We introduce a simple and efficient algorithm for unconstrained zeroth-order stochastic convex bandits and prove its regret is at most $(1 + r/d)[d^{1.5} \sqrt{n} + d^3] polylog(n, d, r)$ where $n$ is the horizon, $d$ the dimension and $r$ is the radius of a known ball containing the minimiser of the loss.

翻译：我们提出了一种简单高效的无约束零阶随机凸带状算法，并证明其遗憾值不超过$(1 + r/d)[d^{1.5} \sqrt{n} + d^3] polylog(n, d, r)$，其中$n$为时间范围，$d$为维度，$r$为包含损失函数最小值的已知球半径。