In repeated bilateral trade with i.i.d. private valuations, a broker can learn the best incentive-compatible profit-maximizing mechanism with $\tilde{O}(\sqrt{T})$ regret, which is nearly optimal, while sublinear regret is impossible against an adversarial sequence.
In particular, the first mechanism to achieve a constant factor approximation of the optimal gain from trade in the Bayesian setting [Deng et al., 2022] is BIC but not DSIC
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Nearly Tight Regret Bounds for Profit Maximization in Bilateral Trade
In repeated bilateral trade with i.i.d. private valuations, a broker can learn the best incentive-compatible profit-maximizing mechanism with $\tilde{O}(\sqrt{T})$ regret, which is nearly optimal, while sublinear regret is impossible against an adversarial sequence.