广义特征值问题（GEP）是数值线性代数中的基本概念。它捕获了许多经典的机器学习问题的解决方案，例如规范相关分析，独立组件分析，部分最小二乘，线性判别分析，主要组件，后继功能等。尽管如此，在处理大量数据集时，大多数通用求解器都非常昂贵，而研究则集中在为特定问题实例找到有效的解决方案。在这项工作中，我们开发了顶级$ K $ GEP的游戏理论公式，其NASH平衡是一组广义特征向量。我们还提出了一种可行的算法，并保证了与NASH的渐近收敛。当前的最新方法需要$ \ MATHCAL {O}（d^2k）$复杂性，当尺寸数量（$ d $）较大时，这是高昂的昂贵。我们展示了如何实现$ \ MATHCAL {O}（dk）$复杂性，比例缩放到数据集$ 100 \ times $ $比先前方法评估的$。从经验上讲，我们证明我们的算法能够解决各种GEP问题实例，包括对神经网络激活的大规模分析。

现实世界中的数据是高维的：即使在压缩后，书籍，图像或音乐表演也很容易包含数十万个元素。但是，最常用的自回归模型，变压器非常昂贵，以缩放捕获这种远程结构所需的输入和层数。我们开发了感知者AR，这是一种自回归的模态 - 不合骨架构，它使用交叉注意力将远程输入映射到少数潜在的潜在，同时还可以维护端到端的因果关系掩盖。感知器AR可以直接进行十万个令牌，从而实现了实用的长篇小写密度估计，而无需手工制作的稀疏模式或记忆机制。当对图像或音乐进行培训时，感知器AR会生成具有清晰长期连贯性和结构的输出。我们的架构还获得了长期基准测试的最新可能性，包括64 x 64个Imagenet图像和PG-19书籍。

Reinforcement Learning (RL) is currently one of the most commonly used techniques for traffic signal control (TSC), which can adaptively adjusted traffic signal phase and duration according to real-time traffic data. However, a fully centralized RL approach is beset with difficulties in a multi-network scenario because of exponential growth in state-action space with increasing intersections. Multi-agent reinforcement learning (MARL) can overcome the high-dimension problem by employing the global control of each local RL agent, but it also brings new challenges, such as the failure of convergence caused by the non-stationary Markov Decision Process (MDP). In this paper, we introduce an off-policy nash deep Q-Network (OPNDQN) algorithm, which mitigates the weakness of both fully centralized and MARL approaches. The OPNDQN algorithm solves the problem that traditional algorithms cannot be used in large state-action space traffic models by utilizing a fictitious game approach at each iteration to find the nash equilibrium among neighboring intersections, from which no intersection has incentive to unilaterally deviate. One of main advantages of OPNDQN is to mitigate the non-stationarity of multi-agent Markov process because it considers the mutual influence among neighboring intersections by sharing their actions. On the other hand, for training a large traffic network, the convergence rate of OPNDQN is higher than that of existing MARL approaches because it does not incorporate all state information of each agent. We conduct an extensive experiments by using Simulation of Urban MObility simulator (SUMO), and show the dominant superiority of OPNDQN over several existing MARL approaches in terms of average queue length, episode training reward and average waiting time.

Mean-field games have been used as a theoretical tool to obtain an approximate Nash equilibrium for symmetric and anonymous $N$-player games in literature. However, limiting applicability, existing theoretical results assume variations of a "population generative model", which allows arbitrary modifications of the population distribution by the learning algorithm. Instead, we show that $N$ agents running policy mirror ascent converge to the Nash equilibrium of the regularized game within $\tilde{\mathcal{O}}(\varepsilon^{-2})$ samples from a single sample trajectory without a population generative model, up to a standard $\mathcal{O}(\frac{1}{\sqrt{N}})$ error due to the mean field. Taking a divergent approach from literature, instead of working with the best-response map we first show that a policy mirror ascent map can be used to construct a contractive operator having the Nash equilibrium as its fixed point. Next, we prove that conditional TD-learning in $N$-agent games can learn value functions within $\tilde{\mathcal{O}}(\varepsilon^{-2})$ time steps. These results allow proving sample complexity guarantees in the oracle-free setting by only relying on a sample path from the $N$ agent simulator. Furthermore, we demonstrate that our methodology allows for independent learning by $N$ agents with finite sample guarantees.

Correlated Equilibrium is a solution concept that is more general than Nash Equilibrium (NE) and can lead to outcomes with better social welfare. However, its natural extension to the sequential setting, the \textit{Extensive Form Correlated Equilibrium} (EFCE), requires a quadratic amount of space to solve, even in restricted settings without randomness in nature. To alleviate these concerns, we apply \textit{subgame resolving}, a technique extremely successful in finding NE in zero-sum games to solving general-sum EFCEs. Subgame resolving refines a correlation plan in an \textit{online} manner: instead of solving for the full game upfront, it only solves for strategies in subgames that are reached in actual play, resulting in significant computational gains. In this paper, we (i) lay out the foundations to quantify the quality of a refined strategy, in terms of the \textit{social welfare} and \textit{exploitability} of correlation plans, (ii) show that EFCEs possess a sufficient amount of independence between subgames to perform resolving efficiently, and (iii) provide two algorithms for resolving, one using linear programming and the other based on regret minimization. Both methods guarantee \textit{safety}, i.e., they will never be counterproductive. Our methods are the first time an online method has been applied to the correlated, general-sum setting.

