论文标题
使用二次局部近似
Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations
论文作者
论文摘要
我们解决了黑框凸优化问题，其中目的和约束函数尚未明确知道，但可以在可行的集合中进行采样。因此，挑战是生成一系列可行点，这些点会收敛到最佳解决方案。通过利用目标和约束函数的平滑性特性的知识，我们提出了一种新颖的零阶方法Szo-QQ，即迭代地计算约束函数的二次近似值，构建局部可行集合并在它们上进行了优化。我们证明，每次迭代生成的目标值的序列都会收敛到最小值。通过实验，我们表明我们的方法可以与最先进的零阶方法进行凸优化相比，可以实现更快的收敛速度。
We address black-box convex optimization problems, where the objective and constraint functions are not explicitly known but can be sampled within the feasible set. The challenge is thus to generate a sequence of feasible points converging towards an optimal solution. By leveraging the knowledge of the smoothness properties of the objective and constraint functions, we propose a novel zeroth-order method, SZO-QQ, that iteratively computes quadratic approximations of the constraint functions, constructs local feasible sets and optimizes over them. We prove convergence of the sequence of the objective values generated at each iteration to the minimum. Through experiments, we show that our method can achieve faster convergence compared with state-of-the-art zeroth-order approaches to convex optimization.
