In certain reinforcement learning (RL) scenarios there are adversaries trying to interfere with the underlying reward process for their own benefit. We introduce Threatened Markov Decision Processes (TMDPs) as a framework to support an agent against potential opponents in an RL context as well as schemes resulting in novel learning approaches to deal with TMDPs. After introducing our framework and deriving theoretical results, empirical evidence is given via extensive experiments, showing the importance for an RL agent of acknowledging adversarial awareness.
University of Maryland（马里兰大学）；University of Colorado（科罗拉多大学）；Massachusetts Institute of Technology（麻省理工学院）
Opponent modeling is necessary in multi-agent settings where secondary agents with competing goals also adapt their strategies, yet it remains challenging because strategies interact with each other and change. Most previous work focuses on developing probabilistic models or parameterized strategies for specific applications. Inspired by the recent success of deep reinforcement learning, we present neural-based models that jointly learn a policy and the behavior of opponents. Instead of explicitly predicting the opponent's action, we encode observation of the opponents into a deep Q-Network (D…
This paper presents an algorithmic framework for learning robust policies in asymmetric imperfect-information games, where the joint reward could depend on the uncertain opponent type (a private information known only to the opponent itself and its ally). In order to maximize the reward, the protagonist agent has to infer the opponent type through agent modeling. We use multiagent reinforcement learning (MARL) to learn opponent models through self-play, which captures the full strategy interaction and reasoning between agents. However, agent policies learned from self-play can suffer from mutu…
Models and games are simplified representations of the world. There are many different kinds of models, all differing in complexity and which aspect of the world they allow us to further our understanding of. In this paper we focus on a specific instance of agent-based models, which uses reinforcement learning (RL) to train the agent how to act in its environment. Reinforcement learning agents are usually also Markov processes, which is another type of model that can be used. We test this reinforcement learning agent in a Colonel Blotto environment1, and measure its performance against Random …
Vrije Universiteit Brussel（布鲁塞尔自由大学）；Universiteit van Amsterdam（阿姆斯特丹大学）；National University of Ireland Galway（爱尔兰国立大学戈尔韦分校）；HU Univ. of Appl. Sci. Utrecht（乌得勒支HU应用科学大学）
Many real-world multi-agent interactions consider multiple distinct criteria, i.e. the payoffs are multi-objective in nature. However, the same multi-objective payoff vector may lead to different utilities for each participant. Therefore, it is essential for an agent to learn about the behaviour of other agents in the system. In this work, we present the first study of the effects of such opponent modelling on multi-objective multi-agent interactions with non-linear utilities. Specifically, we consider two-player multi-objective normal form games with non-linear utility functions under the sca…
University College London（伦敦大学学院）；Delft University of Technology（代尔夫特理工大学）；MediaGamma Ltd.（MediaGamma有限公司）
Humans are capable of attributing latent mental contents such as beliefs or intentions to others. The social skill is critical in daily life for reasoning about the potential consequences of others' behaviors so as to plan ahead. It is known that humans use such reasoning ability recursively by considering what others believe about their own beliefs. In this paper, we start from level-$1$ recursion and introduce a probabilistic recursive reasoning (PR2) framework for multi-agent reinforcement learning. Our hypothesis is that it is beneficial for each agent to account for how the opponents woul…
We consider a scenario in which two reinforcement learning agents repeatedly play a matrix game against each other and update their parameters after each round. The agents' decision-making is transparent to each other, which allows each agent to predict how their opponent will play against them. To prevent an infinite regress of both agents recursively predicting each other indefinitely, each agent is required to give an opponent-independent response with some probability at least epsilon. Transparency also allows each agent to anticipate and shape the other agent's gradient step, i.e. to move…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；University of Oxford（牛津大学）；FLAIR（未来人工智能研究院）
