Modelling Stock Markets by Multi-agent Reinforcement Learning

For the task under Markov Decision Process, this paper presents a novel multiagent Reinforcement Learning (RL) with perception and conversion action mechanism that learning agents observe adversary agent and convert adversarial action to learning agents' corresponding action as observing state variation incurred by the adversary agent in the task environment during learning processes. Meanwhile, this paper surveys inexpensive communication ways among learning agents utilizing both the direct communication and the indirect media communication to realize agents' cooperation. The direct communication is realized by sharing sensation; the indirect media communication is realized by updating reinforcement values on the common environment observation. Then, a multiagent RL algorithm, Q-ac multiagent RL method, is proposed. By perception and conversion action, the learning agents extend learning episodes and derive more observation by less action. The direct communication enhances agents' observation ability to the environment, and the indirect media communication improves agents' ability deriving the optimal action policy. The simulation results on hunter game demonstrate the efficiency of the proposed method.

Based on the network observations and learning parameters shared by the neighboring learning agents, multi-agent reinforcement learning (RL) has to enhance the performance over adversarial communications, in which spoofing attackers send fake learning messages to fool the learning agent and thus degrade the performance of wireless applications. In this paper, we propose a safe multi-agent RL algorithm for wireless applications against adversarial communications, in which each learning agent chooses the cooperative agents to share the learning information and authenticates the received learning messages before integrating them into the RL state formulation and the learning parameter update. The communication policy distribution for the cooperative agent selection is formulated based on the long-term discounted reward and the sharing reputation for each neighboring agent, which is updated based on the authentication results to indicate the probability as a spoofing attacker. Neural networks are designed to estimate the long-term discounted reward and the sharing reputation for the learning agent with sufficient computational resources in large-scale wireless networks to enhance the agent selection security. As a case study, our proposed algorithm is implemented in the unmanned aerial vehicle swarm anti-jamming video transmission against spoofing attackers that send fake received jamming power as well as Q-values and neural network weights in the anti-jamming transmission policy learning. Both simulation and experimental results are provided to verify the performance gain over the benchmark.

Reinforcement learning (RL) and multi-agent reinforcement learning (MARL) are disciplines concerned with defining automatically the behaviour of an agent, or a set of interacting agents, by means of reward mechanisms coming from the environment. An important research issue in the context of RL and MARL is the definition of approaches to combine the knowledge of multiple learning agents to improve the overall performance of the multi-agent system (MAS). This paper illustrates how to improve RL and MARL algorithms by utilizing results from multi-linear algebra such as tensors and tensor factorizations. In particular, the focus is on showing how to modify existing algorithms from literature to include a tensor factorization step applied to the Q-Tables learned by the individual agents to generalize the knowledge about the actions performed in the environment. The modified algorithms are then evaluated in three RL and MARL scenarios against their unmodified version to show the benefits of the tensor factorization step.

This article shows that seemingly diverse implementations of multi-agent reinforcement learning share the same basic building block in their learning dynamics: a mathematical term that is closely related to the gradient of the expected reward. Specifically, two independent branches of multi-agent learning research can be distinguished based on their respective assumptions and premises. The first branch assumes that the value function of the game is known to all players, which is then used to update the learning policy based on Gradient Ascent. Notable algorithms in this branch include Infinitesimal Gradient Ascent (IGA) [7], the variation Win or Learn Fast IGA (WoLF) [3] and the Weighted Policy Learner [1]. The second branch of multi-agent learning is concerned with learning in unknown environments, using interaction-based Reinforcement Learning, and contains those algorithms which have been shown to be formally connected to the replicator equations of Evolutionary Game Theory. In this case, the learning agent updates its policy based on a sequence of pairs that indicate the quality of the actions taken. Notable algorithms include Cross Learning (CL) [4], Regret Minimization (RM) [6], and Frequency Adjusted Q-learning (FAQ) [5]. This article demonstrates inherent similarities between these diverse families of algorithms by comparing their underlying learning dynamics, derived as the continuous time limit of their policy updates. These dynamics have already been investigated for algorithms from each family separately [1, 2, 3, 5, 6, 7], however, they have not yet been discussed in context of the relation to each other, and the origin of their similarity has not been discussed satisfactorily. In addition to the formal derivation, directional field plots of the learning dynamics in representative classes of two-player two-action games illustrate the similarities and strengthen the theoretical findings.

