ENH Add FISTA solver (#91)

Co-authored-by: Badr MOUFAD <[email protected]>

Author: PABannier

doc/api.rst

@@ -70,6 +70,7 @@ Solvers
    :toctree: generated/
 
    AndersonCD
+   FISTA
    GramCD
    GroupBCD
    MultiTaskBCD

skglm/datafits/single_task.py

@@ -4,6 +4,7 @@
 from numba import float64
 
 from skglm.datafits.base import BaseDatafit
+from skglm.utils import spectral_norm
 
 
 class Quadratic(BaseDatafit):
@@ -22,6 +23,10 @@ class Quadratic(BaseDatafit):
         The coordinatewise gradient Lipschitz constants. Equal to
         norm(X, axis=0) ** 2 / n_samples.
 
+    global_lipschitz : float
+        Global Lipschitz constant. Equal to
+        norm(X, ord=2) ** 2 / n_samples.
+
     Note
     ----
     The class is jit compiled at fit time using Numba compiler.
@@ -35,6 +40,7 @@ def get_spec(self):
         spec = (
             ('Xty', float64[:]),
             ('lipschitz', float64[:]),
+            ('global_lipschitz', float64),
         )
         return spec
 
@@ -44,14 +50,18 @@ def params_to_dict(self):
     def initialize(self, X, y):
         self.Xty = X.T @ y
         n_features = X.shape[1]
+        self.global_lipschitz = norm(X, ord=2) ** 2 / len(y)
         self.lipschitz = np.zeros(n_features, dtype=X.dtype)
         for j in range(n_features):
             self.lipschitz[j] = (X[:, j] ** 2).sum() / len(y)
 
-    def initialize_sparse(
-            self, X_data, X_indptr, X_indices, y):
+    def initialize_sparse(self, X_data, X_indptr, X_indices, y):
         n_features = len(X_indptr) - 1
         self.Xty = np.zeros(n_features, dtype=X_data.dtype)
+
+        self.global_lipschitz = spectral_norm(X_data, X_indptr, X_indices, len(y)) ** 2
+        self.global_lipschitz /= len(y)
+
         self.lipschitz = np.zeros(n_features, dtype=X_data.dtype)
         for j in range(n_features):
             nrm2 = 0.
@@ -111,6 +121,10 @@ class Logistic(BaseDatafit):
         The coordinatewise gradient Lipschitz constants. Equal to
         norm(X, axis=0) ** 2 / (4 * n_samples).
 
+    global_lipschitz : float
+        Global Lipschitz constant. Equal to
+        norm(X, ord=2) ** 2 / (4 * n_samples).
+
     Note
     ----
     The class is jit compiled at fit time using Numba compiler.
@@ -123,6 +137,7 @@ def __init__(self):
     def get_spec(self):
         spec = (
             ('lipschitz', float64[:]),
+            ('global_lipschitz', float64),
         )
         return spec
 
@@ -140,9 +155,14 @@ def raw_hessian(self, y, Xw):
 
     def initialize(self, X, y):
         self.lipschitz = (X ** 2).sum(axis=0) / (len(y) * 4)
+        self.global_lipschitz = norm(X, ord=2) ** 2 / (len(y) * 4)
 
     def initialize_sparse(self, X_data, X_indptr, X_indices, y):
         n_features = len(X_indptr) - 1
+
+        self.global_lipschitz = spectral_norm(X_data, X_indptr, X_indices, len(y)) ** 2
+        self.global_lipschitz /= 4 * len(y)
+
         self.lipschitz = np.zeros(n_features, dtype=X_data.dtype)
         for j in range(n_features):
             Xj = X_data[X_indptr[j]:X_indptr[j+1]]
@@ -187,6 +207,11 @@ class QuadraticSVC(BaseDatafit):
     ----------
     lipschitz : array, shape (n_features,)
         The coordinatewise gradient Lipschitz constants.
+        Equal to norm(yXT, axis=0) ** 2.
+
+    global_lipschitz : float
+        Global Lipschitz constant. Equal to
+        norm(yXT, ord=2) ** 2.
 
