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Dachuan Xu

Publications and source records attributed to Dachuan Xu.

17 recordsLinked to original sources
arXiv2026

Toward Trustworthy AI: Multi-Target Adversarial Attacks and Robust Defenses for Continuous Data Summarization

Trustworthy AI requires reliable data-processing pipelines, not only robust downstream predictive models. As an upstream component, data summarization determines which information is retained and passed to subsequent learning or decision modules. Therefore, adversarial perturbations to the summarization process can compromise trustworthy AI in an upstream manner: they may alter the selected summary, reduce its representativeness, and further degrade the utility of subsequent learning tasks. In this paper, we study adversarial attacks on continuous data summarization under similarity-level perturbations through DR-submodular optimization. We show that a class of multi-resolution image summarization objectives can be formulated as multilinear extensions of non-negative submodular set functions and satisfy DR-submodularity with $m$-weak monotonicity. We then formulate multi-target attack generation as a min-max problem, where one admissible perturbation of the similarity structure is optimized to degrade multiple target summarization models. To mitigate such perturbations, we formulate robust defense against mixed attack types as a regularized max-min problem. For both problems, we develop approximation algorithms with theoretical guarantees. Experiments on real-data and controlled clustered benchmarks show that the proposed attack is effective in representative low-to-moderate budget regimes and can induce downstream task-performance loss. The proposed defense improves the robustness--mitigation trade-off in structured settings, while also revealing the parameter sensitivity of robust protection on real data.

cs.AI↗
arXiv2025

A Provably Convergent Plug-and-Play Framework for Stochastic Bilevel Optimization

Bilevel optimization has recently attracted significant attention in machine learning due to its wide range of applications and advanced hierarchical optimization capabilities. In this paper, we propose a plug-and-play framework, named PnPBO, for developing and analyzing stochastic bilevel optimization methods. This framework integrates both modern unbiased and biased stochastic estimators into the single-loop bilevel optimization framework introduced in [9], with several improvements. In the implementation of PnPBO, all stochastic estimators for different variables can be independently incorporated, and an additional moving average technique is applied when using an unbiased estimator for the upper-level variable. In the theoretical analysis, we provide a unified convergence and complexity analysis for PnPBO, demonstrating that the adaptation of various stochastic estimators (including PAGE, ZeroSARAH, and mixed strategies) within the PnPBO framework achieves optimal sample complexity, comparable to that of single-level optimization. This resolves the open question of whether the optimal complexity bounds for solving bilevel optimization are identical to those for single-level optimization. Finally, we empirically validate our framework, demonstrating its effectiveness on several benchmark problems and confirming our theoretical findings.

math.OC↗
arXiv2025

How cancer emerges: Data-driven universal insights into tumorigenesis via hallmark networks

Cancer is a complex disease driven by dynamic regulatory shifts that cannot be fully captured by individual molecular profiling. We employ a data-driven approach to construct a coarse-grained dynamic network model based on hallmark interactions, integrating stochastic differential equations with gene regulatory network data to explore key macroscopic dynamic changes in tumorigenesis. Our analysis reveals that network topology undergoes significant reconfiguration before hallmark expression shifts, serving as an early indicator of malignancy. A pan-cancer examination across $15$ cancer types uncovers universal patterns, where Tissue Invasion and Metastasis exhibits the most significant difference between normal and cancer states, while the differences in Reprogramming Energy Metabolism are the least pronounced, consistent with the characteristic features of tumor biology. These findings reinforce the systemic nature of cancer evolution, highlighting the potential of network-based systems biology methods for understanding critical transitions in tumorigenesis.

q-bio.QM↗
arXiv2024

SPABA: A Single-Loop and Probabilistic Stochastic Bilevel Algorithm Achieving Optimal Sample Complexity

While stochastic bilevel optimization methods have been extensively studied for addressing large-scale nested optimization problems in machine learning, it remains an open question whether the optimal complexity bounds for solving bilevel optimization are the same as those in single-level optimization. Our main result resolves this question: SPABA, an adaptation of the PAGE method for nonconvex optimization in (Li et al., 2021) to the bilevel setting, can achieve optimal sample complexity in both the finite-sum and expectation settings. We show the optimality of SPABA by proving that there is no gap in complexity analysis between stochastic bilevel and single-level optimization when implementing PAGE. Notably, as indicated by the results of (Dagr\'eou et al., 2022), there might exist a gap in complexity analysis when implementing other stochastic gradient estimators, like SGD and SAGA. In addition to SPABA, we propose several other single-loop stochastic bilevel algorithms, that either match or improve the state-of-the-art sample complexity results, leveraging our convergence rate and complexity analysis. Numerical experiments demonstrate the superior practical performance of the proposed methods.

