Linear-time oracle-efficient FTPL with square-root regret

Determine whether an oracle-efficient linear bandit algorithm for general action sets can achieve polynomial-in-dimension times square-root-in-time regret with computational complexity scaling linearly in the time horizon.

Background

The paper’s FTPL algorithm achieves a square-root regret rate for general convex action sets, but its geometric resampling procedure requires a superlinear total computational cost, scaling as T^{3/2}. The authors identify the removal of this computational bottleneck—while retaining polynomial dependence on the dimension and square-root dependence on the horizon—as an unresolved algorithmic problem.