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I am using Lasso for multi-output regression. However, whatever value of alpha I am using, it is producing the same mse and R^2 values. Am I doing something wrong?

I have tested the code with different values of alpha starting from 0.001 to 10, but with no effect. On the contrary, Ridge gives me different results.

y_mse=[]
y_r2score=[]
#for alp in [0.1, 0.2, 0.3, 0.4, 0.5]:
for alp in [0.01,0.1,0.5,1,5]:
    print('Working with alpha=',alp)
    Lasso_Regr = Lasso(alpha=alp, normalize=True)
    Lasso_Regr.fit(x_train, y_train)
    y_pred = Lasso_Regr.predict(x_test)
    pred_mean = pd.DataFrame(y_pred.mean(axis=0))
    y_mse.append(mean_squared_error(y_test, y_pred))
    y_r2score.append(r2_score(actual_mean, pred_mean))

print("Mean Squared Error (y_test Vs. y_pred): ", y_mse)
print("r2 Score (y_test_mean Vs. y_pred_mean): ", y_r2score)

Output: MSE: 0.0123499507 R^2 Score: 0.98817476 Same pair of results for all alpha values

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