arXiv subjects

Guanyi Wang

Publications and source records attributed to Guanyi Wang.

At least 19 recordsLinked to original sources

arXiv2026

On the $\Omega(n)$ SDP relaxation gap for Submodular Box-Constrained Quadratic Programming

Continuous submodular optimization is an important class of nonconvex problems with global guarantees, for which the submodular box-constrained quadratic programming (BCQP) forms a fundamental subclass. It arises naturally as quadratic subproblems of general twice-differentiable submodular problems and also has direct business and management applications such as pricing. This paper studies the worst-case relaxation gap of semidefinite programming (SDP) relaxations with a finite family of valid linear cuts for submodular BCQP. We show that in dimension $n\geq4$, for any SDP relaxation formulated with a finite family of linear cuts, there always exists a submodular BCQP instance with a strictly positive relaxation gap. By restricting to the normalized BCQP instances that remove the problem's scaling factor, we further quantify this limitation with explicit lower bounds. In general dimension $n\geq4$, when the SDP relaxation is formulated with only Boolean-quadric-polytope (BQP) valid cuts, including the commonly used McCormick and triangle inequalities, we establish an $\Omega(n)$ relaxation gap lower bound. For an arbitrary family of $m$ valid linear cuts, we establish an $\Omega(n/m^2)$ lower bound. These results capture the fundamental limitations of SDP relaxations, especially SDP with BQP valid cuts, and provide guidance on what additional constraints may be needed for more effective convex approximations of submodular BCQP.

math.OC↗

arXiv2026

Sparsity-Cone SDP Relaxations and Applications to Variable Fixing for Sparse Quadratic Programs

Quadratic programs (QPs) with sparsity constraint are generally NP-hard, and their efficient global solution depends crucially on tractable tight convex relaxations. In this paper, we propose a sparsity-cone semidefinite programming (SC-SDP) relaxation for sparse (indefinite) QPs. Unlike standard SDP liftings, such as the SDP--RLT relaxation, which involve a $(2n+1)$-dimensional semidefinite matrix, the proposed SC-SDP formulation uses only a $(n+1)$-dimensional matrix together with a single sparsity-cone constraint $\mathcal{K}$ to handle the relaxation of the $\ell_0$-norm constraint. We prove that SC-SDP is equivalent in strength to the SDP--RLT relaxation. We further study the sparsity cone $\mathcal{K}$, deriving structural characterizations and showing that projection onto $\mathcal{K}$ can be computed efficiently via a one-dimensional subproblem. Building on the dual of SC-SDP, we derive explicit presolving mechanisms, including a dual-fixing rule for individual variables, a screening-cut rule for excluding larger support patterns, and a dual-refinement step for improving presolving certificates. To solve the resulting relaxation SC-SDP efficiently, we develop a two-phase Riemannian-based augmented Lagrangian method and exploits the structured projection subproblems. Numerical experiments on several classes of sparse QPs show that SC-SDP preserves the bound quality of SDP--RLT while offering substantial computational advantages and practically effective presolving capabilities.

math.OC↗

arXiv2026

Individualized Treatment Allocation in Sequential Network Games

Designing individualized allocation of treatments so as to maximize the equilibrium welfare of interacting agents has many policy-relevant applications. Focusing on sequential decision games of interacting agents, this paper develops a method to obtain optimal treatment assignment rules that maximize a social welfare criterion by evaluating stationary distributions of outcomes. Stationary distributions in sequential decision games are given by Gibbs distributions, which are difficult to optimize with respect to a treatment allocation due to analytical and computational complexity. We apply a variational approximation to the stationary distribution and optimize the approximated equilibrium welfare with respect to treatment allocation using a greedy optimization algorithm. We characterize the performance of the variational approximation, deriving a performance guarantee for the greedy optimization algorithm via a welfare regret bound. We implement our proposed method in simulation exercises and an empirical application using the Indian microfinance data (Banerjee et al., 2013), and show it delivers significant welfare gains.

econ.EM↗

arXiv2026

Automated Reformulation of Robust Optimization via Memory-Augmented Large Language Models

