Score vs. Winrate in Score-Based Games: which Reward for Reinforcement Learning?
University of Siena（锡耶纳大学）；University of Chieti-Pescara（基耶蒂-佩斯卡拉大学）；ARS Toscana（托斯卡纳农业研究局）；ISTI-CNR Pisa（意大利国家研究委员会比萨信息科学与技术研究所）；University of Parma（帕尔马大学）
Luca Pasqualini, Gianluca Amato, Marco Fantozzi, Rosa Gini, Alessandro Marchetti, Carlo Metta, Francesco Morandin, Maurizio Parton
备注：
Published at 2022 21st IEEE International Conference on Machine Learning and Applications (ICMLA). This version (v2) is a major revision and superseeds version v1
In the last years, the DeepMind algorithm AlphaZero has become the state of the art to efficiently tackle perfect information two-player zero-sum games with a win/lose outcome. However, when the win/lose outcome is decided by a final score difference, AlphaZero may play score-suboptimal moves because all winning final positions are equivalent from the win/lose outcome perspective. This can be an issue, for instance when used for teaching, or when trying to understand whether there is a better move. Moreover, there is the theoretical quest for the perfect game. A naive approach would be training an AlphaZero-like agent to predict score differences instead of win/lose outcomes. Since the game of Go is deterministic, this should as well produce an outcome-optimal play. However, it is a folklore belief that "this does not work".
In this paper, we first provide empirical evidence for this belief. We then give a theoretical interpretation of this suboptimality in general perfect information two-player zero-sum game where the complexity of a game like Go is replaced by the randomness of the environment. We show that an outcome-optimal policy has a different preference for uncertainty when it is winning or losing. In particular, when in a losing state, an outcome-optimal agent chooses actions leading to a higher score variance. We then posit that when approximation is involved, a deterministic game behaves like a nondeterministic game, where the score variance is modeled by how uncertain the position is. We validate this hypothesis in AlphaZero-like software with a human expert.
Università di Parma（帕尔马大学）；Università di Chieti-Pescara（基耶蒂-佩斯卡拉大学）；Agenzia regionale di sanità della Toscana（托斯卡纳地区卫生局）；Università di Firenze（佛罗伦萨大学）；Mozilla Corporation（Mozilla公司）
We propose a multiple-komi modification of the AlphaGo Zero/Leela Zero paradigm. The winrate as a function of the komi is modeled with a two-parameters sigmoid function, so that the neural network must predict just one more variable to assess the winrate for all komi values. A second novel feature is that training is based on self-play games that occasionally branch -- with changed komi -- when the position is uneven. With this setting, reinforcement learning is showed to work on 7x7 Go, obtaining very strong playing agents. As a useful byproduct, the sigmoid parameters given by the network al…
College of Engineering & Informatics, National University of Ireland, Galway（爱尔兰国立大学戈尔韦工程与信息学院）
While reinforcement learning (RL) has been applied to turn-based board games for many years, more complex games involving decision-making in real-time are beginning to receive more attention. A challenge in such environments is that the time that elapses between deciding to take an action and receiving a reward based on its outcome can be longer than the interval between successive decisions. We explore this in the context of a non-player character (NPC) in a modern first-person shooter game. Such games take place in 3D environments where players, both human and computer-controlled, compete by…
Monte Carlo Tree Search (MCTS) methods have proven powerful in planning for sequential decision-making problems such as Go and video games, but their performance can be poor when the planning depth and sampling trajectories are limited or when the rewards are sparse. We present an adaptation of PGRD (policy-gradient for reward-design) for learning a reward-bonus function to improve UCT (a MCTS algorithm). Unlike previous applications of PGRD in which the space of reward-bonus functions was limited to linear functions of hand-coded state-action-features, we use PGRD with a multi-layer convoluti…
Command and Control Engineering College, Army Engineering University of PLA（中国人民解放军陆军工程大学指挥控制工程学院）；troop of PLA（中国人民解放军31436部队）；Academy of Military Science（军事科学院）
The existing network attack and defense method can be regarded as game, but most of the game only involves network domain, not multiple domain cyberspace. To address this challenge, this paper proposed a multiple domain cyberspace attack and defense game model based on reinforcement learning. We define the multiple domain cyberspace include physical domain, network domain and digital domain. By establishing two agents, representing the attacker and the defender respectively, defender will select the multiple domain actions in the multiple domain cyberspace to obtain defender's optimal reward b…
The State-Action-Reward-State-Action Algorithm in Spatial Prisoner's Dilemma Game
College of Computer and Data Science, Fuzhou University（福州大学计算机与数据科学学院）；Fujian Key Laboratory of Data Science and Statistics, Minnan Normal University（闽南师范大学福建省数据科学与统计重点实验室）
