arXiv subjects

Chuangyin Dang

Publications and source records attributed to Chuangyin Dang.

17 recordsLinked to original sources

arXiv2026

A Sequence-Form Formulation of Logistic Quantal Response Equilibrium in Extensive-Form Games for Selecting Nash Equilibria

For an extensive-form game, logistic quantal response equilibrium (QRE) is defined with respect to its associated normal form and provides a natural equilibrium-selection mechanism as the rationality parameter tends to infinity. However, direct computation of logistic QRE in the normal form is generally impractical because the strategy space grows exponentially in the number of information sets. To address this difficulty, we construct a dilated-entropy-barrier artificial game in the sequence form and prove that its Nash equilibria characterize the corresponding logistic QREs. Building on this characterization, we further develop a sequence-form formulation of logistic QRE relative to a totally mixed strategy profile. This formulation gives rise to a differentiable path-following method for tracing the associated logit-QRE path, and we establish the existence of the corresponding smooth path. By recasting the dilated-entropy terms as the standard entropy terms, we additionally derive an equivalent smooth path. Numerical experiments illustrate the equilibrium-selection process of the proposed methods and evaluate their computational performance.

cs.GT↗

arXiv2026

Robust Nash equilibrium seeking based on semi-Markov switching topologies

This paper investigates a distributed robust Nash Equilibrium (NE) seeking problem for second-order players subject to external disturbances and uncertain dynamics while communicating via semi-Markov switching topologies. To accommodate the above concerns, the following targets require to be reached simultaneously: (1) Disturbances and uncertain dynamics rejection in finite time; (2) NE seeking for the second-order players; (3) Distributed action estimation on non-neighboring players under semi-Markov switching. By combining supertwisting-based Integral Sliding-Mode Control (ISMC) with a leader-follower consensus protocol, a novel robust NE seeking algorithm is constructed. Furthermore, to lessen dispensable information transmission, a sampled-data-based event-triggered mechanism is introduced. Incorporating the advantages of both semi-Markov switching and event-triggered mechanism, another NE seeking algorithm is proposed. Theoretical analysis via a Lyapunov-Krasovskii functional proves the leader-follower consensus can be achieved in the mean-square sense. Finally, a connectivity control game is formulated to validate the algorithms.

math.OC↗

arXiv2026

Time-varying Interaction Graph ODE for Dynamic Graph Representation Learning

Graph neural Ordinary Differential Equations (ODE) combine neural ODE with the message passing mechanism of Graph Neural Networks (GNN), providing a continuous-time modeling method for graph representation learning. However, in dynamic graph scenarios, existing graph neural ODEs typically employ a unified message passing mechanism, assuming that inter-node interactions share the same message passing function at any time, which makes it challenging to capture the diversity and time-varying nature of inter-node interaction patterns. To address this, we propose Time-varying Interaction Graph Ordinary Differential Equations (TI-ODE). The core idea of TI-ODE is to decompose the evolution function of a graph ODE into a set of learnable interaction basis functions, where each basis function corresponds to a distinct type of inter-node interaction. These basis functions are dynamically combined through time-dependent learnable weights, enabling inter-node interaction patterns to adaptively evolve over time. Experimental results on six dynamic graph datasets demonstrate that TI-ODE consistently outperforms existing methods and achieves state-of-the-art performance on attribute prediction tasks, and experiments on the \textit{Covid} dataset further verify the interpretability and generalizability of our TI-ODE. Furthermore, we demonstrate both theoretically and empirically that TI-ODE exhibits superior robustness compared to models utilizing a unified message-passing mechanism.

cs.LG↗

arXiv2026

Continuous-Time Distributed Seeking for Variational Generalized Nash Equilibrium of Online Game