math.OC↗
arXiv2024

Continuous Non-monotone DR-submodular Maximization with Down-closed Convex Constraint

We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can have arbitrarily bad approximation ratios, and they are usually on the boundary of the feasible domain. These findings are in contrast with the monotone case where any stationary point yields a $1/2$-approximation (Hassani et al. (2017)). Moreover, this example offers insights on how to design improved algorithms by avoiding bad stationary points, such as the restricted continuous local search algorithm (Chekuri et al. (2014)) and the aided measured continuous greedy (Buchbinder and Feldman (2019)). However, the analyses in the last two algorithms only work for the discrete domain because both need to invoke the inequality that the multilinear extension of any submodular set function is bounded from below by its Lovasz extension. Our second contribution, therefore, is to remove this restriction and show that both algorithms can be extended to the continuous domain while retaining the same approximation ratios, and hence offering improved approximation ratios over those in Bian et al. (2017a). for the same problem. At last, we also include numerical experiments to demonstrate our algorithms on problems arising from machine learning and artificial intelligence.

cs.DS↗
arXiv2022

On the Population Monotonicity of Independent Set Games

An independent set game is a cooperative game defined on graphs and dealing with profit-sharing in maximum independent set problems. A population monotonic allocation scheme is a rule specifying how to share the profit of each coalition among its participants such that every participant is better off when the coalition expands. In this paper, we provide a necessary and sufficient characterization for population monotonic allocation schemes in independent set games. Moreover, our characterization can be verified efficiently.

cs.GT↗
arXiv2022

Parallel algorithms for maximizing one-sided $σ$-smooth function

In this paper, we study the problem of maximizing a monotone normalized one-sided $σ$-smooth ($OSS$ for short) function $F(x)$, subject to a convex polytope. This problem was first introduced by Mehrdad et al. \cite{GSS2021} to characterize the multilinear extension of some set functions. Different with the serial algorithm with name Jump-Start Continuous Greedy Algorithm by Mehrdad et al. \cite{GSS2021}, we propose Jump-Start Parallel Greedy (JSPG for short) algorithm, the first parallel algorithm, for this problem. The approximation ratio of JSPG algorithm is proved to be $((1-e^{-\left(\fracα{α+1}\right)^{2σ}}) ε)$ for any any number $α\in(0,1]$ and $ε>0$. We also prove that our JSPG algorithm runs in $(O(\log n/ε^{2}))$ adaptive rounds and consumes $O(n \log n/ε^{2})$ queries. In addition, we study the stochastic version of maximizing monotone normalized $OSS$ function, in which the objective function $F(x)$ is defined as $F(x)=\mathbb{E}_{y\sim T}f(x,y)$. Here $f$ is a stochastic function with respect to the random variable $Y$, and $y$ is the realization of $Y$ drawn from a probability distribution $T$. For this stochastic version, we design Stochastic Parallel-Greedy (SPG) algorithm, which achieves a result of $F(x)\geq(1 -e^{-\left(\fracα{α+1}\right)^{2σ}}-ε)OPT-O(κ^{1/2})$, with the same time complexity of JSPG algorithm. Here $κ=\frac{\max \{5\|\nabla F(x_{0})-d_{o}\|^{2}, 16σ^{2}+2L^{2}D^{2}\}}{(t+9)^{2/3}}$ is related to the preset parameters $σ, L, D$ and time $t$.

