Fast, Convexified Stochastic Optimal Open-Loop Control For Linear Systems Using Empirical Characteristic Functions

Convexified Open-Loop Stochastic Optimal Control for Linear Non-Gaussian Systems

We consider stochastic optimal control of linear dynamical systems with additive non-Gaussian disturbance. We propose a novel, sampling-free approach, based on Fourier transformations and convex optimization, to cast the stochastic optimal control problem as a difference-of-convex program. In contrast to existing moment based approaches, our approach invokes higher moments, resulting in less conservatism. We employ piecewise affine approximations and the well-known convex-concave procedure, to efficiently solve the resulting optimization problem via standard conic solvers. We demonstrate that …

Cut-and-Play 算法：通过外部近似计算纳什均衡

The Cut-and-Play Algorithm: Computing Nash Equilibria via Outer Approximations

本文提出 Cut-and-Play 算法，通过凸近似、切割平面和分支操作迭代求解非凸非合作博弈的纳什均衡，无需凸性或连续性假设，并在离散决策和双层博弈上验证其高效性和优越性。

Distributed Block-diagonal Approximation Methods for Regularized Empirical Risk Minimization

In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging research topic. In this paper, we propose a flexible framework for distributed ERM training through solving the dual problem, which provides a unified description and comparison of existing methods. Our approach requires only approximate solutions of the sub-problems involved in the optimization process, and is versatile to be applied on many large-scale ma…

A Fast Scalable Heuristic for Bin Packing

In this paper we present a fast scalable heuristic for bin packing that partitions the given problem into identical sub-problems of constant size and solves these constant size sub-problems by considering only a constant number of bin configurations with bounded unused space. We present some empirical evidence to support the scalability of our heuristic and its tighter empirical analysis of hard instances due to improved lower bound on the necessary wastage in an optimal solution.

Stochastic Primal-Dual Method for Empirical Risk Minimization with $\mathcal{O}(1)$ Per-Iteration Complexity

Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning. In this paper, we propose a new stochastic primal-dual method to solve this class of problems. Different from existing methods, our proposed methods only require O(1) operations in each iteration. We also develop a variance-reduction variant of the algorithm that converges linearly. Numerical experiments suggest that our methods are faster than existing ones such as proximal SGD, SVRG and SAGA on high-dimensional problems.

Muon在重尾噪声下收敛：非凸Hölder光滑经验风险最小化

Muon Converges under Heavy-Tailed Noise: Nonconvex Hölder-Smooth Empirical Risk Minimization

本文研究Muon在重尾噪声下的收敛性，证明其在非凸Hölder光滑经验风险最小化中能收敛到 stationary 点，并优于mini-batch SGD。