Multi-Agent systems consist of multiple interacting agents that solve complex problems too difficult for monolithic systems to solve.Each agent has a different role and is not aware of the state of other agents.Multi-Agent Reinforcement Learning is a common approach to training agents in these systems.Many researchers tend to focus on the implementation of reinforcement learning for training agents towards a particular goal.This paper, in contrast, implements reinforcement learning for a different purpose.This paper is about the analysis of emergent cooperative strategies between agents while achieving their goals.The research will be done using simulations of a cooperative game and documenting the strategies the agents create over a set number of episodes.

The combination of deep neural networks and reinforcement learning had received more and more attention in recent years, and the attention of reinforcement learning of single agent was slowly getting transferred to multiagent. Regret minimization was a new concept in the theory of gaming. In some game issues that Nash equilibrium was not the optimal solution, the regret minimization had better performance. Herein, we introduce the regret minimization into multiagent reinforcement learning and propose a multiagent regret minimum algorithm. This chapter first introduces the Nash Q-learning algorithm and uses the overall framework of Nash Q-learning to minimize regrets into the multiagent reinforcement learning and then verify the effectiveness of the algorithm in the experiment.

This article investigates the multirobot efficient search (MuRES) for a nonadversarial moving target problem from the multiagent reinforcement learning (MARL) perspective. MARL is deemed as a promising research field for cooperative multiagent applications. However, one of the main bottlenecks of applying MARL to the MuRES problem is the nonstationarity introduced by multiple learning agents. With learning agents simultaneously updating their policies, the environment cannot be modeled as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stationary</i> Markov decision process, which results in the inapplicability of fundamental reinforcement learning techniques such as deep <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -network and policy gradient (PG). In view of that, we adopt the centralized training and decentralized execution scheme and thereby propose a cross-entropy regularized policy gradient (CE-PG) method to train the learning agents/robots. We let the robots <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">commit</i> to a predetermined policy during execution, collect the trajectories, and then perform centralized training for the corresponding policy improvement. In this way, the nonstationarity problem is overcome, in that the robots do not update their policies during execution. During the centralized training stage, we improve the canonical PG method to consider the interactions among robots by adding a cross-entropy regularization term, which essentially functions to “disperse” the robots in the environment. Extensive simulation results and comparisons with state of the art show CE-PG's superior performance, and we also validate the algorithm with a real multirobot system in an indoor moving target search scenario.

This paper investigates a relatively new direction in Multiagent Reinforcement Learning. Most multiagent learning techniques focus on Nash equilibria as elements of both the learning algorithm and its evaluation criteria. In contrast, we propose a multiagent learning algorithm that is optimal in the sense of finding a best-response policy, rather than in reaching an equilibrium. We present the first learning algorithm that is provably optimal against restricted classes of non-stationary opponents. The algorithm infers an accurate model of the opponentýs non-stationary strategy, and simultaneously creates a best-response policy against that strategy. Our learning algorithm works within the very general framework of n-player, general-sum stochastic games, and learns both the game structure and its associated optimal policy.

Entropy regularized actor-critic based multi-agent deep reinforcement learning for stochastic games

