We consider the problem of finding Nash equilibrium for two-player turn-based zero-sum games. Inspired by the AlphaGo Zero (AGZ) algorithm, we develop a Reinforcement Learning based approach. Specifically, we propose Explore-Improve-Supervise (EIS) method that combines "exploration", "policy improvement"' and "supervised learning" to find the value function and policy associated with Nash equilibrium. We identify sufficient conditions for convergence and correctness for such an approach. For a concrete instance of EIS where random policy is used for "exploration", Monte-Carlo Tree Search is used for "policy improvement" and Nearest Neighbors is used for "supervised learning", we establish that this method finds an $\varepsilon$-approximate value function of Nash equilibrium in $\widetilde{O}(\varepsilon^{-(d+4)})$ steps when the underlying state-space of the game is continuous and $d$-dimensional. This is nearly optimal as we establish a lower bound of $\widetildeΩ(\varepsilon^{-(d+2)})$ for any policy.
Reinforcement learning has exceeded human-level performance in game playing AI with deep learning methods according to the experiments from DeepMind on Go and Atari games. Deep learning solves high dimension input problems which stop the development of reinforcement for many years. This study uses both two techniques to create several agents with different algorithms that successfully learn to play T-rex Runner. Deep Q network algorithm and three types of improvements are implemented to train the agent. The results from some of them are far from satisfactory but others are better than human ex…
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…
University of Amsterdam（阿姆斯特丹大学）；UvA-Bosch Delta Lab（阿姆斯特丹大学-博世德尔塔实验室）；Informatics Institute（信息学研究所）
Due to the capability of deep learning to perform well in high dimensional problems, deep reinforcement learning agents perform well in challenging tasks such as Atari 2600 games. However, clearly explaining why a certain action is taken by the agent can be as important as the decision itself. Deep reinforcement learning models, as other deep learning models, tend to be opaque in their decision-making process. In this work, we propose to make deep reinforcement learning more transparent by visualizing the evidence on which the agent bases its decision. In this work, we emphasize the importance…
New York University（纽约大学）；University of Strathclyde（思克莱德大学）；University of Hertfordshire（赫特福德大学）；Maastricht University（马斯特里赫特大学）
Deep reinforcement learning has learned to play many games well, but failed on others. To better characterize the modes and reasons of failure of deep reinforcement learners, we test the widely used Asynchronous Actor-Critic (A2C) algorithm on four deceptive games, which are specially designed to provide challenges to game-playing agents. These games are implemented in the General Video Game AI framework, which allows us to compare the behavior of reinforcement learning-based agents with planning agents based on tree search. We find that several of these games reliably deceive deep reinforceme…
We study what dataset assumption permits solving offline two-player zero-sum Markov games. In stark contrast to the offline single-agent Markov decision process, we show that the single strategy concentration assumption is insufficient for learning the Nash equilibrium (NE) strategy in offline two-player zero-sum Markov games. On the other hand, we propose a new assumption named unilateral concentration and design a pessimism-type algorithm that is provably efficient under this assumption. In addition, we show that the unilateral concentration assumption is necessary for learning an NE strateg…
Deep reinforcement learning has shown its success in game playing. However, 2.5D fighting games would be a challenging task to handle due to ambiguity in visual appearances like height or depth of the characters. Moreover, actions in such games typically involve particular sequential action orders, which also makes the network design very difficult. Based on the network of Asynchronous Advantage Actor-Critic (A3C), we create an OpenAI-gym-like gaming environment with the game of Little Fighter 2 (LF2), and present a novel A3C+ network for learning RL agents. The introduced model includes a Rec…
