Before revision:  Comparing the obtained reward with respect to the unique stable matching, we show that \; achieves O(\log(T)/\Delta^2) regret in T rounds, where \Delta is the minimum gap across all agents and arms. We provide a (orderwise) matching regret lower-bound .
After revision:  Comparing the obtained reward with respect to the unique stable matching, we show that . We prove both, a new regret lower bound for the decentralized serial dictatorship model, and that UCB-D3 is order optimal .