Learning With Opponent-Learning Awareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based cooperation in partially competitive environments. However, LOLA often fails to learn such behaviour on more complex policy spaces parameterized by neural networks, partly because the update rule is sensitive to the policy parameterization. This problem is especially pronounced in the opponent modeling setting, where the opponent's policy is unknown and must be inferred from observations; in such settings, LOLA is ill-specified bec…
University of Virginia（弗吉尼亚大学）；Systems Engineering, Inc.（系统工程公司）
In adversarial environments, one side could gain an advantage by identifying the opponent's strategy. For example, in combat games, if an opponents strategy is identified as overly aggressive, one could lay a trap that exploits the opponent's aggressive nature. However, an opponent's strategy is not always apparent and may need to be estimated from observations of their actions. This paper proposes to use inverse reinforcement learning (IRL) to identify strategies in adversarial environments. Specifically, the contributions of this work are 1) the demonstration of this concept on gaming combat…
Multi-Agent Reinforcement Learning (MARL) considers settings in which a set of coexisting agents interact with one another and their environment. The adaptation and learning of other agents induces non-stationarity in the environment dynamics. This poses a great challenge for value function-based algorithms whose convergence usually relies on the assumption of a stationary environment. Policy search algorithms also struggle in multi-agent settings as the partial observability resulting from an opponent's actions not being known introduces high variance to policy training. Modelling an agent's …
Massachusetts Institute of Technology（麻省理工学院）；Princeton University（普林斯顿大学）
We study online learning in unknown Markov games, a problem that arises in episodic multi-agent reinforcement learning where the actions of the opponents are unobservable. We show that in this challenging setting, achieving sublinear regret against the best response in hindsight is statistically hard. We then consider a weaker notion of regret by competing with the \emph{minimax value} of the game, and present an algorithm that achieves a sublinear $\tilde{\mathcal{O}}(K^{2/3})$ regret after $K$ episodes. This is the first sublinear regret bound (to our knowledge) for online learning in unknow…
The Alan Turing Institute（艾伦图灵研究所）；University College London（伦敦大学学院）
Multi-agent reinforcement learning has received significant interest in recent years notably due to the advancements made in deep reinforcement learning which have allowed for the developments of new architectures and learning algorithms. Using social dilemmas as the training ground, we present a novel learning architecture, Learning through Probing (LTP), where agents utilize a probing mechanism to incorporate how their opponent's behavior changes when an agent takes an action. We use distinct training phases and adjust rewards according to the overall outcome of the experiences accounting fo…
Khoury College of Computer Sciences, Northeastern University（东北大学库里计算机科学学院）
A rise in Advanced Persistent Threats (APTs) has introduced a need for robustness against long-running, stealthy attacks which circumvent existing cryptographic security guarantees. FlipIt is a security game that models attacker-defender interactions in advanced scenarios such as APTs. Previous work analyzed extensively non-adaptive strategies in FlipIt, but adaptive strategies rise naturally in practical interactions as players receive feedback during the game. We model the FlipIt game as a Markov Decision Process and introduce QFlip, an adaptive strategy for FlipIt based on temporal differen…
We study online reinforcement learning in average-reward stochastic games (SGs). An SG models a two-player zero-sum game in a Markov environment, where state transitions and one-step payoffs are determined simultaneously by a learner and an adversary. We propose the UCSG algorithm that achieves a sublinear regret compared to the game value when competing with an arbitrary opponent. This result improves previous ones under the same setting. The regret bound has a dependency on the diameter, which is an intrinsic value related to the mixing property of SGs. If we let the opponent play an optimis…
University College London（伦敦大学学院）；University of Alberta（阿尔伯塔大学）
In a single-agent setting, reinforcement learning (RL) tasks can be cast into an inference problem by introducing a binary random variable o, which stands for the "optimality". In this paper, we redefine the binary random variable o in multi-agent setting and formalize multi-agent reinforcement learning (MARL) as probabilistic inference. We derive a variational lower bound of the likelihood of achieving the optimality and name it as Regularized Opponent Model with Maximum Entropy Objective (ROMMEO). From ROMMEO, we present a novel perspective on opponent modeling and show how it can improve th…