This paper presents a game-theoretic framework to study the interactions of attack and defense for deep learning-based NextG signal classification. NextG systems such as the one envisioned for a massive number of IoT devices can employ deep neural networks (DNNs) for various tasks such as user equipment identification, physical layer authentication, and detection of incumbent users (such as in the Citizens Broadband Radio Service (CBRS) band). By training another DNN as the surrogate model, an adversary can launch an inference (exploratory) attack to learn the behavior of the victim model, predict successful operation modes (e.g., channel access), and jam them. A defense mechanism can increase the adversary's uncertainty by introducing controlled errors in the victim model's decisions (i.e., poisoning the adversary's training data). This defense is effective against an attack but reduces the performance when there is no attack. The interactions between the defender and the adversary are formulated as a non-cooperative game, where the defender selects the probability of defending or the defense level itself (i.e., the ratio of falsified decisions) and the adversary selects the probability of attacking. The defender's objective is to maximize its reward (e.g., throughput or transmission success ratio), whereas the adversary's objective is to minimize this reward and its attack cost. The Nash equilibrium strategies are determined as operation modes such that no player can unilaterally improve its utility given the other's strategy is fixed. A fictitious play is formulated for each player to play the game repeatedly in response to the empirical frequency of the opponent's actions. The performance in Nash equilibrium is compared to the fixed attack and defense cases, and the resilience of NextG signal classification against attacks is quantified.

This paper presents a game theoretic framework for participation and free-riding in federated learning (FL), and determines the Nash equilibrium strategies when FL is executed over wireless links. To support spectrum sensing for NextG communications, FL is used by clients, namely spectrum sensors with limited training datasets and computation resources, to train a wireless signal classifier while preserving privacy. In FL, a client may be free-riding, i.e., it does not participate in FL model updates, if the computation and transmission cost for FL participation is high, and receives the global model (learned by other clients) without incurring a cost. However, the free-riding behavior may potentially decrease the global accuracy due to lack of contribution to global model learning. This tradeoff leads to a non-cooperative game where each client aims to individually maximize its utility as the difference between the global model accuracy and the cost of FL participation. The Nash equilibrium strategies are derived for free-riding probabilities such that no client can unilaterally increase its utility given the strategies of its opponents remain the same. The free-riding probability increases with the FL participation cost and the number of clients, and a significant optimality gap exists in Nash equilibrium with respect to the joint optimization for all clients. The optimality gap increases with the number of clients and the maximum gap is evaluated as a function of the cost. These results quantify the impact of free-riding on the resilience of FL in NextG networks and indicate operational modes for FL participation.

Finding the mixed Nash equilibria (MNE) of a two-player zero sum continuous game is an important and challenging problem in machine learning. A canonical algorithm to finding the MNE is the noisy gradient descent ascent method which in the infinite particle limit gives rise to the {\em Mean-Field Gradient Descent Ascent} (GDA) dynamics on the space of probability measures. In this paper, we first study the convergence of a two-scale Mean-Field GDA dynamics for finding the MNE of the entropy-regularized objective. More precisely we show that for any fixed positive temperature (or regularization parameter), the two-scale Mean-Field GDA with a {\em finite} scale ratio converges to exponentially to the unique MNE without assuming the convexity or concavity of the interaction potential. The key ingredient of our proof lies in the construction of new Lyapunov functions that dissipate exponentially along the Mean-Field GDA. We further study the simulated annealing of the Mean-Field GDA dynamics. We show that with a temperature schedule that decays logarithmically in time the annealed Mean-Field GDA converges to the MNE of the original unregularized objective function.

In many real-world settings agents engage in strategic interactions with multiple opposing agents who can employ a wide variety of strategies. The standard approach for designing agents for such settings is to compute or approximate a relevant game-theoretic solution concept such as Nash equilibrium and then follow the prescribed strategy. However, such a strategy ignores any observations of opponents' play, which may indicate shortcomings that can be exploited. We present an approach for opponent modeling in multiplayer imperfect-information games where we collect observations of opponents' play through repeated interactions. We run experiments against a wide variety of real opponents and exact Nash equilibrium strategies in three-player Kuhn poker and show that our algorithm significantly outperforms all of the agents, including the exact Nash equilibrium strategies.

Various types of Multi-Agent Reinforcement Learning (MARL) methods have been developed, assuming that agents' policies are based on true states. Recent works have improved the robustness of MARL under uncertainties from the reward, transition probability, or other partners' policies. However, in real-world multi-agent systems, state estimations may be perturbed by sensor measurement noise or even adversaries. Agents' policies trained with only true state information will deviate from optimal solutions when facing adversarial state perturbations during execution. MARL under adversarial state perturbations has limited study. Hence, in this work, we propose a State-Adversarial Markov Game (SAMG) and make the first attempt to study the fundamental properties of MARL under state uncertainties. We prove that the optimal agent policy and the robust Nash equilibrium do not always exist for an SAMG. Instead, we define the solution concept, robust agent policy, of the proposed SAMG under adversarial state perturbations, where agents want to maximize the worst-case expected state value. We then design a gradient descent ascent-based robust MARL algorithm to learn the robust policies for the MARL agents. Our experiments show that adversarial state perturbations decrease agents' rewards for several baselines from the existing literature, while our algorithm outperforms baselines with state perturbations and significantly improves the robustness of the MARL policies under state uncertainties.