Robust Stackelberg Equilibria in Extensive-Form Games and Extension to Limited Lookahead

Stackelberg equilibria have become increasingly important as a solution concept in computational game theory, largely inspired by practical problems such as security settings. In practice, however, there is typically uncertainty regarding the model about the opponent. This paper is, to our knowledge, the first to investigate Stackelberg equilibria under uncertainty in extensive-form games, one of the broadest classes of game. We introduce robust Stackelberg equilibria, where the uncertainty is about the opponent's payoffs, as well as ones where the opponent has limited lookahead and the uncertainty is about the opponent's node evaluation function. We develop a new mixed-integer program for the deterministic limited-lookahead setting. We then extend the program to the robust setting for Stackelberg equilibrium under unlimited and under limited lookahead by the opponent. We show that for the specific case of interval uncertainty about the opponent's payoffs (or about the opponent's node evaluations in the case of limited lookahead), robust Stackelberg equilibria can be computed with a mixed-integer program that is of the same asymptotic size as that for the deterministic setting.Comment: Published at AAAI1

Robust Stackelberg Equilibria in Extensive-Form Games and Extension to Limited Lookahead

Stackelberg equilibria have become increasingly important as a solution concept in computational game theory, largely inspired by practical problems such as security settings. In practice, however, there is typically uncertainty regarding the model about the opponent. This paper is, to our knowledge, the first to investigate Stackelberg equilibria under uncertainty in extensive-form games, one of the broadest classes of game. We introduce robust Stackelberg equilibria, where the uncertainty is about the opponent's payoffs, as well as ones where the opponent has limited lookahead and the uncertainty is about the opponent's node evaluation function. We develop a new mixed-integer program for the deterministic limited-lookahead setting. We then extend the program to the robust setting for Stackelberg equilibrium under unlimited and under limited lookahead by the opponent. We show that for the specific case of interval uncertainty about the opponent's payoffs (or about the opponent's node evaluations in the case of limited lookahead), robust Stackelberg equilibria can be computed with a mixed-integer program that is of the same asymptotic size as that for the deterministic setting.Comment: Published at AAAI1

Cloudy with a Chance of Poaching: Adversary Behavior Modeling and Forecasting with Real-World Poaching Data

Wildlife conservation organizations task rangers to deter and capture wildlife poachers. Since rangers are responsible for patrolling vast areas, adversary behavior modeling can help more effectively direct future patrols. In this innovative application track paper, we present an adversary behavior modeling system, INTERCEPT (INTERpretable Classification Ensemble to Protect Threatened species), and provide the most extensive evaluation in the AI literature of one of the largest poaching datasets from Queen Elizabeth National Park (QENP) in Uganda, comparing INTERCEPT with its competitors; we also present results from a month-long test of INTERCEPT in the field. We present three major contributions. First, we present a paradigm shift in modeling and forecasting wildlife poacher behavior. Some of the latest work in the AI literature (and in Conservation) has relied on models similar to the Quantal Response model from Behavioral Game Theory for poacher behavior prediction. In contrast, INTERCEPT presents a behavior model based on an ensemble of decision trees (i) that more effectively predicts poacher attacks and (ii) that is more effectively interpretable and verifiable. We augment this model to account for spatial correlations and construct an ensemble of the best models, significantly improving performance. Second, we conduct an extensive evaluation on the QENP dataset, comparing 41 models in prediction performance over two years. Third, we present the results of deploying INTERCEPT for a one-month field test in QENP - a first for adversary behavior modeling applications in this domain. This field test has led to finding a poached elephant and more than a dozen snares (including a roll of elephant snares) before they were deployed, potentially saving the lives of multiple animals - including elephants.Engineering and Applied Science

Multi-Robot Path Planning for Persistent Monitoring in Stochastic and Adversarial Environments

In this thesis, we study multi-robot path planning problems for persistent monitoring tasks. The goal of such persistent monitoring tasks is to deploy a team of cooperating mobile robots in an environment to continually observe locations of interest in the environment. Robots patrol the environment in order to detect events arriving at the locations of the environment. The events stay at those locations for a certain amount of time before leaving and can only be detected if one of the robots visits the location of an event while the event is there. In order to detect all possible events arriving at a vertex, the maximum time spent by the robots between visits to that vertex should be less than the duration of the events arriving at that vertex. We consider the problem of finding the minimum number of robots to satisfy these revisit time constraints, also called latency constraints. The decision version of this problem is PSPACE-complete. We provide an O(log p) approximation algorithm for this problem where p is the ratio of the maximum and minimum latency constraints. We also present heuristic algorithms to solve the problem and show through simulations that a proposed orienteering-based heuristic algorithm gives better solutions than the approximation algorithm. We additionally provide an algorithm for the problem of minimizing the maximum weighted latency given a fixed number of robots. In case the event stay durations are not fixed but are drawn from a known distribution, we consider the problem of maximizing the expected number of detected events. We motivate randomized patrolling paths for such scenarios and use Markov chains to represent those random patrolling paths. We characterize the expected number of detected events as a function of the Markov chains used for patrolling and show that the objective function is submodular for randomly arriving events. We propose an approximation algorithm for the case where the event durations for all the vertices is a constant. We also propose a centralized and an online distributed algorithm to find the random patrolling policies for the robots. We also consider the case where the events are adversarial and can choose where and when to appear in order to maximize their chances of remaining undetected. The last problem we study in this thesis considers events triggered by a learning adversary. The adversary has a limited time to observe the patrolling policy before it decides when and where events should appear. We study the single robot version of this problem and model this problem as a multi-stage two player game. The adversary observes the patroller’s actions for a finite amount of time to learn the patroller’s strategy and then either chooses a location for the event to appear or reneges based on its confidence in the learned strategy. We characterize the expected payoffs for the players and propose a search algorithm to find a patrolling policy in such scenarios. We illustrate the trade off between hard to learn and hard to attack strategies through simulations