This paper proposes new, end-to-end deep reinforcement learning algorithms for learning two-player zero-sum Markov games. Different from prior efforts on training agents to beat a fixed set of opponents, our objective is to find the Nash equilibrium policies that are free from exploitation by even the adversarial opponents. We propose (a) Nash-DQN algorithm, which integrates the deep learning techniques from single DQN into the classic Nash Q-learning algorithm for solving tabular Markov games; (b) Nash-DQN-Exploiter algorithm, which additionally adopts an exploiter to guide the exploration of…
Fictitious play with reinforcement learning is a general and effective framework for zero-sum games. However, using the current deep neural network models, the implementation of fictitious play faces crucial challenges. Neural network model training employs gradient descent approaches to update all connection weights, and thus is easy to forget the old opponents after training to beat the new opponents. Existing approaches often maintain a pool of historical policy models to avoid the forgetting. However, learning to beat a pool in stochastic games, i.e., a wide distribution over policy models…
Equilibrium Selection in Multi-Agent Policy Gradients via Opponent-Aware Basin Entry
Bloomsbury Technology（布洛姆斯伯里技术）；London School of Economics and Political Science（伦敦政治经济学院）；University of Bristol（布里斯托大学）；Johannes Kepler University Linz（林茨约翰尼斯·开普勒大学）；Odesa Polytechnic National University（敖德萨国立技术大学）
Two player zero sum simultaneous action games are common in video games, financial markets, war, business competition, and many other settings. We first introduce the fundamental concepts of reinforcement learning in two player zero sum simultaneous action games and discuss the unique challenges this type of game poses. Then we introduce two novel agents that attempt to handle these challenges by using joint action Deep Q-Networks (DQN). The first agent, called the Best Response AgenT (BRAT), builds an explicit model of its opponent's policy using imitation learning, and then uses this model t…
This paper investigates the model-based methods in multi-agent reinforcement learning (MARL). We specify the dynamics sample complexity and the opponent sample complexity in MARL, and conduct a theoretic analysis of return discrepancy upper bound. To reduce the upper bound with the intention of low sample complexity during the whole learning process, we propose a novel decentralized model-based MARL method, named Adaptive Opponent-wise Rollout Policy Optimization (AORPO). In AORPO, each agent builds its multi-agent environment model, consisting of a dynamics model and multiple opponent models,…
Tianjin University（天津大学）；Washington State University（华盛顿州立大学）
The Iterated Prisoner's Dilemma has guided research on social dilemmas for decades. However, it distinguishes between only two atomic actions: cooperate and defect. In real-world prisoner's dilemmas, these choices are temporally extended and different strategies may correspond to sequences of actions, reflecting grades of cooperation. We introduce a Sequential Prisoner's Dilemma (SPD) game to better capture the aforementioned characteristics. In this work, we propose a deep multiagent reinforcement learning approach that investigates the evolution of mutual cooperation in SPD games. Our approa…
Deep reinforcement learning (RL) policies are known to be vulnerable to adversarial perturbations to their observations, similar to adversarial examples for classifiers. However, an attacker is not usually able to directly modify another agent's observations. This might lead one to wonder: is it possible to attack an RL agent simply by choosing an adversarial policy acting in a multi-agent environment so as to create natural observations that are adversarial? We demonstrate the existence of adversarial policies in zero-sum games between simulated humanoid robots with proprioceptive observation…
In this paper, we study a long-term planning scenario that is based on drone racing competitions held in real life. We conducted this experiment on a framework created for "Game of Drones: Drone Racing Competition" at NeurIPS 2019. The racing environment was created using Microsoft's AirSim Drone Racing Lab. A reinforcement learning agent, a simulated quadrotor in our case, has trained with the Policy Proximal Optimization(PPO) algorithm was able to successfully compete against another simulated quadrotor that was running a classical path planning algorithm. Agent observations consist of data …
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents are trying to solve. To do so, we extend previous probabilistic approaches for inverse reinforcement learning in known MDPs to the case of unknown dynamics or opponents. We do this by deriving two simplified probabilistic models of the demonstrator's policy and utility. For tractability, we use maximum a posteriori estimation rather than full Bayesian inferen…