     Note
     ----
@@ -200,6 +225,7 @@ def __init__(self):
     def get_spec(self):
         spec = (
             ('lipschitz', float64[:]),
+            ('global_lipschitz', float64),
         )
         return spec
 
@@ -209,12 +235,16 @@ def params_to_dict(self):
     def initialize(self, yXT, y):
         n_features = yXT.shape[1]
         self.lipschitz = np.zeros(n_features, dtype=yXT.dtype)
+        self.global_lipschitz = norm(yXT, ord=2) ** 2
         for j in range(n_features):
             self.lipschitz[j] = norm(yXT[:, j]) ** 2
 
-    def initialize_sparse(
-            self, yXT_data, yXT_indptr, yXT_indices, y):
+    def initialize_sparse(self, yXT_data, yXT_indptr, yXT_indices, y):
         n_features = len(yXT_indptr) - 1
+
+        self.global_lipschitz = spectral_norm(
+            yXT_data, yXT_indptr, yXT_indices, max(yXT_indices)+1) ** 2
+
         self.lipschitz = np.zeros(n_features, dtype=yXT_data.dtype)
         for j in range(n_features):
             nrm2 = 0.
@@ -264,8 +294,16 @@ class Huber(BaseDatafit):
 
     Attributes
     ----------
+    delta : float
+        Threshold hyperparameter.
+
     lipschitz : array, shape (n_features,)
-        The coordinatewise gradient Lipschitz constants.
+        The coordinatewise gradient Lipschitz constants. Equal to
+        norm(X, axis=0) ** 2 / n_samples.
+
+    global_lipschitz : float
+        Global Lipschitz constant. Equal to
+        norm(X, ord=2) ** 2 / n_samples.
 
     Note
     ----
@@ -279,7 +317,8 @@ def __init__(self, delta):
     def get_spec(self):
         spec = (
             ('delta', float64),
-            ('lipschitz', float64[:])
+            ('lipschitz', float64[:]),
+            ('global_lipschitz', float64),
         )
         return spec
 
@@ -289,12 +328,17 @@ def params_to_dict(self):
     def initialize(self, X, y):
         n_features = X.shape[1]
         self.lipschitz = np.zeros(n_features, dtype=X.dtype)
+        self.global_lipschitz = 0.
         for j in range(n_features):
             self.lipschitz[j] = (X[:, j] ** 2).sum() / len(y)
+            self.global_lipschitz += (X[:, j] ** 2).sum() / len(y)
 
-    def initialize_sparse(
-            self, X_data, X_indptr, X_indices, y):
+    def initialize_sparse(self, X_data, X_indptr, X_indices, y):
         n_features = len(X_indptr) - 1
+
+        self.global_lipschitz = spectral_norm(X_data, X_indptr, X_indices, len(y)) ** 2
+        self.global_lipschitz /= len(y)
+
         self.lipschitz = np.zeros(n_features, dtype=X_data.dtype)
         for j in range(n_features):
             nrm2 = 0.

skglm/solvers/__init__.py

@@ -1,9 +1,10 @@
 from .anderson_cd import AndersonCD
 from .base import BaseSolver
+from .fista import FISTA
 from .gram_cd import GramCD
 from .group_bcd import GroupBCD
 from .multitask_bcd import MultiTaskBCD
 from .prox_newton import ProxNewton
 
 
-__all__ = [AndersonCD, BaseSolver, GramCD, GroupBCD, MultiTaskBCD, ProxNewton]
+__all__ = [AndersonCD, BaseSolver, FISTA, GramCD, GroupBCD, MultiTaskBCD, ProxNewton]

