Reviews: On preserving non-discrimination when combining expert advice

The paper theoretically studies the suitability of achieving a particular definition of fairness, equalized odds (which relates to the false positive rate), in the context of online learning with experts advise (Cesa-Bianchi et al. 2006). In particular, the authors show that achieving an online algorithm that jointly satisfies zero-regret and equalized odds is not possible. Afterward, they show that this is not the case when considering fairness in terms of the total number of errors per group. They also discuss that unfortunately this definition of fairness (also previously discussed in Zafar et al., 2017) is not realistic (or even fair) in many real-world scenarios. In the positive side, I believe that (im)possibility theoretical studies on when a fairness definition can be accomplished is definitely a major contribution to the field. However, I also believe that the paper has important gaps to be filled: 1) Their definition of online learning comes from the game theory literature and does not corresponds to the standard ML view on online learning.