Optimization, Systems & Control II

C3L-B: Optimization, Systems & Control II

Session Type: Lecture
Session Code: C3L-B
Location: Room 2
Date & Time: Friday March 24, 2023 (11:20-12:20)
Chair: Holden Lee
Track: 4
Paper IDPaper TitleAuthorsAbstract
3145Output Reachability of Chen-Fliess Series: A Newton-Raphson ApproachIvan Perez Avellaneda, Luis Duffaut EspinosaThe optimization of Chen-Fliess series allows addressing the problem of the computation of reachable sets of nonlinear affine control systems. This provides an input-output approach to reachability analysis. The Newton-Raphson method is one of the most important line search numerical algorithms. The method is based on the computation of the Hessian and the second-order Taylor approximation of the function of interest. Currently, only first-order optimization methods, such as gradient descent, exist for Chen-Fliess series. In this paper, the framework of differential languages is introduced to allow a systematic description of higher-order derivatives of Chen-Fliess series. This is achieved by defining the derivative operation of a word in a monoid that coincides with the G\\^ateaux derivative of a Chen-Fliess series. In this context, the Hessian of a Chen-Fliess series, its second-order Taylor approximation, and the second-order optimization condition are provided for Chen-Fliess series. Then the Newton-Raphson algorithm is adapted to Chen-Fliess series optimization to compute reachable sets. Illustrative examples and simulations are presented throughout the paper.
3189Langevin Monte Carlo with SPSA-Approximated GradientsShiqing Sun{1}, James C. Spall{2}In sampling problems, gradient-based sampling schemes, like Langevin Monte Carlo (LMC), are widely used due to the short burn-in process compared with non-gradient-based sampling methods like the Metropolis-Hastings method. On the other hand, the application of LMC is limited on whether the gradients are accessible. To extend the application scenario of LMC, we propose a sampling algorithm LMC-SPSA. The method approximates the gradients of the target log density and applies the approximated gradients in Langevin Monte Carlo. We prove the convergence of LMC-SPSA in the distributional distance. Numerical experiments are conducted to verify the performance of LMC-SPSA.