arXiv subjects

Guanpu Chen

Publications and source records attributed to Guanpu Chen.

At least 19 recordsLinked to original sources

arXiv2026

Distributed Team Orchestration via Supervisor Networks: Convergence, Optimality, and Resilience

In this paper, we study zero-sum potential team games with a supervisor network, where agents rely on supervisor-provided belief information rather than accurate common beliefs. The main challenge is that such belief information can be inaccurate because of supervisors' belief-estimation errors and the misreporting of joint actions by Byzantine teams. We propose the distributed team-orchestrating algorithm (DTOA), which combines team fictitious play with supervisor-based distributed belief learning. We prove the convergence of supervisors' belief estimates and establish that the induced learning dynamics converge to a near team-Nash equilibrium (TNE) in terms of the team-Nash gap (TNG). In the Byzantine setting, we consider a misreporting attack model and develop a Byzantine-resilient DTOA. We further provide probabilistic guarantees for Byzantine-team identification and establish an asymptotic bound on the honest TNG. Numerical experiments illustrate the theoretical findings, compare DTOA with baseline learning methods, and evaluate its performance in a Markov decision process setting.

cs.MA↗

arXiv2026

Distributed Algorithm for Robust Wardrop Equilibrium in Uncertain Aggregative Congestion Games

This paper considers a class of aggregative congestion games with uncertain coupling constraints, and devises a distributed algorithm to seek the robust generalized Wardrop equilibrium (RGWE) under worst-case uncertainty. Utilizing robust optimization theory, we reformulate the original aggregative congestion game with uncertainty into a tractable and deterministic augmented problem. Building upon this reformulation, we design a fully distributed algorithm to seek the RGWE by integrating a projected primal-dual scheme and a dynamic tracking technique. The convergence of the proposed algorithm is rigorously guaranteed via singular perturbation theory and LaSalle's invariance principle. Furthermore, we explicitly characterize the relationship between the obtained RGWE and the robust generalized Nash equilibrium, as the latter captures full strategic interactions. Finally, numerical simulations on the charging control of plug-in electric vehicles corroborate our theoretical findings.

cs.GT↗

arXiv2026

Zero-determinant Strategy for Moving Target Defense: Existence, Performance, and Computation

Moving Target Defense (MTD) is commonly formulated as a repeated security game to mitigate persistent threats. Although the strong Stackelberg equilibrium (SSE) characterizes the defender's optimal strategy in the leader-follower framework, computing the SSE often incurs high computational complexity, which significantly limits its practical deployment in MTD problems with multiple targets. This paper proposes adopting a zero-determinant (ZD) strategy for constructing an MTD strategy that achieves both high defensive performance and substantially low computational complexity. We first derive a necessary and sufficient condition for the existence of ZD strategies and investigate the performance of ZD strategies, which shows their upper-bound performance matches that of the SSE strategy. We then formulate two programs to find the optimal ZD strategy parameters under different conditions. Moreover, we design an algorithm to compute the proposed ZD strategies, along with the computational complexity analysis in comparison with the traditional SSE computation. Finally, we conduct experiments on two practical applications to verify our results.

cs.GT↗

arXiv2025

A Scenario Approach to the Robustness of Nonconvex-Nonconcave Minimax Problems

This paper investigates probabilistic robustness of nonconvex-nonconcave minimax problems via the scenario approach. Specifically, under convex strategy sets for all players, inspired by recent advances in scenario optimization, we first establish a probabilistic robustness guarantee for an $\varepsilon$-stationary point, overcoming the dependence on the non-degeneracy assumption by proving the monotonicity of the stationary residual in the number of scenarios. Furthermore, in the presence of nonconvex strategy sets, we reveal the fundamental difficulty of obtaining a tight theoretical bound based on this recent framework. Consequently, we establish a relaxed, yet rigorously valid, probabilistic bound for a global minimax point. A numerical experiment corroborates our theoretical findings.

cs.GT↗

arXiv2025

Privacy Guarantee for Nash Equilibrium Computation of Aggregative Games Based on Pointwise Maximal Leakage

