Reviews: Improving Online Algorithms via ML Predictions

Please provide some additional clarification on what is to be compared here – in particular, I also stumbled over why (as stated in several corresponding theorems) one ends up with competitive ratios „at most min{ robustness-ratio, consistency-ratio }". At first glance, I had thought that if an algorithm does well for good predictions but the robustness bound is bad, that the latter should dominate. As this is apparently not the case, I ask for a brief explanation/clarification, preferably already in the introduction, as to why the minimum of the two values yields a bound on the competitive ratio.