[MRG] SinkhornL1L2 bug solve (#313)

* Now limiting alpha to a minimum value as well as a max value

* Docs

* typo

Author: ncassereau

ot/optim.py

@@ -18,8 +18,10 @@
 # The corresponding scipy function does not work for matrices
 
 
-def line_search_armijo(f, xk, pk, gfk, old_fval,
-                       args=(), c1=1e-4, alpha0=0.99):
+def line_search_armijo(
+    f, xk, pk, gfk, old_fval, args=(), c1=1e-4,
+    alpha0=0.99, alpha_min=None, alpha_max=None
+):
     r"""
     Armijo linesearch function that works with matrices
 
@@ -44,6 +46,10 @@ def line_search_armijo(f, xk, pk, gfk, old_fval,
         :math:`c_1` const in armijo rule (>0)
     alpha0 : float, optional
         initial step (>0)
+    alpha_min : float, optional
+        minimum value for alpha
+    alpha_max : float, optional
+        maximum value for alpha
 
     Returns
     -------
@@ -80,13 +86,15 @@ def phi(alpha1):
     if alpha is None:
         return 0., fc[0], phi0
     else:
-        # scalar_search_armijo can return alpha > 1
-        alpha = min(1, alpha)
+        if alpha_min is not None or alpha_max is not None:
+            alpha = np.clip(alpha, alpha_min, alpha_max)
         return alpha, fc[0], phi1
 
 
-def solve_linesearch(cost, G, deltaG, Mi, f_val,
-                     armijo=True, C1=None, C2=None, reg=None, Gc=None, constC=None, M=None):
+def solve_linesearch(
+    cost, G, deltaG, Mi, f_val, armijo=True, C1=None, C2=None,
+    reg=None, Gc=None, constC=None, M=None, alpha_min=None, alpha_max=None
+):
     """
     Solve the linesearch in the FW iterations
 
@@ -117,6 +125,10 @@ def solve_linesearch(cost, G, deltaG, Mi, f_val,
         Constant for the gromov cost. See :ref:`[24] <references-solve-linesearch>`. Only used and necessary when armijo=False
     M : array-like (ns,nt), optional
         Cost matrix between the features. Only used and necessary when armijo=False
+    alpha_min : float, optional
+        Minimum value for alpha
+    alpha_max : float, optional
+        Maximum value for alpha
 
     Returns
     -------
@@ -136,7 +148,9 @@ def solve_linesearch(cost, G, deltaG, Mi, f_val,
         International Conference on Machine Learning (ICML). 2019.
     """
     if armijo:
-        alpha, fc, f_val = line_search_armijo(cost, G, deltaG, Mi, f_val)
+        alpha, fc, f_val = line_search_armijo(
+            cost, G, deltaG, Mi, f_val, alpha_min=alpha_min, alpha_max=alpha_max
+        )
     else:  # requires symetric matrices
         G, deltaG, C1, C2, constC, M = list_to_array(G, deltaG, C1, C2, constC, M)
         if isinstance(M, int) or isinstance(M, float):
@@ -150,6 +164,8 @@ def solve_linesearch(cost, G, deltaG, Mi, f_val,
         c = cost(G)
 
         alpha = solve_1d_linesearch_quad(a, b, c)
+        if alpha_min is not None or alpha_max is not None:
+            alpha = np.clip(alpha, alpha_min, alpha_max)
         fc = None
         f_val = cost(G + alpha * deltaG)
 
@@ -274,7 +290,10 @@ def cost(G):
         deltaG = Gc - G
 
         # line search
-        alpha, fc, f_val = solve_linesearch(cost, G, deltaG, Mi, f_val, reg=reg, M=M, Gc=Gc, **kwargs)
+        alpha, fc, f_val = solve_linesearch(
+            cost, G, deltaG, Mi, f_val, reg=reg, M=M, Gc=Gc,
+            alpha_min=0., alpha_max=1., **kwargs
+        )
 
         G = G + alpha * deltaG
 
@@ -420,7 +439,9 @@ def cost(G):
 
         # line search
         dcost = Mi + reg1 * (1 + nx.log(G))  # ??
-        alpha, fc, f_val = line_search_armijo(cost, G, deltaG, dcost, f_val)
+        alpha, fc, f_val = line_search_armijo(
+            cost, G, deltaG, dcost, f_val, alpha_min=0., alpha_max=1.
+        )
 
         G = G + alpha * deltaG