This paper mainly investigates a class of distributed Variational Generalized Nash Equilibrium (VGNE) seeking problems for both online noncooperative games and online aggregative games with time-varying coupling inequality constraints. Two novel continuous-time distributed VGNE seeking algorithms are proposed, which realize the constant regret bound and sublinear fit bound, superior to those of the criteria for online optimization problems and online games. Furthermore, to reduce unnecessary communication among players, a dynamic event-triggered mechanism involving internal variables is introduced into the distributed VGNE seeking algorithm, while the constant regret bound and sublinear fit bound are still maintained. Also, the Zeno behavior is strictly prohibited. Moreover, we further investigate the impact of communication noise on the player's measurement of its neighbors' relative states. It is demonstrated that both the regret and fit bounds remain valid as long as the noise level is not excessively large. This result reveals, to some extent, the proposed algorithm's noise-resilient capability. Finally, an online Uncrewed Aerial Vehicle (UAV) swarm game and an online Nash-Cournot game are given to demonstrate the validity of the theoretical results.

math.OC↗

arXiv2026

Characterization and Computation of Normal-Form Proper Equilibria in Extensive-Form Games via the Sequence-Form Representation

Normal-form proper equilibrium, introduced by Myerson as a refinement of normal-form perfect equilibrium, occupies a distinctive position in the equilibrium analysis of extensive-form games because its more stringent perturbation structure entails the sequential rationality. However, the size of the normal-form representation grows exponentially with the number of parallel information sets, making the direct determination of normal-form proper equilibria intractable. To address this challenge, we develop a compact sequence-form proper equilibrium by redefining the expected payoffs over sequences, and we prove that it coincides with the normal-form proper equilibrium via strategic equivalence. To facilitate computation, we further introduce an alternative representation by defining a class of perturbed games based on an $\varepsilon$-permutahedron over sequences. Building on this representation, we introduce two differentiable path-following methods for computing normal-form proper equilibria. These methods rely on artificial sequence-form games whose expected payoff functions incorporate logarithmic or entropy regularization through an auxiliary variable. We prove the existence of a smooth equilibrium path induced by each artificial game, starting from an arbitrary positive realization plan and converging to a normal-form proper equilibrium of the original game as the auxiliary variable approaches zero. Finally, our experimental results demonstrate the effectiveness and efficiency of the proposed methods.

cs.GT↗

arXiv2025

A Sequence-Form Characterization and Differentiable Path-Following Method for Computing Normal-Form Perfect Equilibria in Extensive-Form Games

The sequence form, owing to its compact and holistic strategy representation, has demonstrated significant efficiency in computing normal-form perfect equilibria for two-player extensive-form games with perfect recall. Nevertheless, the examination of $n$-player games remains underexplored. To tackle this challenge, we present a sequence-form characterization of normal-form perfect equilibria for $n$-player extensive-form games, achieved through a class of perturbed games formulated in sequence form. Based on this characterization, we develop a differentiable path-following method for computing normal-form perfect equilibria and prove its convergence. This method formulates an artificial logarithmic-barrier game in sequence form, introducing an additional variable to regulate the impact of logarithmic-barrier terms on the payoff functions, as well as the transition of the strategy space. We prove the existence of a smooth equilibrium path defined by the artificial game, starting from an arbitrary positive realization plan and converging to a normal-form perfect equilibrium of the original game as the additional variable approaches zero. Furthermore, we extend Harsanyi's linear and logarithmic tracing procedures to the sequence form and develop two alternative methods for computing normal-form perfect equilibria. Numerical experiments further substantiate the effectiveness and computational efficiency of our methods.

cs.GT↗

arXiv2025

Enhancing Adversarial Robustness with Conformal Prediction: A Framework for Guaranteed Model Reliability

As deep learning models are increasingly deployed in high-risk applications, robust defenses against adversarial attacks and reliable performance guarantees become paramount. Moreover, accuracy alone does not provide sufficient assurance or reliable uncertainty estimates for these models. This study advances adversarial training by leveraging principles from Conformal Prediction. Specifically, we develop an adversarial attack method, termed OPSA (OPtimal Size Attack), designed to reduce the efficiency of conformal prediction at any significance level by maximizing model uncertainty without requiring coverage guarantees. Correspondingly, we introduce OPSA-AT (Adversarial Training), a defense strategy that integrates OPSA within a novel conformal training paradigm. Experimental evaluations demonstrate that our OPSA attack method induces greater uncertainty compared to baseline approaches for various defenses. Conversely, our OPSA-AT defensive model significantly enhances robustness not only against OPSA but also other adversarial attacks, and maintains reliable prediction. Our findings highlight the effectiveness of this integrated approach for developing trustworthy and resilient deep learning models for safety-critical domains. Our code is available at https://github.com/bjbbbb/Enhancing-Adversarial-Robustness-with-Conformal-Prediction.