We introduce a new virtual environment for simulating a card game known as "Big 2". This is a four-player game of imperfect information with a relatively complicated action space (being allowed to play 1,2,3,4 or 5 card combinations from an initial starting hand of 13 cards). As such it poses a challenge for many current reinforcement learning methods. We then use the recently proposed "Proximal Policy Optimization" algorithm to train a deep neural network to play the game, purely learning via self-play, and find that it is able to reach a level which outperforms amateur human players after on…
Testing a video game is a critical step for the production process and requires a great effort in terms of time and resources spent. Some software houses are trying to use the artificial intelligence to reduce the need of human resources using systems able to replace a human agent. We study the possibility to use the Deep Reinforcement Learning to automate the testing process in match-3 video games and suggest to approach the problem in the framework of a Dueling Deep Q-Network paradigm. We test this kind of network on the Jelly Juice game, a match-3 video game developed by the redBit Games. T…
While Reinforcement Learning (RL) approaches lead to significant achievements in a variety of areas in recent history, natural language tasks remained mostly unaffected, due to the compositional and combinatorial nature that makes them notoriously hard to optimize. With the emerging field of Text-Based Games (TBGs), researchers try to bridge this gap. Inspired by the success of RL algorithms on Atari games, the idea is to develop new methods in a restricted game world and then gradually move to more complex environments. Previous work in the area of TBGs has mainly focused on solving individua…
We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves in the finite-horizon setting, where the transition kernel of the underlying Markov games can be parameterized by a linear function over the current state, both players' actions and the next state. In particular, we assume that we can control both players and aim to find the Nash Equilibrium by minimizing the duality gap. We propose an algorithm Nash-UCRL based on the principle "Optimism-in-Face-of-Uncertainty". Our algorithm only needs to find a Coarse Correlated Equilibrium (CCE), which is computatio…
Deep reinforcement learning achieves superhuman performance in a range of video game environments, but requires that a designer manually specify a reward function. It is often easier to provide demonstrations of a target behavior than to design a reward function describing that behavior. Inverse reinforcement learning (IRL) algorithms can infer a reward from demonstrations in low-dimensional continuous control environments, but there has been little work on applying IRL to high-dimensional video games. In our CNN-AIRL baseline, we modify the state-of-the-art adversarial IRL (AIRL) algorithm to…
AlphaStar, the AI that reaches GrandMaster level in StarCraft II, is a remarkable milestone demonstrating what deep reinforcement learning can achieve in complex Real-Time Strategy (RTS) games. However, the complexities of the game, algorithms and systems, and especially the tremendous amount of computation needed are big obstacles for the community to conduct further research in this direction. We propose a deep reinforcement learning agent, StarCraft Commander (SCC). With order of magnitude less computation, it demonstrates top human performance defeating GrandMaster players in test matches …
This paper covers n-tuple-based reinforcement learning (RL) algorithms for games. We present new algorithms for TD-, SARSA- and Q-learning which work seamlessly on various games with arbitrary number of players. This is achieved by taking a player-centered view where each player propagates his/her rewards back to previous rounds. We add a new element called Final Adaptation RL (FARL) to all these algorithms. Our main contribution is that FARL is a vitally important ingredient to achieve success with the player-centered view in various games. We report results on seven board games with 1, 2 and…
This paper presents a theoretical framework for probably approximately correct (PAC) multi-agent reinforcement learning (MARL) algorithms for Markov games. The paper offers an extension to the well-known Nash Q-learning algorithm, using the idea of delayed Q-learning, in order to build a new PAC MARL algorithm for general-sum Markov games. In addition to guiding the design of a provably PAC MARL algorithm, the framework enables checking whether an arbitrary MARL algorithm is PAC. Comparative numerical results demonstrate performance and robustness.
