Method for Chance Constrained Optimal Control Using Biased Kernel Density Estimators

A Warm Start Method for Solving Chance Constrained Optimal Control Problems

A warm start method is developed for efficiently solving complex chance constrained optimal control problems. The warm start method addresses the computational challenges of solving chance constrained optimal control problems using biased kernel density estimators and Legendre-Gauss-Radau collocation with an $hp$ adaptive mesh refinement method. To address the computational challenges, the warm start method improves both the starting point for the chance constrained optimal control problem, as well as the efficiency of cycling through mesh refinement iterations. The improvement is accomplished…

Distributionally Robust Chance Constrained Optimal Power Flow Assuming Unimodal Distributions with Misspecified Modes

Chance constrained optimal power flow (CC-OPF) formulations have been proposed to minimize operational costs while controlling the risk arising from uncertainties like renewable generation and load consumption. To solve CC-OPF, we often need access to the (true) joint probability distribution of all uncertainties, which is rarely known in practice. A solution based on a biased estimate of the distribution can result in poor reliability. To overcome this challenge, recent work has explored distributionally robust chance constraints, in which the chance constraints are satisfied over a family of…

无偏和有偏方差减少的前向-反射-后向分裂方法用于随机复合包含物

Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions

本文提出新的方差减少技术用于前向-反射-后向分裂方法，解决可能非单调的随机复合包含物问题。设计新框架处理无偏和有偏估计器，证明无偏估计器收敛率和有偏估计器的Oracle复杂度。

Stochastic Gradient Descent with Biased but Consistent Gradient Estimators

Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss functions and training nonconvex deep neural networks. The theory assumes that one can easily compute an unbiased gradient estimator, which is usually the case due to the sample average nature of empirical risk minimization. There exist, however, many scenarios (e.g., graphs) where an unbiased estimator may be as expensive to compute as the full gradient beca…

不确定性下的最优控制与联合机会状态约束：几乎处处界、方差缩减及其在（双）线性椭圆型偏微分方程中的应用

Optimal control under uncertainty with joint chance state constraints: almost-everywhere bounds, variance reduction, and application to (bi-)linear elliptic PDEs

本文研究不确定性下带联合机会状态约束的PDE最优控制，证明几乎处处界存在唯一性，并利用球面-径向分解显著降低蒙特卡洛估计方差，数值验证于线性和双线性椭圆PDE。

A Hybrid Stochastic Policy Gradient Algorithm for Reinforcement Learning

We propose a novel hybrid stochastic policy gradient estimator by combining an unbiased policy gradient estimator, the REINFORCE estimator, with another biased one, an adapted SARAH estimator for policy optimization. The hybrid policy gradient estimator is shown to be biased, but has variance reduced property. Using this estimator, we develop a new Proximal Hybrid Stochastic Policy Gradient Algorithm (ProxHSPGA) to solve a composite policy optimization problem that allows us to handle constraints or regularizers on the policy parameters. We first propose a single-looped algorithm then introduc…