Privacy preservation has served as a key metric in designing Nash equilibrium (NE) computation algorithms. Although differential privacy (DP) has been widely employed for privacy guarantees, it does not exploit prior distributional knowledge of datasets and is ineffective in assessing information leakage for correlated datasets. To address these concerns, we establish a pointwise maximal leakage (PML) framework when computing NE in aggregative games. By incorporating prior knowledge of players' cost function datasets, we obtain a precise and computable upper bound of privacy leakage with PML guarantees. In the entire view, we show PML refines DP by offering a tighter privacy guarantee, enabling flexibility in designing NE computation with prior knowledge. Also, in the individual view, we reveal that the lower bound of PML can exceed the upper bound of DP by constructing specific correlated datasets. The results emphasize that PML is a more proper privacy measure than DP since the latter fails to adequately capture privacy leakage in correlated datasets. Moreover, we conduct experiments with adversaries who attempt to infer players' private information to illustrate the effectiveness.

cs.GT↗

arXiv2025

BG-FlipIn: A Bayesian game framework for FlipIt-insider models in advanced persistent threats

In this paper, we study advanced persistent threats (APT) with an insider who has different preferences. To address the uncertainty of the insider's preference, we propose the BG-FlipIn: a Bayesian game framework for FlipIt-insider models with an investigation on malicious, inadvertent, or corrupt insiders. We calculate the closed-form Bayesian Nash Equilibrium expression and further obtain three edge cases with deterministic insiders corresponding to their Nash Equilibrium expressions. On this basis, we further discover several phenomena in APT related to the defender's move rate and cost, as well as the insider's preferences. We then provide decision-making guidance for the defender, given different parametric conditions. Two applications validate that our BG-FlipIn framework enables the defender to make decisions consistently, avoiding detecting the insider's concrete preference or adjusting its strategy frequently.

cs.GT↗

arXiv2024

Bayesian hypergame approach to equilibrium stability and robustness in moving target defense

We investigate the equilibrium stability and robustness in a class of moving target defense problems, in which players have both incomplete information and asymmetric cognition. We first establish a Bayesian Stackelberg game model for incomplete information and then employ a hypergame reformulation to address asymmetric cognition. With the core concept of the hyper Bayesian Nash equilibrium (HBNE), a condition for achieving both the strategic and cognitive stability in equilibria can be realized by solving linear equations. Moreover, to deal with players' underlying perturbed knowledge, we study the equilibrium robustness by presenting a condition of robust HBNE under the given configuration. Experiments evaluate our theoretical results.

cs.GT↗

arXiv2024

A Multi-Player Potential Game Approach for Sensor Network Localization with Noisy Measurements

Sensor network localization (SNL) is a challenging problem due to its inherent non-convexity and the effects of noise in inter-node ranging measurements and anchor node position. We formulate a non-convex SNL problem as a multi-player non-convex potential game and investigate the existence and uniqueness of a Nash equilibrium (NE) in both the ideal setting without measurement noise and the practical setting with measurement noise. We first show that the NE exists and is unique in the noiseless case, and corresponds to the precise network localization. Then, we study the SNL for the case with errors affecting the anchor node position and the inter-node distance measurements. Specifically, we establish that in case these errors are sufficiently small, the NE exists and is unique. It is shown that the NE is an approximate solution to the SNL problem, and that the position errors can be quantified accordingly. Based on these findings, we apply the results to case studies involving only inter-node distance measurement errors and only anchor position information inaccuracies.

math.OC↗

arXiv2024

Non-convex potential games for finding global solutions to sensor network localization

Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results.

math.OC↗

arXiv2024

Inverse learning of black-box aggregator for robust Nash equilibrium

In this note, we investigate the robustness of Nash equilibria (NE) in multi-player aggregative games with coupling constraints. There are many algorithms for computing an NE of an aggregative game given a known aggregator. When the coupling parameters are affected by uncertainty, robust NE need to be computed. We consider a scenario where players' weight in the aggregator is unknown, making the aggregator kind of "a black box". We pursue a suitable learning approach to estimate the unknown aggregator by proposing an inverse variational inequality-based relationship. We then utilize the counterpart to reconstruct the game and obtain first-order conditions for robust NE in the worst case. Furthermore, we characterize the generalization property of the learning methodology via an upper bound on the violation probability. Simulation experiments show the effectiveness of the proposed inverse learning approach.

