from sklearn.decomposition import MiniBatchDictionaryLearning
import numpy as np
 
a = np.hstack(([0], np.logspace(1, 3, num=10).astype(int)))
slices = [slice(a[k], a[k+1]) for k in range(len(a) - 1)]

objs = []
for seed in range(100):
    X = np.random.RandomState(seed).random_sample((1000, 100))
    dl = MiniBatchDictionaryLearning(n_components=15, max_iter=10, random_state=0)
    for sl in slices:
        dl.partial_fit(X[sl])
        obj = 0.5 * (np.sum((X - dl.transform(X) @ dl.components_)**2)) + dl.alpha * np.sum(np.abs(dl.transform(X)))
        objs.append(obj)

(objs_main - objs_this_pr).min()
# 156.0638606704997
(objs_main - objs_this_pr).max()
#  930.3064058826549
# It corresponds to an improvement on the objective function between 1% and 7%.