Optimal Regret for Online Market Making with Limit Order Book
The authors study online market making where a trader posts bids and asks before seeing market prices and private valuations. They establish optimal regret bounds, improving expected regret from $O(T^2/3)$ to high-probability bounds of $O(\sqrt{T})$ under different feedback models. They also prove that sublinear regret is impossible in fully adversarial settings, showing linear lower bounds for the worst-case scenario.