[Fix] Prevent line search from evaluating cost outside of the interpolation range (#504)

* Explicitly check that SinkhornL1l2Transport.fit works with no warnings

* Default value for alpha_min is set to 0

* Fix random_state for SinkhornL1l2Transport test

* Mention changes in releases

---------

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>

Author: kachayev

RELEASES.md

@@ -6,6 +6,7 @@
 + Tweaked `get_backend` to ignore `None` inputs (PR # 525)
 
 #### Closed issues
+- Fix line search evaluating cost outside of the interpolation range (Issue #502, PR #504)
 
 
 ## 0.9.1

ot/optim.py

@@ -27,7 +27,7 @@
 
 def line_search_armijo(
     f, xk, pk, gfk, old_fval, args=(), c1=1e-4,
-    alpha0=0.99, alpha_min=None, alpha_max=None, nx=None, **kwargs
+    alpha0=0.99, alpha_min=0., alpha_max=None, nx=None, **kwargs
 ):
     r"""
     Armijo linesearch function that works with matrices
@@ -56,7 +56,7 @@ def line_search_armijo(
         :math:`c_1` const in armijo rule (>0)
     alpha0 : float, optional
         initial step (>0)
-    alpha_min : float, optional
+    alpha_min : float, default=0.
         minimum value for alpha
     alpha_max : float, optional
         maximum value for alpha
@@ -89,6 +89,14 @@ def line_search_armijo(
     fc = [0]
 
     def phi(alpha1):
+        # it's necessary to check boundary condition here for the coefficient
+        # as the callback could be evaluated for negative value of alpha by
+        # `scalar_search_armijo` function here:
+        #
+        # https://github.com/scipy/scipy/blob/11509c4a98edded6c59423ac44ca1b7f28fba1fd/scipy/optimize/linesearch.py#L686
+        #
+        # see more details https://github.com/PythonOT/POT/issues/502
+        alpha1 = np.clip(alpha1, alpha_min, alpha_max)
         # The callable function operates on nx backend
         fc[0] += 1
         alpha10 = nx.from_numpy(alpha1)
@@ -109,13 +117,12 @@ def phi(alpha1):
 
     derphi0 = np.sum(pk * gfk)  # Quickfix for matrices
     alpha, phi1 = scalar_search_armijo(
-        phi, phi0, derphi0, c1=c1, alpha0=alpha0)
+        phi, phi0, derphi0, c1=c1, alpha0=alpha0, amin=alpha_min)
 
     if alpha is None:
         return 0., fc[0], nx.from_numpy(phi0, type_as=xk0)
     else:
-        if alpha_min is not None or alpha_max is not None:
-            alpha = np.clip(alpha, alpha_min, alpha_max)
+        alpha = np.clip(alpha, alpha_min, alpha_max)
         return nx.from_numpy(alpha, type_as=xk0), fc[0], nx.from_numpy(phi1, type_as=xk0)
 
 

test/test_da.py

@@ -7,6 +7,7 @@
 import numpy as np
 from numpy.testing import assert_allclose, assert_equal
 import pytest
+import warnings
 
 import ot
 from ot.datasets import make_data_classif
@@ -158,15 +159,17 @@ def test_sinkhorn_l1l2_transport_class(nx):
     ns = 50
     nt = 50
 
-    Xs, ys = make_data_classif('3gauss', ns)
-    Xt, yt = make_data_classif('3gauss2', nt)
+    Xs, ys = make_data_classif('3gauss', ns, random_state=42)
+    Xt, yt = make_data_classif('3gauss2', nt, random_state=43)
 
     Xs, ys, Xt, yt = nx.from_numpy(Xs, ys, Xt, yt)
 
-    otda = ot.da.SinkhornL1l2Transport()
+    otda = ot.da.SinkhornL1l2Transport(max_inner_iter=500)
 
     # test its computed
-    otda.fit(Xs=Xs, ys=ys, Xt=Xt)
+    with warnings.catch_warnings():
+        warnings.simplefilter("error")
+        otda.fit(Xs=Xs, ys=ys, Xt=Xt)
     assert hasattr(otda, "cost_")
     assert hasattr(otda, "coupling_")
     assert hasattr(otda, "log_")