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…
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…
We show that computing approximate stationary Markov coarse correlated equilibria (CCE) in general-sum stochastic games is computationally intractable, even when there are two players, the game is turn-based, the discount factor is an absolute constant, and the approximation is an absolute constant. Our intractability results stand in sharp contrast to normal-form games where exact CCEs are efficiently computable. A fortiori, our results imply that there are no efficient algorithms for learning stationary Markov CCE policies in multi-agent reinforcement learning (MARL), even when the interacti…
Multi-agent reinforcement learning has been successfully applied to fully-cooperative and fully-competitive environments, but little is currently known about mixed cooperative/competitive environments. In this paper, we focus on a particular class of multi-agent mixed cooperative/competitive stochastic games called Markov Potential Games (MPGs), which include cooperative games as a special case. Recent results have shown that independent policy gradient converges in MPGs but it was not known whether Independent Natural Policy Gradient converges in MPGs as well. We prove that Independent Natura…
New York University（纽约大学）；Southern University of Science and Technology（南方科技大学）；Queen Mary University of London（伦敦玛丽女王大学）
The General Video Game AI (GVGAI) competition and its associated software framework provides a way of benchmarking AI algorithms on a large number of games written in a domain-specific description language. While the competition has seen plenty of interest, it has so far focused on online planning, providing a forward model that allows the use of algorithms such as Monte Carlo Tree Search. In this paper, we describe how we interface GVGAI to the OpenAI Gym environment, a widely used way of connecting agents to reinforcement learning problems. Using this interface, we characterize how widely us…
Nanjing University（南京大学）；East China Normal University（华东师范大学）
This paper addresses policy learning in non-stationary environments and games with continuous actions. Rather than the classical reward maximization mechanism, inspired by the ideas of follow-the-regularized-leader (FTRL) and mirror descent (MD) update, we propose a no-regret style reinforcement learning algorithm PORL for continuous action tasks. We prove that PORL has a last-iterate convergence guarantee, which is important for adversarial and cooperative games. Empirical studies show that, in stationary environments such as MuJoCo locomotion controlling tasks, PORL performs equally well as,…
Our work aims at developing reinforcement learning algorithms that do not rely on the Markov assumption. We consider the class of Non-Markov Decision Processes where histories can be abstracted into a finite set of states while preserving the dynamics. We call it a Markov abstraction since it induces a Markov Decision Process over a set of states that encode the non-Markov dynamics. This phenomenon underlies the recently introduced Regular Decision Processes (as well as POMDPs where only a finite number of belief states is reachable). In all such kinds of decision process, an agent that uses a…
World-class human players have been outperformed in a number of complex two person games (Go, Chess, Checkers) by Deep Reinforcement Learning systems. However, owing to tractability considerations minimax regret of a learning system cannot be evaluated in such games. In this paper we consider simple games (Noughts-and-Crosses and Hexapawn) in which minimax regret can be efficiently evaluated. We use these games to compare Cumulative Minimax Regret for variants of both standard and deep reinforcement learning against two variants of a new Meta-Interpretive Learning system called MIGO. In our ex…
This paper explores the use of deep reinforcement learning agents to transfer knowledge from one environment to another. More specifically, the method takes advantage of asynchronous advantage actor critic (A3C) architecture to generalize a target game using an agent trained on a source game in Atari. Instead of fine-tuning a pre-trained model for the target game, we propose a learning approach to update the model using multiple agents trained in parallel with different representations of the target game. Visual mapping between video sequences of transfer pairs is used to derive new representa…
General game testing relies on the use of human play testers, play test scripting, and prior knowledge of areas of interest to produce relevant test data. Using deep reinforcement learning (DRL), we introduce a self-learning mechanism to the game testing framework. With DRL, the framework is capable of exploring and/or exploiting the game mechanics based on a user-defined, reinforcing reward signal. As a result, test coverage is increased and unintended game play mechanics, exploits and bugs are discovered in a multitude of game types. In this paper, we show that DRL can be used to increase te…
The combination of deep reinforcement learning and search at both training and test time is a powerful paradigm that has led to a number of successes in single-agent settings and perfect-information games, best exemplified by AlphaZero. However, prior algorithms of this form cannot cope with imperfect-information games. This paper presents ReBeL, a general framework for self-play reinforcement learning and search that provably converges to a Nash equilibrium in any two-player zero-sum game. In the simpler setting of perfect-information games, ReBeL reduces to an algorithm similar to AlphaZero.…