cs.LG↗

arXiv2025

A Characterization of Reny's Weakly Sequentially Rational Equilibrium through $\varepsilon$-Perfect $γ$-Weakly Sequentially Rational Equilibrium

A weakening of sequential rationality of sequential equilibrium yields Reny's (1992) weakly sequentially rational equilibrium (WSRE) in extensive-form games. WSRE requires Kreps and Wilson's (1982) consistent assessment to satisfy global rationality of nonconvex payoff functions at every information set reachable by a player's own strategy. The consistent assessment demands a convergent sequence of totally mixed behavioral strategy profiles and associated Bayesian beliefs. Nonetheless, due to the nonconvexity, proving the existence of WSRE required invoking the existence of a normal-form perfect equilibrium, which is sufficient but not necessary. Furthermore, Reny's WSRE definition does not fully specify how to construct the convergent sequence. To overcome these challenges, this paper develops a characterization of WSRE through $\varepsilon$-perfect $γ$-WSRE with local sequential rationality, which is accomplished by incorporating an extra behavioral strategy profile. For any given $γ>0$, we generate a perfect $γ$-WSRE as a limit point of a sequence of $\varepsilon_k$-perfect $γ$-WSRE with $\varepsilon_k\to 0$. A WSRE is then acquired from a limit point of a sequence of perfect $γ_q$-WSRE with $γ_q\to 0$. This characterization enables analytical identification of all WSREs in small extensive-form games and a direct proof of the existence of WSRE. An application of the characterization yields a polynomial system that serves as a necessary and sufficient condition for verifying whether a totally mixed assessment is an $\varepsilon$-perfect $γ$-WSRE. Exploiting the system, we devise differentiable path-following methods to compute WSREs by establishing the existence of smooth paths, which are secured from the equilibrium systems of barrier and penalty extensive-form games. Comprehensive numerical results further confirm the efficiency of the methods.

econ.TH↗

arXiv2025

A Characterization of Nash Equilibrium in Behavioral Strategies through Local Sequential Rationality

The concept of Nash equilibrium in behavioral strategies (NashEBS) was formulated By Nash~\cite{Nash (1951)} for an extensive-form game through global rationality of nonconvex payoff functions. Kuhn's payoff equivalence theorem resolves the nonconvexity issue, but it overlooks that one Nash equilibrium of the associated normal-form game can correspond to infinitely many NashEBSs of an extensive-form game. To remedy this multiplicity, the traditional approach as documented in Myerson~\cite{Myerson (1991)} involves a two-step process: identifying a Nash equilibrium of the agent normal-form representation, followed by verifying whether the corresponding mixed strategy profile is a Nash equilibrium of the associated normal-form game, which often scales exponentially with the size of the extensive-form game tree. In response to these challenges, this paper develops a characterization of NashEBS through the incorporation of an extra behavioral strategy profile and beliefs, which meet local sequential rationality of linear payoff functions and self-independent consistency. This characterization allows one to analytically determine all NashEBSs for small extensive-form games. Building upon this characterization, we acquire a polynomial system serving as a necessary and sufficient condition for determining whether a behavioral strategy profile is a NashEBS. An application of the characterization yields differentiable path-following methods for computing such an equilibrium.

econ.TH↗

arXiv2025

A Characterization of Sequential Equilibrium through $\varepsilon$-Perfect $γ$-Sequential Equilibrium with Local Sequential Rationality and Its Computation