Centre for Automation and Robotic Engineering Science, The University of Auckland, New Zealand（自动化与机器人工程科学中心，奥克兰大学，新西兰）；New Dexterity research group, The University of Auckland, New Zealand（新灵活性研究组，奥克兰大学，新西兰）
While autonomous racing performance in Time-Trial scenarios has seen significant progress and development, autonomous wheel-to-wheel racing and overtaking are still severely limited. These limitations are particularly apparent in real-life driving scenarios where state-of-the-art algorithms struggle to safely or reliably complete overtaking manoeuvres. This is important, as reliable navigation around other vehicles is vital for safe autonomous wheel-to-wheel racing. The F1Tenth Competition provides a useful opportunity for developing wheel-to-wheel racing algorithms on a standardised physical …
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents are trying to solve. To do so, we extend previous probabilistic approaches for inverse reinforcement learning in known MDPs to the case of unknown dynamics or opponents. We do this by deriving two simplified probabilistic models of the demonstrator's policy and utility. For tractability, we use maximum a posteriori estimation rather than full Bayesian inferen…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；Queen Mary University of London（伦敦玛丽女王大学）
The Fighting Game AI Competition (FTGAIC) provides a challenging benchmark for 2-player video game AI. The challenge arises from the large action space, diverse styles of characters and abilities, and the real-time nature of the game. In this paper, we propose a novel algorithm that combines Rolling Horizon Evolution Algorithm (RHEA) with opponent model learning. The approach is readily applicable to any 2-player video game. In contrast to conventional RHEA, an opponent model is proposed and is optimized by supervised learning with cross-entropy and reinforcement learning with policy gradient …
University of Oxford（牛津大学）；DeepMind（深度思维）；University College London（伦敦大学学院）
A growing number of learning methods are actually differentiable games whose players optimise multiple, interdependent objectives in parallel -- from GANs and intrinsic curiosity to multi-agent RL. Opponent shaping is a powerful approach to improve learning dynamics in these games, accounting for player influence on others' updates. Learning with Opponent-Learning Awareness (LOLA) is a recent algorithm that exploits this response and leads to cooperation in settings like the Iterated Prisoner's Dilemma. Although experimentally successful, we show that LOLA agents can exhibit 'arrogant' behavio…
In multi-agent reinforcement learning, the inherent non-stationarity of the environment caused by other agents' actions posed significant difficulties for an agent to learn a good policy independently. One way to deal with non-stationarity is opponent modeling, by which the agent takes into consideration the influence of other agents' policies. Most existing work relies on predicting other agents' actions or goals, or discriminating between different policies. However, such modeling fails to capture the similarities and differences between policies simultaneously and thus cannot provide enough…
University of Science and Technology of China（中国科学技术大学）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）
Recent years have witnessed the great breakthrough of deep reinforcement learning (DRL) in various perfect and imperfect information games. Among these games, DouDizhu, a popular card game in China, is very challenging due to the imperfect information, large state space, elements of collaboration and a massive number of possible moves from turn to turn. Recently, a DouDizhu AI system called DouZero has been proposed. Trained using traditional Monte Carlo method with deep neural networks and self-play procedure without the abstraction of human prior knowledge, DouZero has outperformed all the e…
Boston University（波士顿大学）；Center for Brains, Minds and Machines, MIT（麻省理工学院脑、心智与机器中心）；CMSA, Harvard University（哈佛大学数学与应用中心）
Reinforcement learning has shown much success in games such as chess, backgammon and Go. However, in most of these games, agents have full knowledge of the environment at all times. In this paper, we describe a deep learning model in which agents successfully adapt to different classes of opponents and learn the optimal counter-strategy using reinforcement learning in a game under partial observability. We apply our model to FlipIt, a two-player security game in which both players, the attacker and the defender, compete for ownership of a shared resource and only receive information on the cur…