cs.GT↗

arXiv2024

Global solution to sensor network localization: A non-convex potential game approach and its distributed implementation

Consider a sensor network consisting of both anchor and non-anchor nodes. We address the following sensor network localization (SNL) problem: given the physical locations of anchor nodes and relative measurements among all nodes, determine the locations of all non-anchor nodes. The solution to the SNL problem is challenging due to its inherent non-convexity. In this paper, the problem takes on the form of a multi-player non-convex potential game in which canonical duality theory is used to define a complementary dual potential function. After showing the Nash equilibrium (NE) correspondent to the SNL solution, we provide a necessary and sufficient condition for a stationary point to coincide with the NE. An algorithm is proposed to reach the NE and shown to have convergence rate $\mathcal{O}(1/\sqrt{k})$. With the aim of reducing the information exchange within a network, a distributed algorithm for NE seeking is implemented and its global convergence analysis is provided. Extensive simulations show the validity and effectiveness of the proposed approach to solve the SNL problem.

math.OC↗

arXiv2023

Equalizer zero-determinant strategy in discounted repeated Stackelberg asymmetric game

This paper focuses on the performance of equalizer zero-determinant (ZD) strategies in discounted repeated Stackerberg asymmetric games. In the leader-follower adversarial scenario, the strong Stackelberg equilibrium (SSE) deriving from the opponents' best response (BR), is technically the optimal strategy for the leader. However, computing an SSE strategy may be difficult since it needs to solve a mixed-integer program and has exponential complexity in the number of states. To this end, we propose to adopt an equalizer ZD strategy, which can unilaterally restrict the opponent's expected utility. We first study the existence of an equalizer ZD strategy with one-to-one situations, and analyze an upper bound of its performance with the baseline SSE strategy. Then we turn to multi-player models, where there exists one player adopting an equalizer ZD strategy. We give bounds of the sum of opponents' utilities, and compare it with the SSE strategy. Finally, we give simulations on unmanned aerial vehicles (UAVs) and the moving target defense (MTD) to verify the effectiveness of our approach.

cs.GT↗

arXiv2023

OmniForce: On Human-Centered, Large Model Empowered and Cloud-Edge Collaborative AutoML System

Automated machine learning (AutoML) seeks to build ML models with minimal human effort. While considerable research has been conducted in the area of AutoML in general, aiming to take humans out of the loop when building artificial intelligence (AI) applications, scant literature has focused on how AutoML works well in open-environment scenarios such as the process of training and updating large models, industrial supply chains or the industrial metaverse, where people often face open-loop problems during the search process: they must continuously collect data, update data and models, satisfy the requirements of the development and deployment environment, support massive devices, modify evaluation metrics, etc. Addressing the open-environment issue with pure data-driven approaches requires considerable data, computing resources, and effort from dedicated data engineers, making current AutoML systems and platforms inefficient and computationally intractable. Human-computer interaction is a practical and feasible way to tackle the problem of open-environment AI. In this paper, we introduce OmniForce, a human-centered AutoML (HAML) system that yields both human-assisted ML and ML-assisted human techniques, to put an AutoML system into practice and build adaptive AI in open-environment scenarios. Specifically, we present OmniForce in terms of ML version management; pipeline-driven development and deployment collaborations; a flexible search strategy framework; and widely provisioned and crowdsourced application algorithms, including large models. Furthermore, the (large) models constructed by OmniForce can be automatically turned into remote services in a few minutes; this process is dubbed model as a service (MaaS). Experimental results obtained in multiple search spaces and real-world use cases demonstrate the efficacy and efficiency of OmniForce.

cs.LG↗

arXiv2023

Global Nash Equilibrium in Non-convex Multi-player Game: Theory and Algorithms

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the non-convexity, obtaining the existence condition of global NE is challenging, let alone designing theoretically guaranteed realization algorithms. This paper takes conjugate transformation to the formulation of non-convex multi-player games, and casts the complementary problem into a variational inequality (VI) problem with a continuous pseudo-gradient mapping. We then prove the existence condition of global NE: the solution to the VI problem satisfies a duality relation. Based on this VI formulation, we design a conjugate-based ordinary differential equation (ODE) to approach global NE, which is proved to have an exponential convergence rate. To make the dynamics more implementable, we further derive a discretized algorithm. We apply our algorithm to two typical scenarios: multi-player generalized monotone game and multi-player potential game. In the two settings, we prove that the step-size setting is required to be $\mathcal{O}(1/k)$ and $\mathcal{O}(1/\sqrt k)$ to yield the convergence rates of $\mathcal{O}(1/ k)$ and $\mathcal{O}(1/\sqrt k)$, respectively. Extensive experiments in robust neural network training and sensor localization are in full agreement with our theory.