In many problem settings, most notably in game playing, an agent receives a possibly delayed reward for its actions. Often, those rewards are handcrafted and not naturally given. Even simple terminal-only rewards, like winning equals one and losing equals minus one, can not be seen as an unbiased statement, since these values are chosen arbitrarily, and the behavior of the learner may change with different encodings. It is hard to argue about good rewards and the performance of an agent often depends on the design of the reward signal. In particular, in domains where states by nature only have…
In many problem settings, most notably in game playing, an agent receives a possibly delayed reward for its actions. Often, those rewards are handcrafted and not naturally given. Even simple terminal-only rewards, like winning equals 1 and losing equals -1, can not be seen as an unbiased statement, since these values are chosen arbitrarily, and the behavior of the learner may change with different encodings, such as setting the value of a loss to -0:5, which is often done in practice to encourage learning. It is hard to argue about good rewards and the performance of an agent often depends on …
In this paper we proposed reinforcement learning algorithms with the generalized reward function. In our proposed method we use Q-learning and SARSA algorithms with generalised reward function to train the reinforcement learning agent. We evaluated the performance of our proposed algorithms on two real-time strategy games called BattleCity and S3. There are two main advantages of having such an approach as compared to other works in RTS. (1) We can ignore the concept of a simulator which is often game specific and is usually hard coded in any type of RTS games (2) our system can learn from int…
Modern video games are becoming richer and more complex in terms of game mechanics. This complexity allows for the emergence of a wide variety of ways to play the game across the players. From the point of view of the game designer, this means that one needs to anticipate a lot of different ways the game could be played. Machine Learning (ML) could help address this issue. More precisely, Reinforcement Learning is a promising answer to the need of automating video game testing. In this paper we present a video game environment which lets us define multiple play-styles. We then introduce CARI: …
Reward shaping (RS) is a powerful method in reinforcement learning (RL) for overcoming the problem of sparse or uninformative rewards. However, RS typically relies on manually engineered shaping-reward functions whose construction is time-consuming and error-prone. It also requires domain knowledge which runs contrary to the goal of autonomous learning. We introduce Reinforcement Learning Optimising Shaping Algorithm (ROSA), an automated reward shaping framework in which the shaping-reward function is constructed in a Markov game between two agents. A reward-shaping agent (Shaper) uses switchi…
We present the first reinforcement-learning model to self-improve its reward-modulated training implemented through a continuously improving "intuition" neural network. An agent was trained how to play the arcade video game Pong with two reward-based alternatives, one where the paddle was placed randomly during training, and a second where the paddle was simultaneously trained on three additional neural networks such that it could develop a sense of "certainty" as to how probable its own predicted paddle position will be to return the ball. If the agent was less than 95% certain to return the …
To solve complex real-world problems with reinforcement learning, we cannot rely on manually specified reward functions. Instead, we can have humans communicate an objective to the agent directly. In this work, we combine two approaches to learning from human feedback: expert demonstrations and trajectory preferences. We train a deep neural network to model the reward function and use its predicted reward to train an DQN-based deep reinforcement learning agent on 9 Atari games. Our approach beats the imitation learning baseline in 7 games and achieves strictly superhuman performance on 2 games…
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…
Reinforcement Learning (RL) is an area of machine learning figuring out how agents take actions in an unknown environment to maximize its rewards. Unlike classical Markov Decision Process (MDP) in which agent has full knowledge of its state, rewards, and transitional probability, reinforcement learning utilizes exploration and exploitation for the model uncertainty. Under the condition that the model usually has a large state space, a neural network (NN) can be used to correlate its input state to its output actions to maximize the agent's rewards. However, building and training an efficient n…
Deep Reinforcement Learning (DRL) has shown its promising capabilities to learn optimal policies directly from trial and error. However, learning can be hindered if the goal of the learning, defined by the reward function, is "not optimal". We demonstrate that by setting the goal/target of competition in a counter-intuitive but intelligent way, instead of heuristically trying solutions through many hours the DRL simulation can quickly converge into a winning strategy. The ICRA-DJI RoboMaster AI Challenge is a game of cooperation and competition between robots in a partially observable environm…
OpenAI；UC Berkeley（加州大学伯克利分校）；Univ. of Edinburgh（爱丁堡大学）