skglm/solvers/fista.py

@@ -0,0 +1,82 @@
+import numpy as np
+from scipy.sparse import issparse
+from skglm.solvers.base import BaseSolver
+from skglm.solvers.common import construct_grad, construct_grad_sparse
+from skglm.utils import _prox_vec
+
+
+class FISTA(BaseSolver):
+    r"""ISTA solver with Nesterov acceleration (FISTA).
+
+    Attributes
+    ----------
+    max_iter : int, default 100
+        Maximum number of iterations.
+
+    tol : float, default 1e-4
+        Tolerance for convergence.
+
+    verbose : bool, default False
+        Amount of verbosity. 0/False is silent.
+
+    References
+    ----------
+    .. [1] Beck, A. and Teboulle M.
+           "A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse
+           problems", 2009, SIAM J. Imaging Sci.
+           https://epubs.siam.org/doi/10.1137/080716542
+    """
+
+    def __init__(self, max_iter=100, tol=1e-4, verbose=0):
+        self.max_iter = max_iter
+        self.tol = tol
+        self.verbose = verbose
+
+    def solve(self, X, y, datafit, penalty, w_init=None, Xw_init=None):
+        p_objs_out = []
+        n_samples, n_features = X.shape
+        all_features = np.arange(n_features)
+        t_new = 1.
+
+        w = w_init.copy() if w_init is not None else np.zeros(n_features)
+        z = w_init.copy() if w_init is not None else np.zeros(n_features)
+        Xw = Xw_init.copy() if Xw_init is not None else np.zeros(n_samples)
+
+        if hasattr(datafit, "global_lipschitz"):
+            lipschitz = datafit.global_lipschitz
+        else:
+            # TODO: OR line search
+            raise Exception("Line search is not yet implemented for FISTA solver.")
+
+        for n_iter in range(self.max_iter):
+            t_old = t_new
+            t_new = (1 + np.sqrt(1 + 4 * t_old ** 2)) / 2
+            w_old = w.copy()
+            if issparse(X):
+                grad = construct_grad_sparse(
+                    X.data, X.indptr, X.indices, y, z, X @ z, datafit, all_features)
+            else:
+                grad = construct_grad(X, y, z, X @ z, datafit, all_features)
+
+            step = 1 / lipschitz
+            z -= step * grad
+            w = _prox_vec(w, z, penalty, step)
+            Xw = X @ w
+            z = w + (t_old - 1.) / t_new * (w - w_old)
+
+            opt = penalty.subdiff_distance(w, grad, all_features)
+            stop_crit = np.max(opt)
+
+            p_obj = datafit.value(y, w, Xw) + penalty.value(w)
+            p_objs_out.append(p_obj)
+            if self.verbose:
+                print(
+                    f"Iteration {n_iter+1}: {p_obj:.10f}, "
+                    f"stopping crit: {stop_crit:.2e}"
+                )
+
+            if stop_crit < self.tol:
+                if self.verbose:
+                    print(f"Stopping criterion max violation: {stop_crit:.2e}")
+                break
+        return w, np.array(p_objs_out), stop_crit

skglm/tests/test_fista.py

@@ -0,0 +1,69 @@
+import pytest
+
+import numpy as np
+from numpy.linalg import norm
+
+import scipy.sparse
+import scipy.sparse.linalg
+from scipy.sparse import csc_matrix, issparse
+
+from skglm.penalties import L1, IndicatorBox
+from skglm.solvers import FISTA, AndersonCD
+from skglm.datafits import Quadratic, Logistic, QuadraticSVC
+from skglm.utils import make_correlated_data, compiled_clone, spectral_norm
+
+
+random_state = 113
+n_samples, n_features = 50, 60
+
+rng = np.random.RandomState(random_state)
+X, y, _ = make_correlated_data(n_samples, n_features, random_state=rng)
+rng.seed(random_state)
+X_sparse = csc_matrix(X * np.random.binomial(1, 0.5, X.shape))
+y_classif = np.sign(y)
+
+alpha_max = norm(X.T @ y, ord=np.inf) / len(y)
+alpha = alpha_max / 10
+
+tol = 1e-10
+
+
+@pytest.mark.parametrize("X", [X, X_sparse])
+@pytest.mark.parametrize("Datafit, Penalty", [
+    (Quadratic, L1),
+    (Logistic, L1),
+    (QuadraticSVC, IndicatorBox),
+])
+def test_fista_solver(X, Datafit, Penalty):
+    _y = y if isinstance(Datafit, Quadratic) else y_classif
+    datafit = compiled_clone(Datafit())
+    _init = y @ X.T if isinstance(Datafit, QuadraticSVC) else X
+    if issparse(X):
+        datafit.initialize_sparse(_init.data, _init.indptr, _init.indices, _y)
+    else:
+        datafit.initialize(_init, _y)
+    penalty = compiled_clone(Penalty(alpha))
+
+    solver = FISTA(max_iter=1000, tol=tol)
+    w_fista = solver.solve(X, _y, datafit, penalty)[0]
+
+    solver_cd = AndersonCD(tol=tol, fit_intercept=False)
+    w_cd = solver_cd.solve(X, _y, datafit, penalty)[0]
+
+    np.testing.assert_allclose(w_fista, w_cd, atol=1e-7)
+
+
+def test_spectral_norm():
+    n_samples, n_features = 50, 60
+    A_sparse = scipy.sparse.random(n_samples, n_features, density=0.7, format='csc',
+                                   random_state=random_state)
+
+    A_bundles = (A_sparse.data, A_sparse.indptr, A_sparse.indices)
+    spectral_norm_our = spectral_norm(*A_bundles, n_samples=len(y))
+    spectral_norm_sp = scipy.sparse.linalg.svds(A_sparse, k=1)[1]
+
+    np.testing.assert_allclose(spectral_norm_our, spectral_norm_sp)
+
+
+if __name__ == '__main__':
+    pass