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its practical use is often limited by the need to manually reformulate uncertain optimization models into tractable deterministic counterparts. Recent large language models (LLMs) have been shown promising for automating optimization formulation, yet RO reformulation remains challenging because it requires precise multi-step reasoning and mathematically consistent transformations. To facilitate systematic evaluation of LLM-based reformulation, for which no dedicated benchmark currently exists, we develop AutoRO-Bench, a benchmark featuring an automated data generation pipeline for the core RO reformulation task and a curated dataset for the RO application task. To address the reformulation challenge, we propose Automated Reformulation with Experience Memory (AutoREM), a tuning-free memory-augmented framework that autonomously builds a structured textual experience memory by reflecting on past failed trajectories through a tailored offline adaptation procedure. AutoREM requires neither domain-specific expert knowledge nor parameter updates, and the resulting memory readily transfers across different base LLMs. Experimental results show that AutoREM consistently improves the accuracy and efficiency of RO reformulation across in-distribution datasets, out-of-distribution datasets, and diverse base LLMs.

cs.AI↗

arXiv2026

Online Decision Making with Fairness over Time

Online platforms increasingly rely on sequential decision-making algorithms to allocate resources, match users, or control exposure, while facing growing pressure to ensure fairness over time. We study a general online decision-making framework in which a platform repeatedly makes decisions from possibly non-convex and discrete feasible sets, such as indivisible assignments or assortment choices, to maximize accumulated reward. Importantly, these decisions must jointly satisfy a set of general, $m$-dimensional, potentially unbounded but convex global constraints, which model diverse long-term fairness goals beyond simple budget caps. We develop a primal-dual algorithm that interprets fairness constraints as dynamic prices and updates them online based on observed outcomes. The algorithm is simple to implement, requiring only the solution of perturbed local optimization problems at each decision step. Under the standard random permutation model, we show that our method achieves $\tilde{O}(\sqrt{mT})$ regret in expected reward while guaranteeing $O(\sqrt{mT})$ violation of long-term fairness constraints deterministically over a horizon of $T$ steps. To capture realistic demand patterns such as periodicity or perturbation, we further extend our guarantees to a grouped random permutation model.

math.OC↗

arXiv2025

Screening Cut Generation for Sparse Ridge Regression

Sparse ridge regression is widely utilized in modern data analysis and machine learning. However, computing globally optimal solutions for sparse ridge regression is challenging, particularly when samples are arbitrarily given or generated under weak modeling assumptions. This paper proposes a novel cut-generation method, Screening Cut Generation (SCG), to eliminate non-optimal solutions for arbitrarily given samples. In contrast to recent safe variable screening approaches, SCG offers superior screening capability by identifying whether a specific $\{\pm 1\}$ combination of multiple features (binaries) lies in the set of optimal solutions. This identification is based on a convex relaxation solution rather than directly solving the original sparse ridge regression. Hence, the cuts generated by SCG can be applied in the pre-processing step of branch-and-bound and its variants to construct safe outer approximations of the optimal solution set. Numerical experiments are reported to validate the theoretical results and demonstrate the efficiency of SCG, particularly in hard real instances and synthetic instances with high dimensions, low ridge regularization parameters, or challenging modeling assumptions.

math.OC↗

arXiv2024

Robust Network Targeting with Multiple Nash Equilibria

Many policy problems involve designing individualized treatment allocation rules to maximize the equilibrium social welfare of interacting agents. Focusing on large-scale simultaneous decision games with strategic complementarities, we develop a method to estimate an optimal treatment allocation rule that is robust to the presence of multiple equilibria. Our approach remains agnostic about changes in the equilibrium selection mechanism under counterfactual policies, and we provide a closed-form expression for the boundary of the set-identified equilibrium outcomes. To address the incompleteness that arises when an equilibrium selection mechanism is not specified, we use the maximin welfare criterion to select a policy, and implement this policy using a greedy algorithm. We establish a performance guarantee for our method by deriving a welfare regret bound, which accounts for sampling uncertainty and the use of the greedy algorithm. We demonstrate our method with an application to the microfinance dataset of Banerjee et al. (2013).