cs.GT↗

arXiv2023

Bayesian Nash Equilibrium Seeking for Distributed Incomplete-information Aggregative Games

In this paper, we consider a distributed Bayesian Nash equilibrium (BNE) seeking problem in incomplete-information aggregative games, which is a generalization of Bayesian games and deterministic aggregative games. We handle the aggregation function for distributed incomplete-information situations. Since the feasible strategies are infinite-dimensional functions and lie in a non-compact set, the continuity of types brings barriers to seeking equilibria. To this end, we discretize the continuous types and then prove that the equilibrium of the derived discretized model is an $ε$-BNE. On this basis, we propose a distributed algorithm for an $ε$-BNE and further prove its convergence.

math.OC↗

arXiv2023

Zero-Determinant Strategy in Stochastic Stackelberg Asymmetric Security Game

In a stochastic Stackelberg asymmetric security game, the strong Stackelberg equilibrium (SSE) strategy is a popular option for the defender to get the highest utility against an attacker with the best response (BR) strategy. However, the attacker may be a boundedly rational player, who adopts a combination of the BR strategy and a fixed stubborn one. In such a condition, the SSE strategy may not maintain the defensive performance due to the stubborn element. In this paper, we focus on how the defender can adopt the unilateral-control zero-determinate (ZD) strategy to confront the boundedly rational attacker. At first, we verify the existence of ZD strategies for the defender. We then investigate the performance of the defender's ZD strategy against a boundedly rational attacker, with a comparison of the SSE strategy. Specifically, when the attacker's strategy is close to the BR strategy, the ZD strategy admits a bounded loss for the defender compared with the SSE strategy. Conversely, when the attacker's strategy is close to the stubborn strategy, the ZD strategy can bring higher defensive performance for the defender than the SSE strategy does.

cs.GT↗

arXiv2022

Coincidence analysis of Stackelberg and Nash equilibria in three-player leader-follower security games

There has been significant recent interest in leader-follower security games, where the leader dominates the decision process with the Stackelberg equilibrium (SE) strategy. However, such a leader-follower scheme may become invalid in practice due to subjective or objective factors, and then the Nash equilibrium (NE) strategy may be an alternative option. In this case, the leader may face a dilemma of choosing an SE strategy or an NE strategy. In this paper, we focus on a unified three-player leader-follower security game and study the coincidence between SE and NE. We first explore a necessary and sufficient condition for the case that each SE is an NE, which can be further presented concisely when the SE is unique. This condition not only provides access to seek a satisfactory SE strategy but also makes a criterion to verify an obtained SE strategy. Then we provide another appropriate condition for the case that at least one SE is an NE. Moreover, since the coincidence condition may not always be satisfied, we describe the closeness between SE and NE, and give an upper bound of their deviation. Finally, we show the applicability of the obtained theoretical results in several practical security cases, including the secure transmission problem and the cybersecurity defense.

cs.GT↗

arXiv2022

Defense for Advanced Persistent Threat with Inadvertent or Malicious Insider Threats

In this paper, we propose a game-theoretical framework to investigate advanced persistent threat problems with two types of insider threats: malicious and inadvertent. Within this framework, a unified three-player game is established and Nash equilibria are obtained in response to different insiders. By analyzing Nash equilibria, we provide quantitative solutions to the advanced persistent threat problems with insider threats. Furthermore, optimal defense strategy and defender's cost comparisons between two insider threats have been performed. The findings suggest that the defender should employ more active defense strategies against inadvertent insider threats than against malicious insider threats, despite the fact that malicious insider threats cost the defender more. Our theoretical analysis is validated by numerical results, including an additional examination of the conditions of the risky strategies adopted by different insiders. This may help the defender in determining monitoring intensities and defensive strategies.

math.OC↗