Configure SGDRegressor "power_t" Parameter

The power_t parameter in scikit-learn’s SGDRegressor controls the learning rate decay during training.

Stochastic Gradient Descent (SGD) is an optimization method used for training linear models. The power_t parameter determines how quickly the learning rate decreases over time, affecting the model’s convergence and performance.

A higher power_t value leads to faster decay, potentially speeding up convergence but risking premature convergence. A lower value results in slower decay, allowing for more exploration but potentially slowing down convergence.

The default value for power_t is 0.25. Common values range from 0 to 1, with 0.5 being another popular choice.

import numpy as np
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.linear_model import SGDRegressor
from sklearn.metrics import mean_squared_error

# Generate synthetic dataset
X, y = make_regression(n_samples=1000, n_features=10, noise=0.1, random_state=42)

# Split into train and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Train with different power_t values
power_t_values = [0, 0.25, 0.5, 1]

# Evaluate final performance
for power_t in power_t_values:
    sgd = SGDRegressor(power_t=power_t, random_state=42, max_iter=1000, tol=1e-3)
    sgd.fit(X_train, y_train)
    y_pred = sgd.predict(X_test)
    mse = mean_squared_error(y_test, y_pred)
    print(f"power_t={power_t}, MSE: {mse:.4f}")

Running the example gives an output like:

power_t=0, MSE: 0.0101
power_t=0.25, MSE: 0.0096
power_t=0.5, MSE: 0.0499
power_t=1, MSE: 13521.9053

The key steps in this example are:

Generate a synthetic regression dataset
Split the data into train and test sets
Train SGDRegressor models with different power_t values
Evaluate the mean squared error of each model on the test set

Some tips and heuristics for setting power_t:

Start with the default value of 0.25 and adjust based on model performance
Use lower values (0.1-0.3) for complex datasets to allow more exploration
Use higher values (0.4-0.7) for simpler datasets to speed up convergence
Monitor learning curves to detect issues like slow convergence or instability

Issues to consider:

The optimal power_t value depends on the dataset’s complexity and noise level
Very high values (close to 1) may cause the learning rate to decay too quickly
Very low values (close to 0) may result in slow convergence
The effect of power_t interacts with other parameters like eta0 (initial learning rate)

See Also