论文标题
二阶在线非convex优化
Second-order Online Nonconvex Optimization
论文作者
论文摘要
我们介绍了在线牛顿的方法，这是一种用于在线非convex优化的单步二阶方法。我们分析其性能，并获得动态遗憾结合，该结合是在圆形优势之间的累积变化中线性的。我们表明，如果圆形Optima之间的变化有限，则该方法会导致持续的遗憾。在一般情况下，在线牛顿的方法优于凸功能的在线凸优化算法，并且与专用算法相似，以实现强烈凸功能。我们在非线性，非convex移动目标本地化示例上模拟了在线牛顿方法的性能，并发现它的表现优于一阶方法。
We present the online Newton's method, a single-step second-order method for online nonconvex optimization. We analyze its performance and obtain a dynamic regret bound that is linear in the cumulative variation between round optima. We show that if the variation between round optima is limited, the method leads to a constant regret bound. In the general case, the online Newton's method outperforms online convex optimization algorithms for convex functions and performs similarly to a specialized algorithm for strongly convex functions. We simulate the performance of the online Newton's method on a nonlinear, nonconvex moving target localization example and find that it outperforms a first-order approach.
