灰箱非线性反馈优化
Gray-Box Nonlinear Feedback Optimization
AI总结：
提出一种灰箱反馈优化控制器，通过可调凸组合将近似灵敏度系统性地融入无模型更新，平衡样本效率与模型失配鲁棒性，并证明非凸问题下的局部最优性。
摘要：
反馈优化通过将动态系统与迭代优化算法闭环互联，实现自主最优性搜索。在各种迭代结构中，基于模型的方法需要系统的输入-输出灵敏度矩阵来构造梯度，而无模型方法通过实时目标评估估计梯度来消除这一需求。这些方法在样本效率和对模型失配（即灵敏度误差）的准确性方面提供了互补优势。为了实现平衡的闭环性能，我们提出了一种灰箱反馈优化控制器，通过可调凸组合将近似灵敏度系统地融入无模型更新中。我们提供了涵盖不同方法的统一性能表征。我们阐明了累积灵敏度误差（基于模型）和随机探索引起的方差（无模型）如何塑造闭环行为，并导致迭代与维度依赖之间的权衡。所提出的控制器在灵敏度不准确的情况下仍能保持样本效率和非凸问题的可证明（局部）最优性。我们进一步开发并表征了一种运行中的灰箱控制器，可处理具有变化目标和稳态输入-输出映射的约束时变问题。
英文摘要：
Feedback optimization enables autonomous optimality seeking of a dynamical system through its closed-loop interconnection with iterative optimization algorithms. Among various iteration structures, model-based approaches require the input-output sensitivity matrix of the system to construct gradients, whereas model-free approaches eliminate this need by estimating gradients from real-time objective evaluations. These approaches offer complementary benefits in sample efficiency and accuracy against model mismatch, i.e., sensitivity errors. To achieve balanced closed-loop performance, we propose a gray-box feedback optimization controller, featuring systematic incorporation of approximate sensitivities into model-free updates via a tunable convex combination. We provide unified performance characterizations covering different approaches. We elucidate how cumulative sensitivity errors (model-based) and variances due to stochastic exploration (model-free) shape the closed-loop behavior and induce a trade-off between iteration and dimensional dependence. The proposed controller retains sample efficiency and provable (local) optimality for nonconvex problems despite inaccurate sensitivities. We further develop and characterize a running gray-box controller that handles constrained time-varying problems with changing objectives and steady-state input-output maps.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