Reinforcement learning, a machine learning technique, has already shown advancement in solving complex sequential decision-making problems. Many tasks involve multiple agents and require sequential decision-making policies to achieve common goals, such as warehouse automation, autonomous driving, and game-playing. To derive the policies for all agents, these problems can be modelled as multi-agent systems and addressed by multi-agent reinforcement learning (MARL). However, optimizing policies in multi-agent scenarios presents significant challenges due to the intricate behaviours of multiple agents and the non-stationary nature of the environments’ complex dynamics. Firstly, optimizing policies in multi-agent scenarios presents significant challenges due to the complexity of multi-agent behaviours, especially in partially observable environments. Also, the dynamic nature of agents’ behaviours and their interactions with other agents lead to changes in the environment’s states and agents’ observations over time, which is more complicated in open environments. Furthermore, the need to balance individual and collective objectives in certain real-world multi-agent environments also complicates the decision-making process. This doctoral thesis aims to tackle the following three fundamental multi-agent research problems and propose a solution for each. Our research covers from theoretical analysis to practical application. We start by studying the problem of learning an efficient policy under partially observable environments. We notice that a group of agents cooperates to com- pete against another group of agents (named opponents), with the limitation that information about the opponents is inaccessible due to partial observability. To address this issue, we propose a novel multi-agent distributional actor-critic algorithm to achieve speculative opponent modeling with purely local information (i.e., the controlled agent’s observations, actions, and rewards). The actor maintains a speculated belief of the opponents, which we call the speculative opponent models, to predict opponents’ actions using local observations and make decisions accordingly. The distributional critic models the return distribution of the policy. It reflects the quality of the actor and thus can guide the training of the imaginary opponent model that the actor relies on. Extensive experiments confirm that our method successfully models opponents’ behaviours without their data and delivers superior performance against baseline methods with a faster convergence speed. Furthermore, in some environments, teammates’ numbers and policies change with the market, requiring workers to adapt to perform different sets of tasks across time. To solve this issue, we propose an RL-based method that allows the controlled agent to collaborate with dynamic teammates in open environments. The controlled agent maintains a dual teamwork situation inference model to capture the current teamwork state and facilitate reasonable decision-making under partial observability. Considering the dynamic types of teammates, we first leverage the Chinese Restaurant Process-based model to categorize versatile teammate policies into distinct clusters, which improves the efficiency of identifying current teamwork situations. Next, to model the heterogeneous relationships among agents and accommodate the varying number of teammates, we apply heterogeneous graph attention neural networks to learn the representation of the teamwork situation. Extensive experiments confirm that our method outperforms state-of-the-art baselines with faster convergence in various ad hoc teamwork tasks. Lastly, in certain real-world applications, such as routing problems and warehouse management, decision-makers must balance overall benefits with individual fairness among agents. Achieving both learning efficiency and fairness concurrently presents a complex, multi-objective, joint-policy optimization challenge. Moreover, existing approaches are predominantly confined to simulation environments. To address the above issues, we present a pioneering MARL approach to balance individual and collective objectives for agents collaboration. Extensive experiments on synthetic and real-world datasets demonstrate that our method not only surpasses the state-of-the-art DRL methods, but also exhibits advantages over established heuristics, notably in achieving significantly faster optimization speeds. This method underlines the essential integration of fairness into real-world applications, representing a major advancement in creating equitable and efficient logistics solutions. To conclude, this doctoral thesis investigates three fundamental multi-agent decision-making research problems that are ubiquitous and unsolved. The proposed three MARL methodology solutions achieve efficient policy training and performance for agents in multi-agent environments with uncertainties raised by the partially observable, the open environment, and the individual-collective objectives of MARL. This thesis delves into novel designs of various critical components of MARL, including MDP formulations, policy networks, training algorithms, and inference methods. These contributions significantly elevate the effectiveness and efficiency of cooperative MARL, establishing new performance benchmarks.

Coordinated multi-agent reinforcement learning (MARL) provides a promising approach to scaling learning in large cooperative multi-agent systems. Distributed constraint optimization (DCOP) techniques have been used to coordinate action selection among agents during both the learning phase and the policy execution phase (if learning is off-line) to ensure good overall system performance. However, running DCOP algorithms for each action selection through the whole system results in significant communication among agents, which is not practical for most applications with limited communication bandwidth. In this paper, we develop a learning approach that generalizes previous coordinated MARL approaches that use DCOP algorithms and enables MARL to be conducted over a spectrum from independent learning (without communication) to fully coordinated learning depending on agents' communication bandwidth. Our approach defines an interaction measure that allows agents to dynamically identify their beneficial coordination set (i.e., whom to coordinate with) in different situations and to trade off its performance and communication cost. By limiting their coordination set, agents dynamically decompose the coordination network in a distributed way, resulting in dramatically reduced communication for DCOP algorithms without significantly affecting overall learning performance. Essentially, our learning approach conducts co-adaptation of agents' policy learning and coordination set identification, which outperforms approaches that sequence them.

Reinforcement learning (RL) is an efficient learning method for Markov decision processes (MDPs); ant colony system (ACS) is an efficient method for solving combinatorial optimization problems. Based on the update policy of reinforcement values in RL and the cooperating method of the indirect media communication in ACS, this paper proposes the Q-ACS multi-agent cooperating learning method for the learning agents to share episodes beneficial to the exploitation of the accumulated knowledge and to utilize the learned reinforcement values efficiently. Further, taking the visited times into account, this paper proposes the T-ACS multi-agent learning method that the learning agents share better policies beneficial to the exploration during agent's learning processes. Meanwhile, in the light of the indirect media communication among heterogeneous multi-agents, this paper presents a heterogeneous multi-agent RL method, the D-ACS. The agents in our methods are given a simply cooperating way exchanging information in the form of reinforcement values updated in the common model of all agents. Owning the advantages of exploring the unknown environment actively and exploiting learned knowledge effectively, the proposed methods are able to solve both MDPs and combinatorial optimization problems effectively. To results of simulations on the hunter game and the traveling salesman problem, this paper discusses the role of the indirect media communication on the multi-agent cooperation learning system and analyzes its efficiency. The results of experiments also demonstrate that our methods perform competitively with representative methods on each domain respectively.