Reinforcement learning algorithms rely on carefully engineering environment rewards that are extrinsic to the agent. However, annotating each environment with hand-designed, dense rewards is not scalable, motivating the need for developing reward functions that are intrinsic to the agent. Curiosity is a type of intrinsic reward function which uses prediction error as reward signal. In this paper: (a) We perform the first large-scale study of purely curiosity-driven learning, i.e. without any extrinsic rewards, across 54 standard benchmark environments, including the Atari game suite. Our resul…
We present a computational framework for synthesis of distributed control strategies for a heterogeneous team of robots in a partially observable environment. The goal is to cooperatively satisfy specifications given as Truncated Linear Temporal Logic (TLTL) formulas. Our approach formulates the synthesis problem as a stochastic game and employs a policy graph method to find a control strategy with memory for each agent. We construct the stochastic game on the product between the team transition system and a finite state automaton (FSA) that tracks the satisfaction of the TLTL formula. We use …
In recent years, reinforcement learning has seen interest because of deep Q-Learning, where the model is a convolutional neural network. Deep Q-Learning has shown promising results in games such as Atari and AlphaGo. Instead of learning the entire Q-table, it learns an estimate of the Q function that determines a state's policy action. We use Q-Learning and deep Q-learning, to learn control policies of four constraint satisfaction games (15-Puzzle, Minesweeper, 2048, and Sudoku). 15-Puzzle is a sliding permutation puzzle and provides a challenge in addressing its large state space. Minesweeper…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Microsoft Research（微软研究院）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
We propose a new framework for imitation learning -- treating imitation as a two-player ranking-based game between a policy and a reward. In this game, the reward agent learns to satisfy pairwise performance rankings between behaviors, while the policy agent learns to maximize this reward. In imitation learning, near-optimal expert data can be difficult to obtain, and even in the limit of infinite data cannot imply a total ordering over trajectories as preferences can. On the other hand, learning from preferences alone is challenging as a large number of preferences are required to infer a hig…
Adversarial self-play in two-player games has delivered impressive results when used with reinforcement learning algorithms that combine deep neural networks and tree search. Algorithms like AlphaZero and Expert Iteration learn tabula-rasa, producing highly informative training data on the fly. However, the self-play training strategy is not directly applicable to single-player games. Recently, several practically important combinatorial optimisation problems, such as the travelling salesman problem and the bin packing problem, have been reformulated as reinforcement learning problems, increas…
To perform well, Deep Reinforcement Learning (DRL) methods require significant memory resources and computational time. Also, sometimes these systems need additional environment information to achieve a good reward. However, it is more important for many applications and devices to reduce memory usage and computational times than to achieve the maximum reward. This paper presents a modified DRL method that performs reasonably well with compressed imagery data without requiring additional environment information and also uses less memory and time. We have designed a lightweight Convolutional Ne…
Deep reinforcement learning methods traditionally struggle with tasks where environment rewards are particularly sparse. One successful method of guiding exploration in these domains is to imitate trajectories provided by a human demonstrator. However, these demonstrations are typically collected under artificial conditions, i.e. with access to the agent's exact environment setup and the demonstrator's action and reward trajectories. Here we propose a two-stage method that overcomes these limitations by relying on noisy, unaligned footage without access to such data. First, we learn to map una…
We propose the first model-free algorithm that achieves low regret performance for decentralized learning in two-player zero-sum tabular stochastic games with infinite-horizon average-reward objective. In decentralized learning, the learning agent controls only one player and tries to achieve low regret performances against an arbitrary opponent. This contrasts with centralized learning where the agent tries to approximate the Nash equilibrium by controlling both players. In our infinite-horizon undiscounted setting, additional structure assumptions is needed to provide good behaviors of learn…
Vector Institute（向量研究所）；University of Toronto（多伦多大学）；Google Brain（谷歌大脑）
Reinforcement learning has enabled agents to solve challenging tasks in unknown environments. However, manually crafting reward functions can be time consuming, expensive, and error prone to human error. Competing objectives have been proposed for agents to learn without external supervision, but it has been unclear how well they reflect task rewards or human behavior. To accelerate the development of intrinsic objectives, we retrospectively compute potential objectives on pre-collected datasets of agent behavior, rather than optimizing them online, and compare them by analyzing their correlat…
