Lei et al.- Traffic Adaptive Moving-window Patrolling Algorithm 1 Traffic Adaptive Moving-window Service Patrolling for Real-time Incident Management during High-impact Events Haozhe Lei a, Y a-Ting Y ang a, Tao Li a, Zilin Bian b,, Fan Zuo b, Sundeep Rangan a, and Kaan Ozbay b a Department of Electrical and Computer Engineering, New Y ork University, United States of America b Department of Civil and Urban Engineering, New Y ork University, United States of AmericaKeywords: High-impact event management, service patrol, dynamic programming, adaptive graph This paper presents the Traffic Adaptive Moving-window Patrolling Algorithm (T AMP A), designed to improve real-time incident management during major events like sports tournaments and concerts. Such events significantly stress transportation networks, requiring efficient and adaptive patrol solutions. Using dynamic programming, the algorithm continuously adjusts patrol strategies within short planning windows, effectively balancing immediate response and efficient routing. Theoretical analyses ensure performance remains closely aligned with optimal solutions. Simulation results from an urban traffic network demonstrate T AMP A's superior performance, showing improvements of approximately 87.5% over stationary methods and 114.2% over random strategies. Future work includes enhancing adaptability and incorporating digital twin technology for improved predictive accuracy, particularly relevant for events like the 2026 FIFA World Cup at MetLife Stadium.1 Introduction 1.1 Motivation Organizing high-impact events, such as sports tournaments, festivals, and concerts, presents substantial social, economic, and transportation challenges. These events can place immense pressure on transportation infrastructure, security protocols, and public services, particularly in regions that are already congested and economically vital, such as the New Y ork-New Jersey (NYNJ) or Los Angeles (LA) metropolitan* Corresponding author. Both regions attract large, diverse crowds as tourists from across state lines and around the world, further complicating special event management logistics. A prime example of this challenge is the hosting of mega-events, such as the FIFA World Cup Ardemagni (2022) and the Olympics (Government, 2022; Harrison, 2021).

We explored the Patrol Security Game (PSG), a robotic patrolling problem modeled as an extensive-form Stackelberg game, where the attacker determines the timing, location, and duration of their attack. Our objective is to devise a patrolling schedule with an infinite time horizon that minimizes the attacker's payoff. We demonstrated that PSG can be transformed into a combinatorial minimax problem with a closed-form objective function. By constraining the defender's strategy to a time-homogeneous first-order Markov chain (i.e., the patroller's next move depends solely on their current location), we proved that the optimal solution in cases of zero penalty involves either minimizing the expected hitting time or return time, depending on the attacker model, and that these solutions can be computed efficiently. Additionally, we observed that increasing the randomness in the patrol schedule reduces the attacker's expected payoff in high-penalty cases. However, the minimax problem becomes non-convex in other scenarios. To address this, we formulated a bi-criteria optimization problem incorporating two objectives: expected maximum reward and entropy. We proposed three graph-based algorithms and one deep reinforcement learning model, designed to efficiently balance the trade-off between these two objectives. Notably, the third algorithm can identify the optimal deterministic patrol schedule, though its runtime grows exponentially with the number of patrol spots. Experimental results validate the effectiveness and scalability of our solutions, demonstrating that our approaches outperform state-of-the-art baselines on both synthetic and real-world crime datasets.

To enable the computation of effective randomized patrol routes for single- or multi-robot teams, we present RoSSO, a Python package designed for solving Markov chain optimization problems. We exploit machine-learning techniques such as reverse-mode automatic differentiation and constraint parametrization to achieve superior efficiency compared to general-purpose nonlinear programming solvers. Additionally, we supplement a game-theoretic stochastic surveillance formulation in the literature with a novel greedy algorithm and multi-robot extension. We close with numerical results for a police district in downtown San Francisco that demonstrate RoSSO's capabilities on our new formulations and the prior work.

This paper presents a novel design of the system aimed at supporting the Wikipedia community in addressing vandalism on the platform. To achieve this, we collected a massive dataset of 47 languages, and applied advanced filtering and feature engineering techniques, including multilingual masked language modeling to build the training dataset from human-generated data. The performance of the system was evaluated through comparison with the one used in production in Wikipedia, known as ORES. Our research results in a significant increase in the number of languages covered, making Wikipedia patrolling more efficient to a wider range of communities. Furthermore, our model outperforms ORES, ensuring that the results provided are not only more accurate but also less biased against certain groups of contributors.

Green Security Games with real-time information (GSG-I) add the real-time information about the agents' movement to the typical GSG formulation. Prior works on GSG-I have used deep reinforcement learning (DRL) to learn the best policy for the agent in such an environment without any need to store the huge number of state representations for GSG-I. However, the decision-making process of DRL methods is largely opaque, which results in a lack of trust in their predictions. To tackle this issue, we present an interpretable DRL method for GSG-I that generates visualization to explain the decisions taken by the DRL algorithm. We also show that this approach performs better and works well with a simpler training regimen compared to the existing method.