Aim and ApproachLarge cooling water system has great potential of energy saving due to improper operation control. The coupled hydraulic and thermodynamic characteristics among chillers, pumps, and cooling towers lead to the difficulty of cooling water system operation. This study investigates an advanced control approach of multi-agent reinforcement learning (RL) for a large cooling water system. The multiple RL agents interact with each other to deal with the complex coupled characteristics in the cooling water system. The proposed approach is implemented in a real-world cooling water system and validated with experiments.Scientific Innovation and RelevanceIn this study, a multi-agent RL approach is proposed to separately control the chillers, pumps, and cooling towers in the cooling water system. The soft actor critic algorithm is used in the RL agent, as it is an efficient and advanced RL algorithm for continuous and discrete control problems. The agents are designed to have private states, private actions, and shared rewards. The reward functions are carefully designed to balance the agents for global optima.To provide a realistic environment for RL training, a detailed physical modeling platform of a cooling water system is established and validated. This platform is capable of hydraulic and thermodynamic calculation of cooling water systems with customized numbers and characteristics of chillers, pumps, and cooling towers, which is scalable for different cooling water systems.The proposed multi-agent RL controller is implemented in the building automation system of a real cooling water system. A one-month experimental study of the multi-agent RL performance is conducted. The proposed multi-agent RL controller is compared with a single-agent RL controller and a rule-based controller through real-world experiments to demonstrate the energy performance. This is a pilot study of multi-agent RL approach to real-world cooling water system control.Preliminary Results and ConclusionsThe preliminary simulation study is conducted in the established cooling water system model. The electricity consumption simulation error is 4.0% in coefficient of variation of mean absolute error (CVMAE) compared with the measured 15-minute electricity consumption. The 6-month simulation shows that the single-agent RL can save 6.2% energy from the rule-based control, while the multi-agent RL can save 7.2% electricity consumption of the cooling water system. In the following study, the multi-agent RL implementation will be practiced with more experiments and applications for cooling water system control.

Recently, the researches on multi-agent reinforcement learning (MARL) have attracted tremendous interest in many applications, especially for autonomous driving. The main problem of MARL is how to deal with the uncertainty in the environment and the interaction between the connected agents. To solve the problem, a distributed robust temporal differential deep Q-network algorithm (MARTD-DQN) was developed in this paper. MARTD-DQN consists of two parts, the decentralized MARL algorithm (DMARL) and the robust TD deep Q-network algorithm (RTD-DQN). DMARL improves the robustness of the policy estimation by fusing the states from the neighbors over communicated networks. RTD- DQN improves the robustness to outliers through on-line estimation of the uncertainty. By combining the two algorithms, the proposed algorithm can be robust not only to node failures but also to the outliers. Then the proposed algorithm is applied to ACC simulations of autonomous cars. The simulation results are given to show the efficiency of the proposed algorithm.

Recently, multiagent reinforcement learning (MARL) has shown great potential for learning cooperative policies in multiagent systems (MASs). However, a noticeable drawback of current MARL is the low sample efficiency, which causes a huge amount of interactions with environment. Such amount of interactions greatly hinders the real-world application of MARL. Fortunately, effectively incorporating experience knowledge can assist MARL to quickly find effective solutions, which can significantly alleviate the drawback. In this article, a novel multiexperience-assisted reinforcement learning (MEARL) method is proposed to improve the learning efficiency of MASs. Specifically, monotonicity-constrained reward shaping is innovatively designed using expert experience to provide additional individual rewards to guide multiagent learning efficiently, with the invariance guarantee of the team optimization objective. Furthermore, a reward distribution estimator is specially developed to model an implicated reward distribution of environment by using transition experience from environment, containing collected samples (state-action pair, reward, and next state). This estimator can predict the expectation reward of each agent for the taken action to accurately estimate the state value function and accelerate its convergence. Besides, the performance of MEARL is evaluated on two multiagent environment platforms: our designed unmanned aerial vehicle combat (UAV-C) and StarCraft II Micromanagement (SCII-M). Simulation results demonstrate that the proposed MEARL can greatly improve the learning efficiency and performance of MASs and is superior to the state-of-the-art methods in multiagent tasks.