Improve Single-Point Zeroth-Order Optimization Using High-Pass and Low-Pass Filters
Improve Single-Point Zeroth-Order Optimization Using High-Pass and Low-Pass Filters
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发表时间：
2021-11
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通讯作者：
Xin Chen;Yujie Tang;N. Li
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作者：
Xin Chen;Yujie Tang;N. Li
单点零阶优化算法(SZO)在解决时变环境下的在线黑箱优化和控制问题时非常有用，因为它在每个时间步只查询一次函数值。然而，传统的SZO方法估计方差大，收敛速度慢，严重限制了它的实际应用。在这项工作中，我们借鉴了极值寻求控制(连续时间版本的SZO)的高通和低通滤波器的思想，将这些滤波器集成在一起，提出了一种新的SZO方法，称为HLF-SZO。结果表明，高通滤波与残差反馈法相吻合，而低通滤波可解释为动量法。结果表明，HLF-SZO方法比普通SZO方法具有更小的方差和更快的收敛速度，并且在实验上优于残差反馈SZO方法，这一点通过大量的数值实验得到了验证。
Single-point zeroth-order optimization (SZO) is useful in solving online black-box optimization and control problems in time-varying environments, as it queries the function value only once at each time step. However, the vanilla SZO method is known to suffer from a large estimation variance and slow convergence, which seriously limits its practical application. In this work, we borrow the idea of high-pass and low-pass filters from extremum seeking control (continuous-time version of SZO) and develop a novel SZO method called HLF-SZO by integrating these filters. It turns out that the high-pass filter coincides with the residual feedback method, and the low-pass filter can be interpreted as the momentum method. As a result, the proposed HLF-SZO achieves a much smaller variance and much faster convergence than the vanilla SZO method and empirically outperforms the residual-feedback SZO method, which is verified via extensive numerical experiments.