论文标题
部分可观测时空混沌系统的无模型预测
Proximal Algorithms for Smoothed Online Convex Optimization with Predictions
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We consider a smoothed online convex optimization (SOCO) problem with predictions, where the learner has access to a finite lookahead window of time-varying stage costs, but suffers a switching cost for changing its actions at each stage. Based on the Alternating Proximal Gradient Descent (APGD) framework, we develop Receding Horizon Alternating Proximal Descent (RHAPD) for proximable, non-smooth and strongly convex stage costs, and RHAPD-Smooth (RHAPD-S) for non-proximable, smooth and strongly convex stage costs. In addition to outperforming gradient descent-based algorithms, while maintaining a comparable runtime complexity, our proposed algorithms also allow us to solve a wider range of problems. We provide theoretical upper bounds on the dynamic regret achieved by the proposed algorithms, which decay exponentially with the length of the lookahead window. The performance of the presented algorithms is empirically demonstrated via numerical experiments on non-smooth regression, dynamic trajectory tracking, and {economic power dispatch} problems.