Sequential equilibrium requires a consistent assessment and sequential rationality, where the consistent assessment emerges from a convergent sequence of totally mixed behavioral strategies and associated beliefs. However, the original definition lacks explicit guidance on constructing such convergent sequences. To overcome this difficulty, this paper presents a characterization of sequential equilibrium by introducing $\varepsilon$-perfect $γ$-sequential equilibrium with local sequential rationality. For any $γ>0$, we establish a perfect $γ$-sequential equilibrium as a limit point of a sequence of $\varepsilon_k$-perfect $γ$-sequential equilibrium with $\varepsilon_k\to 0$. A sequential equilibrium is then derived from a limit point of a sequence of perfect $γ_q$-sequential equilibrium with $γ_q\to 0$. This characterization systematizes the construction of convergent sequences and enables the analytical determination of sequential equilibria and the development of a polynomial system serving as a necessary and sufficient condition for $\varepsilon$-perfect $γ$-sequential equilibrium. Exploiting the characterization, we develop a differentiable path-following method to compute a sequential equilibrium.

econ.TH↗

arXiv2025

Game-Theoretic Defenses for Robust Conformal Prediction Against Adversarial Attacks in Medical Imaging

Adversarial attacks pose significant threats to the reliability and safety of deep learning models, especially in critical domains such as medical imaging. This paper introduces a novel framework that integrates conformal prediction with game-theoretic defensive strategies to enhance model robustness against both known and unknown adversarial perturbations. We address three primary research questions: constructing valid and efficient conformal prediction sets under known attacks (RQ1), ensuring coverage under unknown attacks through conservative thresholding (RQ2), and determining optimal defensive strategies within a zero-sum game framework (RQ3). Our methodology involves training specialized defensive models against specific attack types and employing maximum and minimum classifiers to aggregate defenses effectively. Extensive experiments conducted on the MedMNIST datasets, including PathMNIST, OrganAMNIST, and TissueMNIST, demonstrate that our approach maintains high coverage guarantees while minimizing prediction set sizes. The game-theoretic analysis reveals that the optimal defensive strategy often converges to a singular robust model, outperforming uniform and simple strategies across all evaluated datasets. This work advances the state-of-the-art in uncertainty quantification and adversarial robustness, providing a reliable mechanism for deploying deep learning models in adversarial environments.

cs.LG↗

arXiv2024

A Gradually Reinforced Sample-Average-Approximation Differentiable Homotopy Method for a System of Stochastic Equations

This paper intends to apply the sample-average-approximation (SAA) scheme to solve a system of stochastic equations (SSE), which has many applications in a variety of fields. The SAA is an effective paradigm to address risks and uncertainty in stochastic models from the perspective of Monte Carlo principle. Nonetheless, a numerical conflict arises from the sample size of SAA when one has to make a tradeoff between the accuracy of solutions and the computational cost. To alleviate this issue, we incorporate a gradually reinforced SAA scheme into a differentiable homotopy method and develop a gradually reinforced sample-average-approximation (GRSAA) differentiable homotopy method in this paper. By introducing a series of continuously differentiable functions of the homotopy parameter $t$ ranging between zero and one, we establish a differentiable homotopy system, which is able to gradually increase the sample size of SAA as $t$ descends from one to zero. The set of solutions to the homotopy system contains an everywhere smooth path, which starts from an arbitrary point and ends at a solution to the SAA with any desired accuracy. The GRSAA differentiable homotopy method serves as a bridge to link the gradually reinforced SAA scheme and a differentiable homotopy method and retains the nice property of global convergence the homotopy method possesses while greatly reducing the computational cost for attaining a desired solution to the original SSE. Several numerical experiments further confirm the effectiveness and efficiency of the proposed method.

math.NA↗

arXiv2022

Exact Penalty Algorithm of Strong Convertible Nonconvex Optimization

This paper defines a strong convertible nonconvex(SCN) function for solving the unconstrained optimization problems with the nonconvex or nonsmooth(nondifferentiable) function. First, many examples of SCN function are given, where the SCN functions are nonconvex or nonsmooth. Second, the operational properties of the SCN functions are proved, including addition, multiplication, compound operations and so on. Third, the SCN forms of some special functions common in machine learning and engineering applications are presented respectively where these SCN function optimization problems can be transformed into minmax problems with a convex and concave objective function. Fourth,a minmax optimization problem of SCN function and its penalty function are defined. The optimization condition,exactness and stability of the minmax optimization problem are proved. Finally, an algorithm of penalty function to solve the minmax optimization problem and its convergence are given. This paper provides an efficient technique for solving unconstrained nonconvex or nonsmooth(nondifferentiable) optimization problems to avoid using subdifferentiation or smoothing techniques.

