Getting similar values for Loss Function and MSE while estimating a Regularized ARX model

After estimating a regularized ARX model, while going through the model metrics (LossFcn and MSE), in the "Report.Fit" property of the identified model, it is observed that the values for MSE and loss function are always the same, even when I change the regularization parameter lambda over a large range of values.

In the MATLAB documentation, it is mentioned that regularization modifies the loss function by adding a penalty term, as seen in the below screenshot, and that "LossFcn" gives the value of the loss function when estimation completes (which contains error thresholds, output weight, and regularization used for estimation).

Whereas, MSE is defined as follows (without the penalty term):

I would like to ask if anyone knows the reason why despite both MSE and LossFcn, as per definition being terms with different values, I am getting the same values for both. Also, I would like to know if someone else has faced similar issues.

[Piyush Dubey]

Please provide code snippets that reproduce this issue and/or the steps that you are following when you observe this.

[Tarunima Mandal]

I had followed the steps shown in the sample code (from MATLAB help) in below screenshot. Also, when I had tried to run the sample code, the values for MSE and LossFcn were identical.

(Version used: MATLAB 2019a)

MSE and LossFcn values (for above example):