DeepMind；University of Toronto（多伦多大学）；University of California Berkeley（加州大学伯克利分校）
This paper investigates generalisation in multi-agent games, where the generality of the agent can be evaluated by playing against opponents it hasn't seen during training. We propose two new games with concealed information and complex, non-transitive reward structure (think rock/paper/scissors). It turns out that most current deep reinforcement learning methods fail to efficiently explore the strategy space, thus learning policies that generalise poorly to unseen opponents. We then propose a novel hierarchical agent architecture, where the hierarchy is grounded in the game-theoretic structur…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Reinforcement learning from self-play has recently reported many successes. Self-play, where the agents compete with themselves, is often used to generate training data for iterative policy improvement. In previous work, heuristic rules are designed to choose an opponent for the current learner. Typical rules include choosing the latest agent, the best agent, or a random historical agent. However, these rules may be inefficient in practice and sometimes do not guarantee convergence even in the simplest matrix games. In this paper, we propose a new algorithmic framework for competitive self-pla…
Recent developments in deep reinforcement learning are concerned with creating decision-making agents which can perform well in various complex domains. A particular approach which has received increasing attention is multi-agent reinforcement learning, in which multiple agents learn concurrently to coordinate their actions. In such multi-agent environments, additional learning problems arise due to the continually changing decision-making policies of agents. This paper surveys recent works that address the non-stationarity problem in multi-agent deep reinforcement learning. The surveyed metho…
University of California, Berkeley（加州大学伯克利分校）；Technical University of Munich（慕尼黑工业大学）
Self-play reinforcement learning has achieved state-of-the-art, and often superhuman, performance in a variety of zero-sum games. Yet prior work has found that policies that are highly capable against regular opponents can fail catastrophically against adversarial policies: an opponent trained explicitly against the victim. Prior defenses using adversarial training were able to make the victim robust to a specific adversary, but the victim remained vulnerable to new ones. We conjecture this limitation was due to insufficient diversity of adversaries seen during training. We analyze a defense u…
Active learning from demonstration allows a robot to query a human for specific types of input to achieve efficient learning. Existing work has explored a variety of active query strategies; however, to our knowledge, none of these strategies directly minimize the performance risk of the policy the robot is learning. Utilizing recent advances in performance bounds for inverse reinforcement learning, we propose a risk-aware active inverse reinforcement learning algorithm that focuses active queries on areas of the state space with the potential for large generalization error. We show that risk-…
Alberta Machine Intelligence Institute (Amii)（阿尔伯塔机器智能研究所（Amii））；University of Alberta（阿尔伯塔大学）
In fighting games, individual players of the same skill level often exhibit distinct strategies from one another through their gameplay. Despite this, the majority of AI agents for fighting games have only a single strategy for each "level" of difficulty. To make AI opponents more human-like, we'd ideally like to see multiple different strategies at each level of difficulty, a concept we refer to as "multidimensional" difficulty. In this paper, we introduce a diversity-based deep reinforcement learning approach for generating a set of agents of similar difficulty that utilize diverse strategie…
Department of Computer Science, University College London（计算机科学系，伦敦大学学院）；Centre for Artificial Intelligence, University College London（人工智能中心，伦敦大学学院）；Department of Computer Science, University of Bologna（计算机科学系，博洛尼亚大学）
Coordinated Science Laboratory（协同科学实验室）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Making decisions in the presence of a strategic opponent requires one to take into account the opponent's ability to actively mask its intended objective. To describe such strategic situations, we introduce the non-cooperative inverse reinforcement learning (N-CIRL) formalism. The N-CIRL formalism consists of two agents with completely misaligned objectives, where only one of the agents knows the true objective function. Formally, we model the N-CIRL formalism as a zero-sum Markov game with one-sided incomplete information. Through interacting with the more informed player, the less informed p…
