相关论文: Optimization with Temporal and Logical Specificati…

Control synthesis from temporal logic specifications has gained popularity in recent years. In this paper, we use a model predictive approach to control discrete time linear systems with additive bounded disturbances subject to constraints…

Sparse time-frequency (T-F) representations have been an important research topic for more than several decades. Among them, optimization-based methods (in particular, extensions of basis pursuit) allow us to design the representations…

Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…

This study investigates formal-method-based trajectory optimization (TO) for bipedal locomotion, focusing on scenarios where the robot encounters external perturbations at unforeseen times. Our key research question centers around the…

Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…

We propose a signal temporal logic (STL)-based framework that rigorously verifies the feasibility of a mission described in STL and synthesizes control to safely execute it. The proposed framework ensures safe and reliable operation through…

Robust topology optimization (RTO) improves the robustness of designs with respect to random sources in real-world structures, yet an accurate sensitivity analysis requires the solution of many systems of equations at each optimization…

Smooth convex minimization over the unit trace-norm ball is an important optimization problem in machine learning, signal processing, statistics and other fields, that underlies many tasks in which one wishes to recover a low-rank matrix…

Motivated by a class of applied problems arising from physical layer based security in a digital communication system, in particular, by a secrecy sum-rate maximization problem, this paper studies a nonsmooth, difference-of-convex (dc)…

This article considers the problem of source localization (SL) using possibly unreliable time-of-arrival (TOA) based range measurements. Adopting the strategy of statistical robustification, we formulate TOA SL as minimization of a…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

We study estimation in the low signal-to-noise ratio (SNR) regime for a broad class of Gaussian latent-variable models, including Gaussian mixtures and orbit recovery problems. We show that, in this regime, the generalized method-of-moments…

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

This work considers the problem of finding a first-order stationary point of a non-convex function with potentially unbounded smoothness constant using a stochastic gradient oracle. We focus on the class of $(L_0,L_1)$-smooth functions…

In this paper, we challenge the conventional notion in 3DGS-SLAM that rendering quality is the primary determinant of tracking accuracy. We argue that, compared to solely pursuing a perfect scene representation, it is more critical to…

In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to…

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…

The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…

This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…