arXiv subjects

Lingqing Shen

Publications and source records attributed to Lingqing Shen.

7 recordsLinked to original sources

arXiv2026

From Majorization to Scaling: Advancing Convex Relaxations of Maximum Entropy Sampling Problem

In this paper, we study the maximum entropy sampling problem (MESP) and its variants. MESP seeks to identify a small subset of variables that maximizes the determinant of a covariance submatrix, and is a fundamental model in optimal experimental design and information acquisition. Although MESP is combinatorial and NP-hard, continuous relaxations, most notably linx and $\Gamma$ factorization, provide tractable approximations, yet their derivation, relative strength, and potential for systematic improvement remain poorly understood. We address this gap by introducing two main ideas: a unified majorization-based framework for deriving and analyzing relaxations, and a novel scaling-based bound-enhancement technique, which we call double-scaling. Our approach is motivated by the observation that the difficulty of MESP arises from two distinct sources: the combinatorial selection structure and the lack of permutation symmetry in the spectral objective. Majorization naturally resolves the latter by symmetrizing the spectral function and yielding its convex envelope. In the log-determinant setting, we establish the main theoretical properties of double-scaling and prove that it strictly dominates previously known scaling bounds. Using our majorization-based alternative characterization of $\Gamma$ factorization relaxation, we also derive, for the first time, formal dominance relations between linx- and $\Gamma$ factorization-bounds, as well as between their scaling-strengthened variants. Our numerical results show that our double-scaled linx relaxation consistently and substantially outperforms existing scaling methods and compares quite favorably with other state-of-the-art relaxations in terms of both bound quality and computational efficiency.

math.OC↗

arXiv2026

Parameter-Free Non-Ergodic Extragradient Algorithms for Solving Monotone Variational Inequalities

Monotone variational inequalities (VIs) provide a unifying framework for convex minimization, equilibrium computation, and convex-concave saddle-point problems. Extragradient-type methods are among the most effective first-order algorithms for such problems, but their performance hinges critically on stepsize selection. While most existing theory focuses on ergodic averages of the iterates, practical performance is often driven by the significantly stronger behavior of the last iterate. Moreover, available last-iterate guarantees typically rely on fixed stepsizes chosen using problem-specific global smoothness information, which is often difficult to estimate accurately and may not even be applicable. In this paper, we develop parameter-free extragradient methods with non-asymptotic last-iterate guarantees for constrained monotone VIs. For globally Lipschitz operators, our algorithm achieves an $o(1/\sqrt{T})$ last-iterate rate. We then extend the framework to locally Lipschitz operators via backtracking line search and obtain the same rate while preserving parameter-freeness, thereby making parameter-free last-iterate methods applicable to important problem classes for which global smoothness is unrealistic. Our numerical experiments on bilinear matrix games, LASSO, minimax group fairness, and state-of-the-art maximum entropy sampling relaxations demonstrate wide applicability of our results as well as strong last-iterate performance and significant improvements over existing methods.

math.OC↗

arXiv2025

Adaptive-Sensorless Monitoring of Shipping Containers

Monitoring the internal temperature and humidity of shipping containers is essential to preventing quality degradation during cargo transportation. Sensorless monitoring -- machine learning models that predict the internal conditions of the containers using exogenous factors -- shows promise as an alternative to monitoring using sensors. However, it does not incorporate telemetry information and correct for systematic errors, causing the predictions to differ significantly from the live data and confusing the users. In this paper, we introduce the residual correction method, a general framework for correcting for systematic biases in sensorless models after observing live telemetry data. We call this class of models ``adaptive-sensorless'' monitoring. We train and evaluate adaptive-sensorless models on the 3.48 million data points -- the largest dataset of container sensor readings ever used in academic research -- and show that they produce consistent improvements over the baseline sensorless models. When evaluated on the holdout set of the simulated data, they achieve average mean absolute errors (MAEs) of 2.24 $\sim$ 2.31$^\circ$C (vs 2.43$^\circ$C by sensorless) for temperature and 5.72 $\sim$ 7.09% for relative humidity (vs 7.99% by sensorless) and average root mean-squared errors (RMSEs) of 3.19 $\sim$ 3.26$^\circ$C for temperature (vs 3.38$^\circ$C by sensorless) and 7.70 $\sim$ 9.12% for relative humidity (vs 10.0% by sensorless). Adaptive-sensorless models enable more accurate cargo monitoring, early risk detection, and less dependence on full connectivity in global shipping.