math.OC↗
arXiv2022

Maximizing Modular plus Non-monotone Submodular Functions

The research problem in this work is the relaxation of maximizing non-negative submodular plus modular with the entire real number domain as its value range over a family of down-closed sets. We seek a feasible point $\mathbf{x}^*$ in the polytope of the given constraint such that $\mathbf{x}^*\in\arg\max_{\mathbf{x}\in\mathcal{P}\subseteq[0,1]^n}F(\mathbf{x})+L(\mathbf{x})$, where $F$, $L$ denote the extensions of the underlying submodular function $f$ and modular function $\ell$. We provide an approximation algorithm named \textsc{Measured Continuous Greedy with Adaptive Weights}, which yields a guarantee $F(\mathbf{x})+L(\mathbf{x})\geq \left(1/e-\mathcal{O}(ε)\right)\cdot f(OPT)+\left(\frac{β-e}{e(β-1)}-\mathcal{O}(ε)\right)\cdot\ell(OPT)$ under the assumption that the ratio of non-negative part within $\ell(OPT)$ to the absolute value of its negative part is demonstrated by a parameter $β\in[0, \infty]$, where $OPT$ is the optimal integral solution for the discrete problem. It is obvious that the factor of $\ell(OPT)$ is $1$ when $β=0$, which means the negative part is completely dominant at this time; otherwise the factor is closed to $1/e$ whe $β\rightarrow\infty$. Our work first breaks the restriction on the specific value range of the modular function without assuming non-positivity or non-negativity as previous results and quantifies the relative variation of the approximation guarantee for optimal solutions with arbitrary structure. Moreover, we also give an analysis for the inapproximability of the problem we consider. We show a hardness result that there exists no polynomial algorithm whose output $S$ satisfies $f(S)+\ell(S)\geq0.478\cdot f(OPT)+\ell(OPT)$.

cs.DS↗
arXiv2022

An improved approximation algorithm for maximizing a DR-submodular function over a convex set

Maximizing a DR-submodular function subject to a general convex set is an NP-hard problem arising from many applications in combinatorial optimization and machine learning. While it is highly desirable to design efficient approximation algorithms under this general setting where neither the objective function is monotonic nor the feasible set is down-closed, our main contribution is to present a 0.25-approximation Frank-Wolfe type of algorithm with a sub-exponential time-complexity under the value oracle model.

cs.DS↗
arXiv2022

Approximate the individually fair k-center with outliers

In this paper, we propose and investigate the individually fair $k$-center with outliers (IF$k$CO). In the IF$k$CO, we are given an $n$-sized vertex set in a metric space, as well as integers $k$ and $q$. At most $k$ vertices can be selected as the centers and at most $q$ vertices can be selected as the outliers. The centers are selected to serve all the not-an-outlier (i.e., served) vertices. The so-called individual fairness constraint restricts that every served vertex must have a selected center not too far way. More precisely, it is supposed that there exists at least one center among its $\lceil (n-q) / k \rceil$ closest neighbors for every served vertex. Because every center serves $(n-q) / k$ vertices on the average. The objective is to select centers and outliers, assign every served vertex to some center, so as to minimize the maximum fairness ratio over all served vertices, where the fairness ratio of a vertex is defined as the ratio between its distance with the assigned center and its distance with a $\lceil (n - q )/k \rceil_{\rm th}$ closest neighbor. As our main contribution, a 4-approximation algorithm is presented, based on which we develop an improved algorithm from a practical perspective.

cs.DS↗
arXiv2020

Outliers Detection Is Not So Hard: Approximation Algorithms for Robust Clustering Problems Using Local Search Techniques

In this paper, we consider two types of robust models of the $k$-median/$k$-means problems: the outlier-version ($k$-MedO/$k$-MeaO) and the penalty-version ($k$-MedP/$k$-MeaP), in which we can mark some points as outliers and discard them. In $k$-MedO/$k$-MeaO, the number of outliers is bounded by a given integer. In $k$-MedP/$k$-MeaP, we do not bound the number of outliers, but each outlier will incur a penalty cost. We develop a new technique to analyze the approximation ratio of local search algorithms for these two problems by introducing an adapted cluster that can capture useful information about outliers in the local and the global optimal solution. For $k$-MeaP, we improve the best known approximation ratio based on local search from $25+\varepsilon$ to $9+\varepsilon$. For $k$-MedP, we obtain the best known approximation ratio. For $k$-MedO/$k$-MeaO, there exists only two bi-criteria approximation algorithms based on local search. One violates the outlier constraint (the constraint on the number of outliers), while the other violates the cardinality constraint (the constraint on the number of clusters). We consider the former algorithm and improve its approximation ratios from $17+\varepsilon$ to $3+\varepsilon$ for $k$-MedO, and from $274+\varepsilon$ to $9+\varepsilon$ for $k$-MeaO.

