What is a good reward function when objective is to minimize the average along with the variance?

I am trying to formulate a problem where we are trying to minimize the average resource allocated to different users. Due to some inherent properties of the environment, some users can be easily minimized while it is difficult for other users due to which a fairness issue arises. While the main objective is to minimize the average resource consumed by all the users, I also want to ensure that the allocation is fair so the variance of the resource allocation is less.

So is the average+variance a proper reward function? By proper I mean does it capture what I am trying to achieve - a low average while ensuring some degree of fairness? I have seen optimization problems being formulated as x*average + y*variance where x+y=1. Would this kind of formulation be better suited for my case?

Topic reward objective-function machine-learning

Category Data Science

1
answered at

There are several possible approaches.

If you really care about variance, you can take Bayesian approach which models relevant properties as distributions.

It sounds like you don't really care about variance, you want proportional outcomes for different groups. This is sometimes called equalized odds. This can be done by post-processing to create a calibrated classifier score that changes the output labels to your desired objective.

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