In this paper, we study the notion of adversarial Stackelberg value for two-player non-zero sum games played on bi-weighted graphs with the mean-payoff and the discounted sum functions. The adversarial Stackelberg value of Player 0 is the largest value that Player 0 can obtain when announcing her strategy to Player 1 which in turn responds with any of his best response. For the mean-payoff function, we show that the adversarial Stackelberg value is not always achievable but epsilon-optimal strategies exist. We show how to compute this value and prove that the associated threshold problem is in NP. For the discounted sum payoff function, we draw a link with the target discounted sum problem which explains why the problem is difficult to solve for this payoff function. We also provide solutions to related gap problems.
Robust Reinforcement Learning (RL) focuses on improving performances under model errors or adversarial attacks, which facilitates the real-life deployment of RL agents. Robust Adversarial Reinforcement Learning (RARL) is one of the most popular frameworks for robust RL. However, most of the existing literature models RARL as a zero-sum simultaneous game with Nash equilibrium as the solution concept, which could overlook the sequential nature of RL deployments, produce overly conservative agents, and induce training instability. In this paper, we introduce a novel hierarchical formulation of ro…
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Adversarial deep learning is to train robust DNNs against adversarial attacks, which is one of the major research focuses of deep learning. Game theory has been used to answer some of the basic questions about adversarial deep learning such as the existence of a classifier with optimal robustness and the existence of optimal adversarial samples for a given class of classifiers. In most previous work, adversarial deep learning was formulated as a simultaneous game and the strategy spaces are assumed to be certain probability distributions in order for the Nash equilibrium to exist. But, this as…
Stackelberg Security Games (SSGs) have been adopted widely for modeling adversarial interactions. With increasing size of the applications of SSGs, scalability of equilibrium computation is an important research problem. While prior research has made progress with regards to scalability, many real world problems cannot be solved satisfactorily yet as per current requirements; these include the deployed federal air marshals (FAMS) application and the threat screening (TSG) problem at airports. Further, these problem domains are inherently limited by NP hardness shown in prior literature. We ini…
Two-player mean-payoff Stackelberg games are nonzero-sum infinite duration games played on a bi-weighted graph by Leader (Player 0) and Follower (Player 1). Such games are played sequentially: first, Leader announces her strategy, second, Follower chooses his best-response. If we cannot impose which best-response is chosen by Follower, we say that Follower, though strategic, is adversarial towards Leader. The maximal value that Leader can get in this nonzero-sum game is called the adversarial Stackelberg value (ASV) of the game. We study the robustness of strategies for Leader in these games a…
Stackelberg Games are gaining importance in the last years due to the raise of Adversarial Machine Learning (AML). Within this context, a new paradigm must be faced: in classical game theory, intervening agents were humans whose decisions are generally discrete and low dimensional. In AML, decisions are made by algorithms and are usually continuous and high dimensional, e.g. choosing the weights of a neural network. As closed form solutions for Stackelberg games generally do not exist, it is mandatory to have efficient algorithms to search for numerical solutions. We study two different proced…
Online Learning in Stackelberg Security Games with Time-Varying Attack Intensities
Robotics and Autonomous Systems Thrust, Systems Hub, The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州）系统枢纽机器人与自主系统推力）；Department of Electrical and Computer Engineering, University of Central Florida（中佛罗里达大学电气与计算机工程系）
This article investigates the anti-jamming communications problem in wireless networks from a Stackelberg game perspective. By exploring and analyzing the inherent characteristics of the anti-jamming problem, we present and discuss some technical challenges and fundamental requirements to address them. To be specific, the adversarial characteristic, incomplete information constraints, dynamics, uncertainty, dense deployment, and heterogeneous feature bring technical challenges to anti-jamming communications in wireless networks. Then, for the purpose of improving system performance, four requi…
Zero-sum stochastic games have found important applications in a variety of fields, from machine learning to economics. Work on this model has primarily focused on the computation of Nash equilibrium due to its effectiveness in solving adversarial board and video games. Unfortunately, a Nash equilibrium is not guaranteed to exist in zero-sum stochastic games when the payoffs at each state are not convex-concave in the players' actions. A Stackelberg equilibrium, however, is guaranteed to exist. Consequently, in this paper, we study zero-sum stochastic Stackelberg games. Going beyond known exis…
