Discrepancy between the outputs of ot.sinkhorn and ot.optim.gcg with reg2=0 #758
Description
Describe the bug
In optim.gcg, the inner solver is ot.sinkhorn. Thus, if I am not mistaken, I would expect the output of
ot.optim.gcg(a, b, M, reg, 0., lambda x: 0., lambda x: np.zeros(x.shape), numInnerItermax=1000)and
ot.sinkhorn(a, b, M, reg, numItermax=1000)to be the same. However, it is not always the case, even when using the same tolerances.
Do I miss something?
To Reproduce
n = 100
X = ot.datasets.make_2D_samples_gauss(n, m=[0, 0], sigma=np.eye(2))
Y = ot.datasets.make_2D_samples_gauss(n, m=[1, 1], sigma=np.eye(2))
M = ot.dist(X, Y)
M /= M.max()
a = ot.unif(n)
b = ot.unif(n)
reg = 1e-2
pi1 = ot.optim.gcg(a, b, M, reg, 0., lambda x: 0., lambda x: np.zeros(x.shape), numInnerItermax=1000)
pi2 = ot.sinkhorn(a, b, M, reg, numItermax=1000)
assert np.allclose(pi1, pi2, atol=1e-5) # Fail