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…
Imperial College London（伦敦帝国理工学院）；Laiye Network Technology Co.Ltd.（来也网络科技有限公司）
Cooperative game is a critical research area in the multi-agent reinforcement learning (MARL). Global reward game is a subclass of cooperative games, where all agents aim to maximize the global reward. Credit assignment is an important problem studied in the global reward game. Most of previous works stood by the view of non-cooperative-game theoretical framework with the shared reward approach, i.e., each agent being assigned a shared global reward directly. This, however, may give each agent an inaccurate reward on its contribution to the group, which could cause inefficient learning. To dea…
New York University（纽约大学）；Game Innovation Lab（游戏创新实验室）
We present a new concept called Game Mechanic Alignment theory as a way to organize game mechanics through the lens of systemic rewards and agential motivations. By disentangling player and systemic influences, mechanics may be better identified for use in an automated tutorial generation system, which could tailor tutorials for a particular playstyle or player. Within, we apply this theory to several well-known games to demonstrate how designers can benefit from it, we describe a methodology for how to estimate "mechanic alignment", and we apply this methodology on multiple games in the GVGAI…
In the realm of games research, Artificial General Intelligence algorithms often use score as main reward signal for learning or playing actions. However this has shown its severe limitations when the point rewards are very rare or absent until the end of the game. This paper proposes a new approach based on event logging: the game state triggers an event every time one of its features changes. These events are processed by an Event-value Function (EF) that assigns a value to a single action or a sequence. The experiments have shown that such approach can mitigate the problem of scarce point r…
Reinforcement learning is concerned with identifying reward-maximizing behaviour policies in environments that are initially unknown. State-of-the-art reinforcement learning approaches, such as deep Q-networks, are model-free and learn to act effectively across a wide range of environments such as Atari games, but require huge amounts of data. Model-based techniques are more data-efficient, but need to acquire explicit knowledge about the environment. In this paper, we take a step towards using model-based techniques in environments with a high-dimensional visual state space by demonstrating t…
Reward function, as an incentive representation that recognizes humans' agency and rationalizes humans' actions, is particularly appealing for modeling human behavior in human-robot interaction. Inverse Reinforcement Learning is an effective way to retrieve reward functions from demonstrations. However, it has always been challenging when applying it to multi-agent settings since the mutual influence between agents has to be appropriately modeled. To tackle this challenge, previous work either exploits equilibrium solution concepts by assuming humans as perfectly rational optimizers with unbou…
UC Berkeley（加州大学伯克利分校）；UCSD（加利福尼亚大学圣地亚哥分校）；CMU（卡内基梅隆大学）；University of Washington（华盛顿大学）；Tsinghua University（清华大学）；Shanghai Qi Zhi Institute（上海期智研究院）；Peking University（北京大学）
We propose a simple, general and effective technique, Reward Randomization for discovering diverse strategic policies in complex multi-agent games. Combining reward randomization and policy gradient, we derive a new algorithm, Reward-Randomized Policy Gradient (RPG). RPG is able to discover multiple distinctive human-interpretable strategies in challenging temporal trust dilemmas, including grid-world games and a real-world game Agar.io, where multiple equilibria exist but standard multi-agent policy gradient algorithms always converge to a fixed one with a sub-optimal payoff for every player …
ShanghaiTech University（上海科技大学）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Ariel University（阿里埃勒大学）
The research on coalitional games has focused on how to share the reward among a coalition such that players are incentivised to collaborate together. It assumes that the (deterministic or stochastic) characteristic function is known in advance. This paper studies a new setting (a task allocation problem) where the characteristic function is not known and it is controlled by some private information from the players. Hence, the challenge here is twofold: (i) incentivize players to reveal their private information truthfully, (ii) incentivize them to collaborate together. We show that existing …
Stanford University（斯坦福大学）；University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）
Coordination is often critical to forming prosocial behaviors -- behaviors that increase the overall sum of rewards received by all agents in a multi-agent game. However, state of the art reinforcement learning algorithms often suffer from converging to socially less desirable equilibria when multiple equilibria exist. Previous works address this challenge with explicit reward shaping, which requires the strong assumption that agents can be forced to be prosocial. We propose using a less restrictive peer-rewarding mechanism, gifting, that guides the agents toward more socially desirable equili…
