  We design decentralized algorithms for regret minimization in the two-sided
matching market with one-sided bandit feedback that significantly improves upon
the prior works (Liu et al. 2020a, 2020b, Sankararaman et al. 2020). First, for
general markets, for any $\varepsilon > 0$, we design an algorithm that
achieves a $O(\log^{1+\varepsilon}(T))$ regret to the agent-optimal stable
matching, with unknown time horizon $T$, improving upon the $O(\log^{2}(T))$
regret achieved in (Liu et al. 2020b). Second, we provide the optimal
$\Theta(\log(T))$ agent-optimal regret for markets satisfying uniqueness
consistency -- markets where leaving participants don't alter the original
stable matching. Previously, $\Theta(\log(T))$ regret was achievable
(Sankararaman et al. 2020, Liu et al. 2020b) in the much restricted serial
dictatorship setting, when all arms have the same preference over the agents.
We propose a phase-based algorithm, wherein each phase, besides deleting the
globally communicated dominated arms the agents locally delete arms with which
they collide often. This local deletion is pivotal in breaking deadlocks
arising from rank heterogeneity of agents across arms. We further demonstrate
the superiority of our algorithm over existing works through simulations.