cs.DS↗
arXiv2020

Eigenvalue-corrected Natural Gradient Based on a New Approximation

Using second-order optimization methods for training deep neural networks (DNNs) has attracted many researchers. A recently proposed method, Eigenvalue-corrected Kronecker Factorization (EKFAC) (George et al., 2018), proposes an interpretation of viewing natural gradient update as a diagonal method, and corrects the inaccurate re-scaling factor in the Kronecker-factored eigenbasis. Gao et al. (2020) considers a new approximation to the natural gradient, which approximates the Fisher information matrix (FIM) to a constant multiplied by the Kronecker product of two matrices and keeps the trace equal before and after the approximation. In this work, we combine the ideas of these two methods and propose Trace-restricted Eigenvalue-corrected Kronecker Factorization (TEKFAC). The proposed method not only corrects the inexact re-scaling factor under the Kronecker-factored eigenbasis, but also considers the new approximation method and the effective damping technique proposed in Gao et al. (2020). We also discuss the differences and relationships among the Kronecker-factored approximations. Empirically, our method outperforms SGD with momentum, Adam, EKFAC and TKFAC on several DNNs.

cs.LG↗
arXiv2020

A Trace-restricted Kronecker-Factored Approximation to Natural Gradient

Second-order optimization methods have the ability to accelerate convergence by modifying the gradient through the curvature matrix. There have been many attempts to use second-order optimization methods for training deep neural networks. Inspired by diagonal approximations and factored approximations such as Kronecker-Factored Approximate Curvature (KFAC), we propose a new approximation to the Fisher information matrix (FIM) called Trace-restricted Kronecker-factored Approximate Curvature (TKFAC) in this work, which can hold the certain trace relationship between the exact and the approximate FIM. In TKFAC, we decompose each block of the approximate FIM as a Kronecker product of two smaller matrices and scaled by a coefficient related to trace. We theoretically analyze TKFAC's approximation error and give an upper bound of it. We also propose a new damping technique for TKFAC on convolutional neural networks to maintain the superiority of second-order optimization methods during training. Experiments show that our method has better performance compared with several state-of-the-art algorithms on some deep network architectures.

cs.LG↗
arXiv2019

A constant FPT approximation algorithm for hard-capacitated k-means

Hard-capacitated $k$-means (HCKM) is one of the fundamental problems remaining open in combinatorial optimization and data mining areas. In this problem, one is required to partition a given $n$-point set into $k$ disjoint clusters with known capacity so as to minimize the sum of within-cluster variances. It is known to be at least APX-hard and for which most of the work is from a meta heuristic perspective. To the best our knowledge, no constant approximation algorithm or existence proof of such an algorithm is known. As our main contribution, we propose an FPT($k$) algorithm with performance guarantee of $69+ε$ for any HCKM instances in this paper.

cs.DS↗
arXiv2018

Selfishness need not be bad: a general proof

This article studies the user behavior in non-atomic congestion games. We consider non-atomic congestion games with continuous and non-decreasing functions and investigate the limit of the price of anarchy when the total user volume approaches infinity. We deepen the knowledge on {\em asymptotically well designed games} \cite{Wu2017Selfishness}, {\em limit games} \cite{Wu2017Selfishness}, {\em scalability} \cite{Wu2017Selfishness} and {\em gaugeability} \cite{Colini2017b} that were recently used in the limit analyses of the price of anarchy for non-atomic congestion games. We develop a unified framework and derive new techniques that allow a general limit analysis of the price of anarchy. With these new techniques, we are able to prove a global convergence on the price of anarchy for non-atomic congestion games with arbitrary polynomial price functions and arbitrary user volume vector sequences. Moreover, we show that these new techniques are very flexible and robust and apply also to non-atomic congestion games with price functions of other types. In particular, we prove that non-atomic congestion games with regularly varying price functions are also asymptotically well designed, provided that the price functions are slightly restricted. Our results greatly generalize recent results. In particular, our results further support the view with a general proof that selfishness need not be bad for non-atomic congestion games.

cs.GT↗
arXiv2015

An improved approximation algorithm for k-median problem using a new factor-revealing LP

The k-median problem is a well-known strongly NP-hard combinatorial optimization problem of both theoretical and practical significance. The previous best approximation ratio for this problem is 2.611+ε(Bryka et al. 2014) based on an (1, 1.95238219) bi-factor approximation algorithm for the classical facility location problem (FLP). This work offers an improved algorithm with an approximation ratio 2.592 +εbased on a new (1, 1.93910094) bi-factor approximation algorithm for the FLP.

cs.DS↗