Recent times have witnessed sharp improvements in reinforcement learning tasks using deep reinforcement learning techniques like Deep Q Networks, Policy Gradients, Actor Critic methods which are based on deep learning based models and back-propagation of gradients to train such models. An active area of research in reinforcement learning is about training agents to play complex video games, which so far has been something accomplished only by human intelligence. Some state of the art performances in video game playing using deep reinforcement learning are obtained by processing the sequence of…
Optimistic Policy Gradient in Multi-Player Markov Games with a Single Controller: Convergence Beyond the Minty Property
Meta AI；University of California Irvine（加州大学欧文分校）；Archimedes research unit（阿基米德研究单元）；Massachusetts Institute of Technology（麻省理工学院）；Strategy Robot, Inc.（战略机器人公司）；Strategic Machine, Inc.（战略机器公司）；Optimized Markets, Inc.（优化市场公司）；Carnegie Mellon University（卡内基梅隆大学）
College of Computer and Information Sciences（计算机与信息科学学院）；Northeastern University（东北大学）
Reinforcement Learning has recently surfaced as a very powerful tool to solve complex problems in the domain of board games, wherein an agent is generally required to learn complex strategies and moves based on its own experiences and rewards received. While RL has outperformed existing state-of-the-art methods used for playing simple video games and popular board games, it is yet to demonstrate its capability on ancient games. Here, we solve one such problem, where we train our agents using different methods namely Monte Carlo, Qlearning and Expected Sarsa to learn optimal policy to play the …
Reinforcement learning combined with deep neural networks has performed remarkably well in many genres of games recently. It has surpassed human-level performance in fixed game environments and turn-based two player board games. However, to the best of our knowledge, current research has yet to produce a result that has surpassed human-level performance in modern complex fighting games. This is due to the inherent difficulties with real-time fighting games, including: vast action spaces, action dependencies, and imperfect information. We overcame these challenges and made 1v1 battle AI agents …
School of Computer Science（计算机科学学院）；Carnegie Mellon University（卡内基梅隆大学）
Advances in deep reinforcement learning have allowed autonomous agents to perform well on Atari games, often outperforming humans, using only raw pixels to make their decisions. However, most of these games take place in 2D environments that are fully observable to the agent. In this paper, we present the first architecture to tackle 3D environments in first-person shooter games, that involve partially observable states. Typically, deep reinforcement learning methods only utilize visual input for training. We present a method to augment these models to exploit game feature information such as …
Real Time Strategy (RTS) games require macro strategies as well as micro strategies to obtain satisfactory performance since it has large state space, action space, and hidden information. This paper presents a novel hierarchical reinforcement learning model for mastering Multiplayer Online Battle Arena (MOBA) games, a sub-genre of RTS games. The novelty of this work are: (1) proposing a hierarchical framework, where agents execute macro strategies by imitation learning and carry out micromanipulations through reinforcement learning, (2) developing a simple self-learning method to get better s…
University of Maryland（马里兰大学）；Montgomery Blair High School（蒙哥马利布莱尔高中）；Wootton High School（伍顿高中）
Reinforcement Learning (RL) algorithms have been successfully applied to real world situations like illegal smuggling, poaching, deforestation, climate change, airport security, etc. These scenarios can be framed as Stackelberg security games (SSGs) where defenders and attackers compete to control target resources. The algorithm's competency is assessed by which agent is controlling the targets. This review investigates modeling of SSGs in RL with a focus on possible improvements of target representations in RL algorithms.
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…
University of Oxford（牛津大学）；University of Toronto（多伦多大学）
The main focus of this paper is on enhancement of two types of game-theoretic learning algorithms: log-linear learning and reinforcement learning. The standard analysis of log-linear learning needs a highly structured environment, i.e. strong assumptions about the game from an implementation perspective. In this paper, we introduce a variant of log-linear learning that provides asymptotic guarantees while relaxing the structural assumptions to include synchronous updates and limitations in information available to the players. On the other hand, model-free reinforcement learning is able to per…
University of Southern California（南加州大学）；Massachusetts Institute of Technology（麻省理工学院）
We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space and/or the number of players can be very large, we propose new independent policy gradient algorithms that are run by all players in tandem. When there is no uncertainty in the gradient evaluation, we show that our algorithm finds an $ε$-Nash equilibrium with $O(1/ε^2)$ iteration complexity which does not explicitly depend on the state space size. When the e…
In this paper, we utilize results from convex analysis and monotone operator theory to derive additional properties of the softmax function that have not yet been covered in the existing literature. In particular, we show that the softmax function is the monotone gradient map of the log-sum-exp function. By exploiting this connection, we show that the inverse temperature parameter determines the Lipschitz and co-coercivity properties of the softmax function. We then demonstrate the usefulness of these properties through an application in game-theoretic reinforcement learning.
