Improved Regret for Zeroth-Order Adversarial Bandit Convex Optimisation

Understand

We prove that the information-theoretic upper bound on the minimax regret for zeroth-order adversarial bandit convex optimisation is at most $O(d^{2.5} \sqrt{n} \log(n))$, where $d$ is the dimension and $n$ is the number of interactions.

• This improves on $O(d^{9.5} \sqrt{n} \log(n)^{7.5}$ by Bubeck et al.
• (2017).
• The proof is based on identifying an improved exploratory distribution for convex functions.