math.OC↗

arXiv2022

Optimization Condition and Algorithm of Optimization with Convertible Nonconvex Function

The paper introduces several new concepts for solving nonconvex or nonsmooth optimization problems, including convertible nonconvex function, exact convertible nonconvex function and differentiable convertible nonconvex function. It is proved herein many nonconvex functions or nonsmooth (or discontinuous) functions are actually convertible nonconvex functions and convertible nonconvex function operations such as addition, subtraction, multiplication or division result in convertible nonconvex functions. The sufficient condition for judging a global optimal solution to unconstrained optimization problems with differentiable convertible nonconvex functions is proved, which is equivalent to Karush-Kuhn-Tucker(KKT) condition. Two Lagrange functions of differentiable convertible nonconvex function are defined with their dual problems defined accordingly. The strong duality theorem is proved, showing that the optimal objective value of the global optimal solution is equal to the optimal objective value of the dual problem, which is equivalent to KKT condition. An augmented Lagrangian penalty function algorithm is proposed and its convergence is proved. So the paper provides a new idea for solving unconstrained nonconvex or non-smooth optimization problems and avoids subdifferentiation or smoothing techniques by using some gradient search algorithms, such as gradient descent algorithm, Newton algorithm and so on.

math.OC↗

arXiv2020

Computations and Complexities of Tarski's Fixed Points and Supermodular Games

We consider two models of computation for Tarski's order preserving function f related to fixed points in a complete lattice: the oracle function model and the polynomial function model. In both models, we find the first polynomial time algorithm for finding a Tarski's fixed point. In addition, we provide a matching oracle bound for determining the uniqueness in the oracle function model and prove it is Co-NP hard in the polynomial function model. The existence of the pure Nash equilibrium in supermodular games is proved by Tarski's fixed point theorem. Exploring the difference between supermodular games and Tarski's fixed point, we also develop the computational results for finding one pure Nash equilibrium and determining the uniqueness of the equilibrium in supermodular games.

cs.GT↗

arXiv2018

A new alternating direction trust region method based on conic model for solving unconstrained optimization

In this paper, a new alternating direction trust region method based on conic model is used to solve unconstrained optimization problems. By use of the alternating direction method, the new conic model trust region subproblem is solved by two steps in two orthogonal directions. This new idea overcomes the shortcomings of conic model subproblem which is difficult to solve. Then the global convergence of the method under some reasonable conditions is established. Numerical experiment shows that this method may be better than the dogleg method to solve the subproblem, especially for large-scale problems.

math.OC↗

arXiv2013

A Comparative Study of the Signal-to-Noise Ratios of Different Representations for Symbolic Sequences

Based on the numerical representations by T basic vectors of a symbolic sequence consisting of T symbols, first, we prove mathematical that the total Fourier spectrum of the sequence is the square of the length of the sequence. In the meantime, we define the indicator sequences vector. Using the orthogonal or row orthogonal transformations of the indicator sequences vector, we construct some special numerical representations of the symbolic sequence and characterize the signal-to-noise ratios of the power spectrum of the numerical representations. After calculating the discrete Fourier transform of those special numerical representations, the signal-to-noise ratios of them can be figured out. Mathematical theorems prove that the signal-to-noise ratio of the Fourier spectrum of those special representations of the symbolic sequence is T/(T-1) times the signal-to-noise ratio of the representation by T base vectors. The results are applied in analyzing the properties of the DNA sequences or protein sequences in the frequency domain, if one uses the signal-to-noise ratios of special representations as the distinguishing criterion, the distinguishing results only depend upon the distribution of the symbols in the symbolic sequence and their mathematical constructions of representations, but do not relate to the chemical or biological meanings of the representations.

cs.DM↗