We take advantage of the correspondence between online learning algorithms design for
negative regrets under certain predictable (or regular) losses and protable prediction market makers
design under some patterns of trade sequences. Thus, we adopt the optimistic (or double) lazy-update
mirror descent algorithm: when in each time step, a leader is called a \strong" one compared with the
other non-minimizers in terms of its much little current cumulative loss, the regret would be negative
in this case, and the more frequent changes of leaders the more negative of the regret. Moreover, if
the immediately previous loss vector is a good estimator of the current loss vector, the regret stays
negative. On the other hand, we are using the modified double-update multiplicative update algorithm of for catching the switches of \dominant experts" quickly enough to beat a fixed best expert in
hindsight in cumulative losses thereby to obtain negative regrets.
Relation:
Proceedings of the 14th Annual Meeting of the Asian Association for Algorithms and Computation (AAAC'2021)
