A Derivative-Free Optimization Method With Application to Functions With Exploding and Vanishing Gradients
A Derivative-Free Optimization Method With Application to Functions With Exploding and Vanishing Gradients
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DOI：
10.1109/lcsys.2020.3004747
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发表时间：
2021-04-01
影响因子：
3
通讯作者：
Zhang, Fumin
中科院分区：
文献类型：
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作者：
Al-Abri, Said;Lin, Tony X.;Zhang, Fumin
在这封信中，我们提出了一种生物启发的无导数优化算法，能够最大限度地减少目标函数与消失或爆炸梯度。所提出的方法搜索改进，利用PCA为基础的策略类似于鱼类觅食。该策略不需要显式的梯度计算或估计，并在模拟中显示，需要很少的功能评估。此外，我们的分析证明，该算法的搜索方向收敛到梯度方向以外的小邻域局部极小值。数据驱动的LQR问题和嘈杂的Rosenbrock优化问题的应用程序进行了演示。实验结果表明，所提出的方法具有快速收敛性，能够找到任何可控系统，包括不稳定系统的LQR增益，并具有鲁棒性的噪声函数评估。
In this letter, we propose a bio-inspired derivative-free optimization algorithm capable of minimizing objective functions with vanishing or exploding gradients. The proposed method searches for improvements by leveraging a PCA-based strategy similar to fish foraging. The strategy does not require explicit gradient computation or estimation and is shown in simulation to require few function evaluations. Additionally, our analysis proves that the proposed algorithm's search direction converges to the gradient direction everywhere outside of small neighborhoods around local minima. Applications to a data-driven LQR problem and noisy Rosenbrock optimization problem are demonstrated. Empirical results show the proposed method exhibits fast convergence and is able to find the LQR gains for any controllable system, including unstable systems, and is robust to noisy function evaluations.