Hyper Parameter Tuning for MIP

[Parisa Keshavarz]

Hello,

I am trying to solve a mixed-integer model in Matlab using Yalmip based on the following paper (it is not the exact same model but very similar), and I have attached the model as well:

https://pubsonline.informs.org/doi/abs/10.1287/opre.2018.1757?journalCode=opre

There is a parameter lambda used for the regularization of one of the variables and I am wondering how I can tune this parameter? I mean I know that I have to try different values, but I was wondering if there is an easier way to do it rather than a loop. I know Matlab has a regression learner but it only works for predefined models. 

I appreciate your help. 

[Johan Löfberg]

no there is no magic (except you can speed it up using an optimizer construct (and then you have to reparameterize it slightly to use z'*z with q==z*lambda with a new variable z)). note that you can write max(b*(d-q),h*(q-d)) and skip manual modelling

[Parisa Keshavarz]

Thank you so much for the answer. Is it possible not to get improved results when using hyperparameters? I have been trying many values and I am getting the worst train and test performance at the same time and many values just give me the same result as an untuned model. I have different datasets to try but all of them are less than 1000 data points. I thought maybe this is an issue because of the small number of data points.

[Johan Löfberg]

No idea what you are talking about. As I said, there is no magic, the proof is in the pudding. If a certain setting works better, then that's is the case. If not, well then it didn't improve