We study regret minimization for learning CDF-related objectives of the form
g(x)⋅PX∼D(X≤x),
over
[0,1]2, where
g is a known Lipschitz function and
D is an unknown distribution. At each round
t, the learner selects a point
xt and observes the binary feedback
I(Xt≤xt), where
Xt∼D. We design an algorithm achieving regret
O(T7/10), improving over the previous best-known bound of
O(T3/4) and showing that the curse of dimensionality can be at least partially lifted for this class of objectives, though a gap remains with the
Ω(T2/3) lower bound. As an application, our techniques yield the same
O(T7/10) regret bound for profit maximization in repeated bilateral trade with fixed prices.