In this paper, the problem of network connectivity is studied for an adversarial Internet of Battlefield Things (IoBT) system in which an attacker aims at disrupting the connectivity of the network by choosing to compromise one of the IoBT nodes at each time epoch. To counter such attacks, an IoBT defender attempts to reestablish the IoBT connectivity by either deploying new IoBT nodes or by changing the roles of existing nodes. This problem is formulated as a dynamic multistage Stackelberg connectivity game that extends classical connectivity games and that explicitly takes into account the c…
Merging in the form of a mandatory lane-change is an important issue in transportation research. Even when safely completed, merging may disturb the mainline traffic and reduce the efficiency or capacity of the roadway. In this paper, we consider a Stackelberg game-theoretic driver behavior model where the so-called utilities or payoffs reflect the merging vehicle's aggressiveness as it pertains the decision to merge as the situation stands or to accelerate, decelerate prior to the actual lane-change maneuver. The interaction of the merging vehicle with the mainline traffic is also considered …
In recent times deep learning has been widely used for automating various security tasks in Cyber Domains. However, adversaries manipulate data in many situations and diminish the deployed deep learning model's accuracy. One notable example is fooling CAPTCHA data to access the CAPTCHA-based Classifier leading to the critical system being vulnerable to cybersecurity attacks. To alleviate this, we propose a computational framework of game theory to analyze the CAPTCHA-based Classifier's vulnerability, strategy, and outcomes by forming a simultaneous two-player game. We apply the Fast Gradient S…
Tongji University（同济大学）；Shanghai Research Institute for Intelligent Autonomous Systems（上海智能自主系统研究院）；Institute for Advanced Study, Tongji University（同济大学高等研究院）
Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner, but without obvious malice to other players. However, in many practical applications, such as poker, chess, evader pursuing, drug interdiction, coast guard, cyber-security, and national defense, players often have apparently adversarial stances, that is, selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. …
From a perspective of designing or engineering for opinion formation games in social networks, the "opinion maximization (or minimization)" problem has been studied mainly for designing subset selecting algorithms. We define a two-player zero-sum Stackelberg game of competitive opinion optimization by letting the player under study as the leader minimize the sum of expressed opinions by doing so-called "internal opinion design", knowing that the other adversarial player as the follower is to maximize the same objective by also conducting her own internal opinion design. We furthermore consider…
Identifying the actual adversarial threat against a system vulnerability has been a long-standing challenge for cybersecurity research. To determine an optimal strategy for the defender, game-theoretic based decision models have been widely used to simulate the real-world attacker-defender scenarios while taking the defender's constraints into consideration. In this work, we focus on understanding human attacker behaviors in order to optimize the defender's strategy. To achieve this goal, we model attacker-defender engagements as Markov Games and search for their Bayesian Stackelberg Equilibri…
Università degli Studi di Milano（米兰大学）；Toulouse School of Economics（图卢兹经济学院）；IBM Research - Tokyo（IBM研究院（东京））；Luiss University（路易斯大学）；IBM Research - Haifa（IBM研究院（海法））
We study a repeated game between a supplier and a retailer who want to maximize their respective profits without full knowledge of the problem parameters. After characterizing the uniqueness of the Stackelberg equilibrium of the stage game with complete information, we show that even with partial knowledge of the joint distribution of demand and production costs, natural learning dynamics guarantee convergence of the joint strategy profile of supplier and retailer to the Stackelberg equilibrium of the stage game. We also prove finite-time bounds on the supplier's regret and asymptotic bounds o…
While social networks are widely used as a media for information diffusion, attackers can also strategically employ analytical tools, such as influence maximization, to maximize the spread of adversarial content through the networks. We investigate the problem of limiting the diffusion of negative information by blocking nodes and edges in the network. We formulate the interaction between the defender and the attacker as a Stackelberg game where the defender first chooses a set of nodes to block and then the attacker selects a set of seeds to spread negative information from. This yields an ex…
Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case and cooperative strategies exist, admissible strategies are guaranteed to exist. Second, we give a characterization of admissible strategies using the no- tion of adversarial and cooperative values of a history, and we characterize the set of outcomes that are compatible with admissible strategies. Finally, we show how these characterizations can be used to…