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…
Southern University of Science and Technology（南方科技大学）；NetEase Games AI Lab（网易游戏人工智能实验室）
Despite the emerging progress of integrating evolutionary computation into reinforcement learning, the absence of a high-performance platform endowing composability and massive parallelism causes non-trivial difficulties for research and applications related to asynchronous commercial games. Here we introduce Lamarckian - an open-source platform featuring support for evolutionary reinforcement learning scalable to distributed computing resources. To improve the training speed and data efficiency, Lamarckian adopts optimized communication methods and an asynchronous evolutionary reinforcement l…
Many real-world applications can be described as large-scale games of imperfect information. To deal with these challenging domains, prior work has focused on computing Nash equilibria in a handcrafted abstraction of the domain. In this paper we introduce the first scalable end-to-end approach to learning approximate Nash equilibria without prior domain knowledge. Our method combines fictitious self-play with deep reinforcement learning. When applied to Leduc poker, Neural Fictitious Self-Play (NFSP) approached a Nash equilibrium, whereas common reinforcement learning methods diverged. In Limi…
The combination of Formal Methods with Reinforcement Learning (RL) has recently attracted interest as a way for single-agent RL to learn multiple-task specifications. In this paper we extend this convergence to multi-agent settings and formally define Extended Markov Games as a general mathematical model that allows multiple RL agents to concurrently learn various non-Markovian specifications. To introduce this new model we provide formal definitions and proofs as well as empirical tests of RL algorithms running on this framework. Specifically, we use our model to train two different logic-bas…
Italian Institute of Technology（意大利理工学院）；University of British Columbia（英属哥伦比亚大学）
Recent advances in reinforcement learning with social agents have allowed us to achieve human-level performance on some interaction tasks. However, most interactive scenarios do not have as end-goal performance alone; instead, the social impact of these agents when interacting with humans is as important and, in most cases, never explored properly. This preregistration study focuses on providing a novel learning mechanism based on a rivalry social impact. Our scenario explored different reinforcement learning-based agents playing a competitive card game against human players. Based on the conc…
School of Interactive Computing（交互式计算学院）；Georgia Institute of Technology（佐治亚理工学院）
Text-based adventure games provide a platform on which to explore reinforcement learning in the context of a combinatorial action space, such as natural language. We present a deep reinforcement learning architecture that represents the game state as a knowledge graph which is learned during exploration. This graph is used to prune the action space, enabling more efficient exploration. The question of which action to take can be reduced to a question-answering task, a form of transfer learning that pre-trains certain parts of our architecture. In experiments using the TextWorld framework, we s…
High-Probability Nash Regret for Decentralized Learning in Markov $α$-Potential Games: Episodic and Fully Online Asynchronous Algorithms with Applications to Markov Congestion Games
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
University of Virginia（弗吉尼亚大学）；IBM Research（IBM研究院）
The focus of this paper is a Bayesian framework for solving a class of problems termed multi-agent inverse reinforcement learning (MIRL). Compared to the well-known inverse reinforcement learning (IRL) problem, MIRL is formalized in the context of stochastic games, which generalize Markov decision processes to game theoretic scenarios. We establish a theoretical foundation for competitive two-agent zero-sum MIRL problems and propose a Bayesian solution approach in which the generative model is based on an assumption that the two agents follow a minimax bi-policy. Numerical results are presente…
In this paper, we formulate the challenge of re-conceptualising the language game experimental paradigm in the framework of multi-agent reinforcement learning (MARL). If successful, future language game experiments will benefit from the rapid and promising methodological advances in the MARL community, while future MARL experiments on learning emergent communication will benefit from the insights and results gained from language game experiments. We strongly believe that this cross-pollination has the potential to lead to major breakthroughs in the modelling of how human-like languages can eme…