Queues, Planes and Games: Algorithms for Scheduling Passengers, and Decision Making in Stackelberg Games

In this dissertation, I present three theoretical results with real-world applications related to scheduling and distributionally-robust games, important fields in discrete optimization, and computer science. The first chapter provides simple, technology-free interventions to manage elevator queues in high-rise buildings when passenger demand far exceeds the capacity of the elevator system. The problem was motivated by the need to manage passengers safely in light of reduced elevator capacities during the COVID-19 pandemic. We use mathematical modeling, epidemiological expertise, and simulation to design and evaluate our algorithmic solutions. The key idea is to explicitly or implicitly group passengers that are going to the same floor into the same elevator as much as possible, substantiated theoretically using a technique from queuing theory known as stability analysis. This chapter is joint work with Charles Branas, Adam Elmachtoub, Clifford Stein, and Yeqing Zhou, directly in collaboration with the New York City Mayor’s Office of the Chief Technology Officer and the Department of Citywide Administrative Services. The second chapter proposes new algorithms for recomputing passenger itineraries for airlines during major disruptions when carefully planned schedules are thrown into disarray. An airline network is a massive temporal graph, often with tight regulatory and operational constraints. When disruptions propagate through an airline network, the objective is to \textit{recover} within a given time frame from a disruption, meaning we replan schedules affected by the disruption such that the new schedules have to match the originally planned schedules after the time frame. We aim to solve the large-scale airline recovery problem with quick, user-independent, consistent, and near-optimal algorithms. We provide new algorithms to solve the passenger recovery problem, given recovered flight and crew solutions. We build a preprocessing step and construct an Integer Program as well as a network-based approach based on solving multiple-label shortest path problems. Experiments show the tractability of our proposed algorithms on airline data sets with heavy flight disruptions. This chapter is joint work with Clifford Stein, stemming from an internship and collaboration with the Machine Learning team (Artificial Intelligence organization) of GE Global Research, Niskayuna, New York. The third chapter is about computing distributionally-robust strategies for a popular game theory model called Stackelberg games, where one player, called the leader, is able to commit to a strategy first, assuming the other player(s), called follower(s) would best respond to the strategy. In many of the real-world applications of Stackelberg games, parameters such as payoffs of the follower(s) are not known with certainty. Distributionally-robust optimization allows a distribution over possible model parameters, where this distribution comes from a set of possible distributions. The goal for the leader is to maximize their expected utility with respect to the worst-case distribution from the set. We initiate the study of distributionally-robust models for Stackelberg games, show that a distributionally-robust Stackelberg equilibrium always exists across a wide array of uncertainty models, and provide tractable algorithms for some general settings with experimental results. This chapter is joint work with Christian Kroer

Security Games with Interval Uncertainty

Security games provide a framework for allocating limited security resources in adversarial domains, and are currently used in deployed systems for LAX, the Federal Air Marshals, and the U.S. Coast Guard. One of the major challenges in security games is finding solutions that are robust to uncertainty about the game model. Bayesian game models have been used to model uncertainty, but algorithms for these games do not scale well enough for many applications. We take an alternative approach based on using intervals to model uncertainty in security games. We present a fast polynomial time algorithm for security games with interval uncertainty, which represents the first viable approach for computing robust solutions to very large security games. We also introduce a methodology for using intervals to approximate solutions to infinite Bayesian games with distributional uncertainty. Our experiments show that intervals can be an effective approach for these more general Bayesian games; our algorithm is faster and results in higher quality solutions than previous methods

Security Games with Interval Uncertainty

Game theory has become an important tool in solving real-life decision making problems. Security games use the concept of game theory in adversarial scenarios to protect critical infrastructure. The main purpose of security games is to allocate security resources among various targets and maximize payoff for the defender considering various kinds of attackers. It is hard for domain experts to predict the attacker\u27s behavior, so one of the major challenges in describing this game model is representing uncertainty about the attacker\u27s payoff. Several approaches have been developed to generate these game models based on uncertainty, such as Bayesian games. However Bayesian approaches have drawbacks in solution quality and time. The work of this thesis proposes a polynomial time algorithm that represents uncertainty based on intervals and generates a robust solution for large security games unlike previous methods. I also present a methodology to transform Bayesian games with distributional uncertainty into interval games, and use this novel interval algorithm to generate an approximate solution. At the end of this thesis, empirical data shows that this novel technique is faster and generates higher quality solution compared to previous Bayesian approaches

Efficient Approximation for Security Games with Interval Uncertainty

There are an increasing number of applications of security games. One of the key challenges for this field going forward is to address the problem of model uncertainty and the robustness of the game-theoretic solutions. Most existing methods for dealing with payoff uncertainty are Bayesian methods which are NP-hard and have difficulty scaling to very large problems. In this work we consider an alternative approach based on interval uncertainty. For a variant of security games with interval uncertainty we introduce a polynomial-time approximation algorithm that can compute very accurate solutions within a given error bound