econ.EM↗

arXiv2024

Sparse Principal Component Analysis with Non-Oblivious Adversarial Perturbations

Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are adversarially perturbed. Notably, most existing statistical studies on this variant focus on recovering the ground truth and verifying the robustness of classical algorithms when the given samples are corrupted under oblivious adversarial perturbations. In contrast, this paper aims to find a robust sparse principal component that maximizes the variance of the given samples corrupted by non-oblivious adversarial perturbations, say sparse PCA with Non-Oblivious Adversarial Perturbations (sparse PCA-NOAP). Specifically, we introduce a general formulation for the proposed sparse PCA-NOAP. We then derive Mixed-Integer Programming (MIP) reformulations to upper bound it with provable worst-case guarantees when adversarial perturbations are controlled by two typical norms, i.e., $\ell_{2 \rightarrow \infty}$-norm (sample-wise $\ell_2$-norm perturbation) and $\ell_{1 \rightarrow 2}$-norm (feature-wise $\ell_2$-norm perturbation). Moreover, when samples are drawn from the spiked Wishart model, we show that the proposed MIP reformulations ensure vector recovery properties under a more general parameter region compared with existing results. Numerical simulations are also provided to validate the theoretical findings and demonstrate the accuracy of the proposed formulations.

math.OC↗

arXiv2024

Solving Sparse \& High-Dimensional-Output Regression via Compression

Multi-Output Regression (MOR) has been widely used in scientific data analysis for decision-making. Unlike traditional regression models, MOR aims to simultaneously predict multiple real-valued outputs given an input. However, the increasing dimensionality of the outputs poses significant challenges regarding interpretability and computational scalability for modern MOR applications. As a first step to address these challenges, this paper proposes a Sparse \& High-dimensional-Output REgression (SHORE) model by incorporating additional sparsity requirements to resolve the output interpretability, and then designs a computationally efficient two-stage optimization framework capable of solving SHORE with provable accuracy via compression on outputs. Theoretically, we show that the proposed framework is computationally scalable while maintaining the same order of training loss and prediction loss before-and-after compression under arbitrary or relatively weak sample set conditions. Empirically, numerical results further validate the theoretical findings, showcasing the efficiency and accuracy of the proposed framework.

cs.LG↗

arXiv2023

Do algorithms and barriers for sparse principal component analysis extend to other structured settings?

We study a principal component analysis problem under the spiked Wishart model in which the structure in the signal is captured by a class of union-of-subspace models. This general class includes vanilla sparse PCA as well as its variants with graph sparsity. With the goal of studying these problems under a unified statistical and computational lens, we establish fundamental limits that depend on the geometry of the problem instance, and show that a natural projected power method exhibits local convergence to the statistically near-optimal neighborhood of the solution. We complement these results with end-to-end analyses of two important special cases given by path and tree sparsity in a general basis, showing initialization methods and matching evidence of computational hardness. Overall, our results indicate that several of the phenomena observed for vanilla sparse PCA extend in a natural fashion to its structured counterparts.

stat.ML↗

arXiv2023

A Variance-Reduced and Stabilized Proximal Stochastic Gradient Method with Support Identification Guarantees for Structured Optimization

This paper introduces a new proximal stochastic gradient method with variance reduction and stabilization for minimizing the sum of a convex stochastic function and a group sparsity-inducing regularization function. Since the method may be viewed as a stabilized version of the recently proposed algorithm PStorm, we call our algorithm S-PStorm. Our analysis shows that S-PStorm has strong convergence results. In particular, we prove an upper bound on the number of iterations required by S-PStorm before its iterates correctly identify (with high probability) an optimal support (i.e., the zero and nonzero structure of an optimal solution). Most algorithms in the literature with such a support identification property use variance reduction techniques that require either periodically evaluating an exact gradient or storing a history of stochastic gradients. Unlike these methods, S-PStorm achieves variance reduction without requiring either of these, which is advantageous. Moreover, our support-identification result for S-PStorm shows that, with high probability, an optimal support will be identified correctly in all iterations with the index above a threshold. We believe that this type of result is new to the literature since the few existing other results prove that the optimal support is identified with high probability at each iteration with a sufficiently large index (meaning that the optimal support might be identified in some iterations, but not in others). Numerical experiments on regularized logistic loss problems show that S-PStorm outperforms existing methods in various metrics that measure how efficiently and robustly iterates of an algorithm identify an optimal support.

