Tight Regret Bounds for Bilateral Trade under Semi Feedback

The study of $\mathit{\text{regret}}\mathit{\text{minimization}}\mathit{\text{in}}\mathit{\text{fixed-price}}\mathit{\text{bilateral}}\mathit{\text{trade}}$ has received considerable attention in recent research. Previous works [CCC+24a, CCC+24b, AFF24, BCCF24, CJLZ25, LCM25a, GDFS25] have acquired a thorough understanding of the problem, except for determining the tight regret bound for GBB semi-feedback fixed-price mechanisms under adversarial values. In this paper, we resolve this open question by devising an $\tilde{O}(T^{2\mathrm{/}3})$-regret mechanism, matching the $\mathrm{\Omega }(T^{2\mathrm{/}3})$ lower bound from [CJLZ25] up to polylogarithmic factors.