10])
w = np.array([0, 1])
self.assertTrue(is_equal(simplex_projection(v), w))
for _ in range(20):
v = (np.random.rand(20) - np.ones(20) * 0.5) * 100
self.assertTrue(is_equal(np.sum(simplex_projection(v)), 1))
self.assertTrue(is_equal(np.sum(simplex_projection(v, 5)), 5))
def test_simplex_projection(self):
v = np.array([1, 0, 0, 0, 0, 0])
self.assertTrue(is_equal(simplex_projection(v), v))
v = np.array([0.1, 0.2, 0.3, 0.4])
self.assertTrue(is_equal(simplex_projection(v), v))
v = np.array([10, 10])
w = np.array([0.5, 0.5])
self.assertTrue(is_equal(simplex_projection(v), w))
v = np.array([-10, -10])
w = np.array([0.5, 0.5])
self.assertTrue(is_equal(simplex_projection(v), w))
v = np.array([-10, 10])
w = np.array([0, 1])
self.assertTrue(is_equal(simplex_projection(v), w))
for _ in range(20):
v = (np.random.rand(20) - np.ones(20) * 0.5) * 100
self.assertTrue(is_equal(np.sum(simplex_projection(v)), 1))
self.assertTrue(is_equal(np.sum(simplex_projection(v, 5)), 5))