Conservation efforts in green security domains to protect wildlife and forests are constrained by the limited availability of defenders (i.e., patrollers), who must patrol vast areas to protect from attackers (e.g., poachers or illegal loggers). Defenders must choose how much time to spend in each region of the protected area, balancing exploration of infrequently visited regions and exploitation of known hotspots. We formulate the problem as a stochastic multi-armed bandit, where each action represents a patrol strategy, enabling us to guarantee the rate of convergence of the patrolling policy. However, a naive bandit approach would compromise short-term performance for long-term optimality, resulting in animals poached and forests destroyed. To speed up performance, we leverage smoothness in the reward function and decomposability of actions. We show a synergy between Lipschitz-continuity and decomposition as each aids the convergence of the other. In doing so, we bridge the gap between combinatorial and Lipschitz bandits, presenting a no-regret approach that tightens existing guarantees while optimizing for short-term performance. We demonstrate that our algorithm, LIZARD, improves performance on real-world poaching data from Cambodia.

Green Security Games (GSGs) have been proposed and applied to optimize patrols conducted by law enforcement agencies in green security domains such as combating poaching, illegal logging and overfishing. However, real-time information such as footprints and agents' subsequent actions upon receiving the information, e.g., rangers following the footprints to chase the poacher, have been neglected in previous work. To fill the gap, we first propose a new game model GSG-I which augments GSGs with sequential movement and the vital element of real-time information. Second, we design a novel deep reinforcement learning-based algorithm, DeDOL, to compute a patrolling strategy that adapts to the real-time information against a best-responding attacker. DeDOL is built upon the double oracle framework and the policy-space response oracle, solving a restricted game and iteratively adding best response strategies to it through training deep Q-networks. Exploring the game structure, DeDOL uses domain-specific heuristic strategies as initial strategies and constructs several local modes for efficient and parallelized training. To our knowledge, this is the first attempt to use Deep Q-Learning for security games.

We focus on adversarial patrolling games on arbitrary graphs, where the Defender can control a mobile resource, the targets are alarmed by an alarm system, and the Attacker can observe the actions of the mobile resource of the Defender and perform different attacks exploiting multiple resources. This scenario can be modeled as a zero-sum extensive-form game in which each player can play multiple times. The game tree is exponentially large both in the size of the graph and in the number of attacking resources. We show that when the number of the Attacker's resources is free, the problem of computing the equilibrium path is NP-hard, while when the number of resources is fixed, the equilibrium path can be computed in poly-time. We provide a dynamic-programming algorithm that, given the number of the Attacker's resources, computes the equilibrium path requiring poly-time in the size of the graph and exponential time in the number of the resources. Furthermore, since in real-world scenarios it is implausible that the Defender knows the number of attacking resources, we study the robustness of the Defender's strategy when she makes a wrong guess about that number. We show that even the error of just a single resource can lead to an arbitrary inefficiency, when the inefficiency is defined as the ratio of the Defender's utilities obtained with a wrong guess and a correct guess. However, a more suitable definition of inefficiency is given by the difference of the Defender's utilities: this way, we observe that the higher the error in the estimation, the higher the loss for the Defender. Then, we investigate the performance of online algorithms when no information about the Attacker's resources is available. Finally, we resort to randomized online algorithms showing that we can obtain a competitive factor that is twice better than the one that can be achieved by any deterministic online algorithm.

We propose an algorithm for constructing efficient patrolling strategies in the Internet environment, where the protected targets are nodes connected to the network and the patrollers are software agents capable of detecting/preventing undesirable activities on the nodes. The algorithm is based on a novel compositional principle designed for a special class of strategies, and it can quickly construct (sub)optimal solutions even if the number of targets reaches hundreds of millions.

Traditional security games concern the optimal randomized allocation of human patrollers, who can directly catch attackers or interdict attacks. Motivated by the emerging application of utilizing mobile sensors (e.g., UAVs) for patrolling, in this paper we propose the novel Sensor-Empowered security Game (SEG) model which captures the joint allocation of human patrollers and mobile sensors. Sensors differ from patrollers in that they cannot directly interdict attacks, but they can notify nearby patrollers (if any). Moreover, SEGs incorporate mobile sensors' natural functionality of strategic signaling. On the technical side, we first prove that solving SEGs is NP-hard even in zero-sum cases. We then develop a scalable algorithm SEGer based on the branch-and-price framework with two key novelties: (1) a novel MILP formulation for the slave; (2) an efficient relaxation of the problem for pruning. To further accelerate SEGer, we design a faster combinatorial algorithm for the slave problem, which is provably a constant-approximation to the slave problem in zero-sum cases and serves as a useful heuristic for general-sum SEGs. Our experiments demonstrate the significant benefit of utilizing mobile sensors.