math.OC↗

arXiv2022

A Framework for Fair Decision-making Over Time with Time-invariant Utilities

Fairness is a major concern in contemporary decision problems. In these situations, the objective is to maximize fairness while preserving the efficacy of the underlying decision-making problem. This paper examines repeated decisions on problems involving multiple stakeholders and a central decision maker. Repetition of the decision-making provides additional opportunities to promote fairness while increasing the complexity from symmetry to finding solutions. This paper presents a general mathematical programming framework for the proposed fairness-over-time (FOT) decision-making problem. The framework includes a natural abstraction of how a stakeholder's acquired utilities can be aggregated over time. In contrast with a natural, descriptive formulation, we demonstrate that if the aggregation function possesses certain basic properties, a strong reformulation can be written to remove symmetry from the problem, making it amenable to branch-and-cut solvers. Finally, we propose a particular relaxation of this reformulation that can assist in the construction of high-quality approximate solutions to the original problem and can be solved using simultaneous row and column generation techniques.

math.OC↗

arXiv2022

Solving sparse principal component analysis with global support

Sparse principal component analysis with global support (SPCAgs), is the problem of finding the top-$r$ leading principal components such that all these principal components are linear combinations of a common subset of at most $k$ variables. SPCAgs is a popular dimension reduction tool in statistics that enhances interpretability compared to regular principal component analysis (PCA). Methods for solving SPCAgs in the literature are either greedy heuristics (in the special case of $r = 1$) with guarantees under restrictive statistical models or algorithms with stationary point convergence for some regularized reformulation of SPCAgs. Crucially, none of the existing computational methods can efficiently guarantee the quality of the solutions obtained by comparing them against dual bounds. In this work, we first propose a convex relaxation based on operator norms that provably approximates the feasible region of SPCAgs within a $c_1 + c_2 \sqrt{\log r} = O(\sqrt{\log r})$ factor for some constants $c_1, c_2$. To prove this result, we use a novel random sparsification procedure that uses the Pietsch-Grothendieck factorization theorem and may be of independent interest. We also propose a simpler relaxation that is second-order cone representable and gives a $(2\sqrt{r})$-approximation for the feasible region. Using these relaxations, we then propose a convex integer program that provides a dual bound for the optimal value of SPCAgs. Moreover, it also has worst-case guarantees: it is within a multiplicative/additive factor of the original optimal value, and the multiplicative factor is $O(\log r)$ or $O(r)$ depending on the relaxation used. Finally, we conduct computational experiments that show that our convex integer program provides, within a reasonable time, good upper bounds that are typically significantly better than the natural baselines.

math.OC↗

arXiv2021

Only Train Once: A One-Shot Neural Network Training And Pruning Framework

Structured pruning is a commonly used technique in deploying deep neural networks (DNNs) onto resource-constrained devices. However, the existing pruning methods are usually heuristic, task-specified, and require an extra fine-tuning procedure. To overcome these limitations, we propose a framework that compresses DNNs into slimmer architectures with competitive performances and significant FLOPs reductions by Only-Train-Once (OTO). OTO contains two keys: (i) we partition the parameters of DNNs into zero-invariant groups, enabling us to prune zero groups without affecting the output; and (ii) to promote zero groups, we then formulate a structured-sparsity optimization problem and propose a novel optimization algorithm, Half-Space Stochastic Projected Gradient (HSPG), to solve it, which outperforms the standard proximal methods on group sparsity exploration and maintains comparable convergence. To demonstrate the effectiveness of OTO, we train and compress full models simultaneously from scratch without fine-tuning for inference speedup and parameter reduction, and achieve state-of-the-art results on VGG16 for CIFAR10, ResNet50 for CIFAR10 and Bert for SQuAD and competitive result on ResNet50 for ImageNet. The source code is available at https://github.com/tianyic/only_train_once.

