LBFGS Convergence Warning in Logistic Regression

Problem Statement

When training a Logistic Regression model with Scikit-Learn, you may encounter the following warning:

ConvergenceWarning: lbfgs failed to converge (status=1):
STOP: TOTAL NO. OF ITERATIONS REACHED LIMIT.

This warning indicates that the optimization algorithm failed to find a stable solution within the default iteration limit. Despite this warning, you might still see a high model score (e.g., 0.988 in the example), which can be confusing for machine learning practitioners.

The warning typically occurs when using the default LBFGS solver, which has a maximum iteration limit of 100 by default.

Understanding LBFGS and Convergence

LBFGS stands for "Limited-memory Broyden–Fletcher–Goldfarb–Shanno Algorithm," a popular optimization method for machine learning models. It's a limited-memory quasi-Newton method that approximates the Hessian matrix rather than storing it entirely.

Algorithm convergence means the optimization process has found a stable solution where the error changes very little between iterations. When the algorithm doesn't converge, it means the error is still varying noticeably, even if the overall performance seems good.

Solutions

1. Increase Maximum Iterations

The most straightforward solution is to increase the max_iter parameter:

from sklearn.linear_model import LogisticRegression

clf = Pipeline(steps=[
    ('preprocessor', preprocessor),
    ('classifier', LogisticRegression(max_iter=1000))
])

For more complex problems, you might need even higher values (2000, 3000, or more).

2. Scale Your Data

Although you're already scaling numeric features, ensure your preprocessing is working correctly:

numeric_transformer = Pipeline(steps=[
    ('knnImputer', KNNImputer(n_neighbors=2, weights="uniform")),
    ('scaler', StandardScaler())])

WARNING

Even with scaling, some edge cases might require additional preprocessing or different scaling techniques.

3. Try Different Solvers

LBFGS might not be the best solver for your specific dataset. Consider alternative solvers:

# Try different solvers
solvers_to_try = ['newton-cg', 'sag', 'saga']

for solver in solvers_to_try:
    model = LogisticRegression(solver=solver, max_iter=1000)
    # Train and evaluate model

TIP

Different solvers have different strengths:

• liblinear: Good for small datasets
• sag and saga: Faster for large datasets
• newton-cg: Good for multi-class problems

4. Regularization Tuning

Adjusting regularization can help with convergence:

# Experiment with different regularization strengths
clf = LogisticRegression(C=0.1, max_iter=1000)  # Stronger regularization

5. Feature Engineering

Improve your features to help the algorithm converge:

# Example: Add polynomial features to the numeric transformer
from sklearn.preprocessing import PolynomialFeatures

numeric_transformer = Pipeline(steps=[
    ('knnImputer', KNNImputer(n_neighbors=2, weights="uniform")),
    ('poly', PolynomialFeatures(degree=2, include_bias=False)),
    ('scaler', StandardScaler())])

Why High Scores Despite the Warning?

A high model score with a convergence warning might indicate that:

1. The algorithm found a good solution but needs more iterations to fully converge
2. Your problem is relatively easy to solve, even with a suboptimal solution
3. There might be overfitting despite the good test score

DANGER

Always validate your model thoroughly with multiple metrics and cross-validation, even when you get high scores.

Complete Solution Example

from sklearn.pipeline import Pipeline
from sklearn.impute import KNNImputer, SimpleImputer
from sklearn.preprocessing import StandardScaler, OneHotEncoder
from sklearn.compose import ColumnTransformer
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split

# Define preprocessors
numeric_transformer = Pipeline(steps=[
    ('knnImputer', KNNImputer(n_neighbors=2, weights="uniform")),
    ('scaler', StandardScaler())])

categorical_transformer = Pipeline(steps=[
    ('imputer', SimpleImputer(strategy='constant', fill_value='missing')),
    ('onehot', OneHotEncoder(handle_unknown='ignore'))])

# Create column transformer
preprocessor = ColumnTransformer(transformers=[
    ('num', numeric_transformer, selector(dtype_exclude="object")),
    ('cat', categorical_transformer, selector(dtype_include="object"))
])

# Full pipeline with increased max_iter
clf = Pipeline(steps=[
    ('preprocessor', preprocessor),
    ('classifier', LogisticRegression(max_iter=1000, random_state=42))
])

# Split and train
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
clf.fit(X_train, y_train)
print("model score: %.3f" % clf.score(X_test, y_test))

Additional Considerations

• Random State: Set a random state for reproducible results
• Cross-Validation: Use cross-validation to ensure your model generalizes well
• Class Imbalance: If present, consider using class_weight='balanced'
• Multicollinearity: Check for highly correlated features that might affect convergence

By implementing these solutions, you should be able to resolve the convergence warning while maintaining or even improving your model's performance.