When using the ScikitLearn library, you might encounter a situation where your logistic regression model does not converge.
You may get a warning message similar to this:
ConvergenceWarning: lbfgs failed to converge (status=1):
STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
Increase the number of iterations (max_iter) or scale the data as shown in:
https://scikitlearn.org/stable/modules/preprocessing.html
Please also refer to the documentation for alternative solver options:
https://scikitlearn.org/stable/modules/linear_model.html#logisticregression
n_iter_i = _check_optimize_result(
This article aims to help you understand why this happens and how to resolve it.
What Does It Mean For A Logistic Regression Model To Converge?
Imagine you’re on a hike, trying to reach the top of a hill.
You start at the bottom and with each step, you get a little bit closer to the top.
Eventually, you reach a point where you can’t go any higher  you’ve reached the peak.
This is similar to what we mean when we say a logistic regression model has “converged”.
When we’re training our model, we start with some initial parameters.
These are like our starting point at the bottom of the hill.
With each step (or iteration), we tweak these parameters (weights) a little bit to try and improve our model’s predictions. This is like taking a step up the hill.
Now, here’s the key part.
Just like our hike, there’s a point where we can’t improve anymore  we’ve reached the maximum.
When this happens, we say our model has “converged”. It has found the best parameters for making predictions on our dataset.
So, when you hear that a logistic regression model has converged, it means the model has found the best fit for the data.
Although our analogy to hiking is going up, it usually means the model has reached the lowest point in the cost function.
Remember, reaching convergence doesn’t necessarily mean the model is perfect.
It just means the model can’t do any better with the current setup.
It’s always important to evaluate your model to make sure it’s making good predictions.
Reasons For NonConvergence In Logistic Regression
Multicollinearity
One common reason is the presence of highly correlated features in your dataset.
This can make it difficult for the logistic regression model to determine the relationship between each feature and the target variable, leading to nonconvergence.
Here are some fixes for you to try:

Remove some of the correlated features: If you have two features that are highly correlated, consider dropping one.

Combine correlated features: Another option is to combine correlated features into one. For example, if you have two features like “age in years” and “age in months”, you could combine them into a single feature.
Inadequate Solver
Another potential reason could be the choice of solver.
In scikitlearn’s logistic regression, a solver is an algorithm or method that the model uses to find the minimum cost  the top of the hill.
Different solvers use different strategies to find this minimum.
For example, some solvers might take big leaps towards the minimum, while others take small, careful steps.
Some solvers might be better for large datasets, while others work best with small datasets.
If your solver isn’t suited to your data, it might struggle to find the minimum cost.
Changing the solver in ScikitLearn’s LogisticRegression function is quite straightforward.
Here’s an example:
from sklearn.linear_model import LogisticRegression
# Create a LogisticRegression instance using the 'sag' solver
model = LogisticRegression(solver='sag')
In this example, we’re using the ‘sag’ solver, which stands for Stochastic Average Gradient descent.
It’s a variant of gradient descent, and it’s often a good choice for large datasets.
There are several solvers available in ScikitLearn, including ’newtoncg’, ’lbfgs’, ‘sag’, ‘saga’, and ’liblinear’.
Treat it as a hyperparameter and experiment with different values.
Low Number Of Iterations
By default, ScikitLearn’s LogisticRegression function sets the maximum number of iterations to 100.
Sometimes, the model just needs a bit more time to find the best fit.
In our hiking analogy, each step is an iteration.
By increasing the maximum number of iterations, you’re giving the model more opportunities to find the best parameters.
To do this you can adjust the max_iter
parameter when you create your LogisticRegression instance. For example:
from sklearn.linear_model import LogisticRegression
# Create a LogisticRegression instance with a higher max_iter
model = LogisticRegression(max_iter=1000)
In this example, the model will iterate up to 1000 times, instead of the default 100.
But remember, more iterations means more computation time. So, it’s a bit of a tradeoff.
You’ll need to balance the need for a good model fit with the resources you have available.
Wrong Regularization Type And Penalty
Regularization is a technique used to prevent overfitting by adding a penalty term to the cost function.
The two most common types of regularization are L1 and L2, which refer to the absolute and square values of the coefficients, respectively.
In ScikitLearn, you can change the regularization type using the penalty
parameter, and adjust the strength of the penalty with the C
parameter.
Here’s an example:
from sklearn.linear_model import LogisticRegression
# Create a LogisticRegression instance with L1 regularization and a high penalty
model = LogisticRegression(penalty='l1', C=0.01, solver='liblinear')
The C
parameter in logistic regression controls the inverse of the regularization strength.
This means a smaller value of C
specifies stronger regularization, and a larger value specifies weaker regularization.
In this example, we’re using L1 regularization with a high penalty (C is the inverse of regularization strength, so smaller values specify stronger regularization).
Note that not all solvers support both L1 and L2 regularization, so we’ve also specified ’liblinear’ as the solver, which does support both.
In terms of convergence, inappropriate C
values can cause the model to oscillate around the minimum of the cost function without actually converging.
Unscaled Data
Data scaling can play a crucial role in the convergence of a logistic regression model.
When your dataset features have different scales, it can make the logistic regression algorithm’s job more difficult.
It’s trying to find the best values for the coefficients of each feature, but when those features are on different scales, it can cause instability in the convergence process.
If one feature ranges from 0 to 1 and another ranges from 1,000 to 10,000, it’s going to be quite challenging for the algorithm to handle these disparities and find the optimal coefficients.
Scaling your data, such as by using StandardScaler in ScikitLearn, can help.
This process adjusts your features so that they have the same scale, usually a mean of 0 and a standard deviation of 1.
It makes it easier for the logistic regression algorithm to find the optimal coefficients, thus improving the chances of convergence.
Here’s an example of how you might scale your data using StandardScaler:
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression
# Initialize the scaler
scaler = StandardScaler()
# Fit the scaler and transform the features
X_scaled = scaler.fit_transform(X)
# Now use the scaled features to train your logistic regression model
model = LogisticRegression()
model.fit(X_scaled, y)
In this example, X
is your feature matrix and y
is your target vector. After scaling, all your features will be in similar scales, which can aid in the convergence of your logistic regression model.