cs.LG↗

arXiv2021

Using L1-relaxation and integer programming to obtain dual bounds for sparse PCA

Principal component analysis (PCA) is one of the most widely used dimensionality reduction tools in data analysis. The PCA direction is a linear combination of all features with nonzero loadings -- this impedes interpretability. Sparse PCA (SPCA) is a framework that enhances interpretability by incorporating an additional sparsity requirement in the feature weights. However, unlike PCA, the SPCA problem is NP-hard. Most conventional methods for solving SPCA are heuristics with no guarantees, such as certificates of optimality on the solution-quality via associated dual bounds. Dual bounds are available via standard semidefinite programming (SDP) based relaxations, which may not be tight, and the SDPs are difficult to scale by off-the-shelf solvers. In this paper, we present a convex integer programming (IP) framework to derive dual bounds. At the heart of our approach is the so-called $\ell_1$-relaxation of SPCA. While the $\ell_1$-relaxation leads to convex optimization problems for $\ell_0$-sparse linear regression and relatives, it results in a non-convex optimization problem for the PCA problem. We first show that the $\ell_1$-relaxation gives a tight multiplicative bound on SPCA. Then we show how to use standard integer programming techniques to further relax the $\ell_1$-relaxation into a convex IP. We present worst-case results on the quality of the dual bound from the convex IP. We observe that the dual bounds are significantly better than worst-case performance and are superior to the SDP bounds in some real-life instances. Moreover, solving the convex IP model using commercial IP solvers appears to scale much better than solving the SDP-relaxation using commercial solvers. To the best of our knowledge, we obtain the best dual bounds for real and artificial instances for SPCA problems involving covariance matrices of size up to $2000\times 2000$.

math.OC↗

arXiv2021

Who Should Get Vaccinated? Individualized Allocation of Vaccines Over SIR Network

How to allocate vaccines over heterogeneous individuals is one of the important policy decisions in pandemic times. This paper develops a procedure to estimate an individualized vaccine allocation policy under limited supply, exploiting social network data containing individual demographic characteristics and health status. We model spillover effects of the vaccines based on a Heterogeneous-Interacted-SIR network model and estimate an individualized vaccine allocation policy by maximizing an estimated social welfare (public health) criterion incorporating the spillovers. While this optimization problem is generally an NP-hard integer optimization problem, we show that the SIR structure leads to a submodular objective function, and provide a computationally attractive greedy algorithm for approximating a solution that has theoretical performance guarantee. Moreover, we characterise a finite sample welfare regret bound and examine how its uniform convergence rate depends on the complexity and riskiness of social network. In the simulation, we illustrate the importance of considering spillovers by comparing our method with targeting without network information.

econ.EM↗

arXiv2021

Two-phase interfacial structure of bubbly-to-slug transition flows in a 12.7 mm ID vertical tube

This experimental study focuses on the characteristics of air-water two-phase interfacial structure. Interfacial parameters including void fraction, interfacial area concentration, and bubble interfacial velocity are measured using four-sensor electrical conductivity probe on a 12.7 mm ID vertical tube. The tube size is approximately equal to the maximum distorted bubble size. Therefore, the bubbly-to-slug transition characteristics can be different from in other sizes of tubes. Comparing with previous studies, this study provides an experimental database with a wide range on the bubbly-to-slug transition flows, with 4 different superficial liquid velocities (0.3, 0.5, 1.0, and 2.0 m/s) and void fraction ranging from 0.07 to 0.66. Experimental results show that the wall-peak void distribution does not appear in a small diameter tube under the bubbly-to-slug flow transition flow. The distribution is related with both void fraction and the relative bubble size to the tube size. In this sense, a new correlation of distribution parameter in the Drift Flux model is proposed based on the previous studies by Ishii and Hibiki et al. This experimental study can be a good reference for the model development of flow regime transition and the Interfacial Area Transport Equation.

physics.flu-dyn↗

arXiv2021

Half-Space Proximal Stochastic Gradient Method for Group-Sparsity Regularized Problem

Optimizing with group sparsity is significant in enhancing model interpretability in machining learning applications, e.g., feature selection, compressed sensing and model compression. However, for large-scale stochastic training problems, effective group sparsity exploration are typically hard to achieve. Particularly, the state-of-the-art stochastic optimization algorithms usually generate merely dense solutions. To overcome this shortage, we propose a stochastic method -- Half-space Stochastic Projected Gradient (HSPG) method to search solutions of high group sparsity while maintain the convergence. Initialized by a simple Prox-SG Step, the HSPG method relies on a novel Half-Space Step to substantially boost the sparsity level. Numerically, HSPG demonstrates its superiority in deep neural networks, e.g., VGG16, ResNet18 and MobileNetV1, by computing solutions of higher group sparsity, competitive objective values and generalization accuracy.

math.OC↗