cs.LG↗

arXiv2025

Efficient Online Large-Margin Classification via Dual Certificates

Online classification is a central problem in optimization, statistical learning and data science. Classical algorithms such as the perceptron offer efficient updates and finite mistake guarantees on linearly separable data, but they do not exploit the underlying geometric structure of the classification problem. We study the offline maximum margin problem through its dual formulation and use the resulting geometric insights to design a principled and efficient algorithm for the online setting. A key feature of our method is its translation invariance, inherited from the offline formulation, which plays a central role in its performance analysis. Our theoretical analysis yields improved mistake and margin bounds that depend only on translation-invariant quantities, offering stronger guarantees than existing algorithms under the same assumptions in favorable settings. In particular, we identify a parameter regime where our algorithm makes at most two mistakes per sequence, whereas the perceptron can be forced to make arbitrarily many mistakes. Our numerical study on real data further demonstrates that our method matches the computational efficiency of existing online algorithms, while significantly outperforming them in accuracy.

math.OC↗

arXiv2025

Convergence, Duality and Well-Posedness in Convex Bilevel Optimization

We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater constraint qualification. Secondly, we demonstrate through an example that convergence of algorithms is not guaranteed even when usual subotimality gap bounds are present, due to the possibility of encountering super-optimal solutions. We show that strong duality (but not necessarily dual solvability) is exactly equivalent to ensuring correct asymptotic convergence of both inner and outer function values, and provide a simple condition that guarantees strong duality. Unfortunately, we also show that this simple condition is not sufficient to guarantee convergence to the optimal solution set. We draw connections to Levitin-Polyak well-posedness, and leverage this together with our strong duality equivalence to provide another condition that ensures convergence to the optimal solution set. We also discuss how our conditions have been implicitly present in existing algorithmic work.

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arXiv2024

Mistake, Manipulation and Margin Guarantees in Online Strategic Classification

We consider an online strategic classification problem where each arriving agent can manipulate their true feature vector to obtain a positive predicted label, while incurring a cost that depends on the amount of manipulation. The learner seeks to predict the agent's true label given access to only the manipulated features. After the learner releases their prediction, the agent's true label is revealed. Previous algorithms such as the strategic perceptron guarantee finitely many mistakes under a margin assumption on agents' true feature vectors. However, these are not guaranteed to encourage agents to be truthful. Promoting truthfulness is intimately linked to obtaining adequate margin on the predictions, thus we provide two new algorithms aimed at recovering the maximum margin classifier in the presence of strategic agent behavior. We prove convergence, finite mistake and finite manipulation guarantees for a variety of agent cost structures. We also provide generalized versions of the strategic perceptron with mistake guarantees for different costs. Our numerical study on real and synthetic data demonstrates that the new algorithms outperform previous ones in terms of margin, number of manipulation and number of mistakes.

cs.LG↗

arXiv2021

Stochastic Zeroth-order Discretizations of Langevin Diffusions for Bayesian Inference

Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining gradient evaluations might either be computationally expensive, or simply impossible. In this work, we propose and analyze stochastic zeroth-order sampling algorithms for discretizing overdamped and underdamped Langevin diffusions. Our approach is based on estimating the gradients, based on Gaussian Stein's identities, widely used in the stochastic optimization literature. We provide a comprehensive sample complexity analysis -- number noisy function evaluations to be made to obtain an $ε$-approximate sample in Wasserstein distance -- of stochastic zeroth-order discretizations of both overdamped and underdamped Langevin diffusions, under various noise models. We also propose a variable selection technique based on zeroth-order gradient estimates and establish its theoretical guarantees. Our theoretical contributions extend the practical applicability of sampling algorithms to the noisy black-box and high-dimensional settings.

math.ST↗