Differentiable Arbitrating in Zero-sum Markov Games

Evaluating semi-cooperative Nash/Stackelberg Q-learning for traffic routes plan in a single intersection

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.

Early threat detection is an increasing part of the cybersecurity landscape, given the growing scale and scope of cyberattacks in the recent years. Increasing exploitation of software vulnerabilities, especially in the manufacturing sector, demonstrates the ongoing need for autonomous network defence. In this work, we model the problem as a zero-sum Markov game between an attacker and defender reinforcement learning agents. Previous methods test their approach on a single topology or limit the agents to a subset of the network. However, real world networks are rarely fixed and often add or remove hosts based on demand, link failures, outages, or other factors. We do not confine our research to a fixed network in terms of size and topology, but instead are interested in larger networks and varied topologies to determine the scalability and robustness of the approach. We consider additional topologies and a robust training curriculum that incorporates network topologies to build more general, capable agents. We also use PPO which offers a good balance of computational complexity and convergence speed.

With the development of jamming systems, the jammer is becoming much smarter and can change its strategy with radar, which forms a competitive game between the radar and jammer and poses a significant threat to the radar. In this paper, the anti-jamming game of frequency-agile (FA) radar is investigated, in which the jammer is capable of transmitting jamming signals with multiple frequency channels and different power allocation manners. To characterize the sequential interaction and partial observation of the anti-jamming game, an extensive-form game is introduced to model the confrontation between the radar and jammer. Subsequently, a novel multi-agent reinforcement learning (MARL) algorithm, termed NFSP-DDPG, is devised by combining neural fictitious self-play (NFSP) with deep deterministic policy gradient (DDPG) and modifying the supervised learning process of NFSP to solve Nash equilibrium (NE) strategies, which can handle the anti-jamming games featuring both discrete and continuous action spaces. Finally, simulation results show that the learning strategies acquired through the proposed method approximate NE and outperform the rule-based strategies. The signal-to-interference-pulse-noise ratio (SINR) improvements of radar taking NE strategy are 9.13dB, 9.12dB, and 9.15dB in the worst-case in the anti-jamming game with five frequencies compared to three rule-based strategies.

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.

Coordination is one of the essential problems in multi-agent systems. Typically multi-agent reinforcement learning (MARL) methods treat agents equally and the goal is to solve the Markov game to an arbitrary Nash equilibrium (NE) when multiple equilibra exist, thus lacking a solution for NE selection. In this paper, we treat agents unequally and consider Stackelberg equilibrium as a potentially better convergence point than Nash equilibrium in terms of Pareto superiority, especially in cooperative environments. Under Markov games, we formally define the bi-level reinforcement learning problem in finding Stackelberg equilibrium. We propose a novel bi-level actor-critic learning method that allows agents to have different knowledge base (thus intelligent), while their actions still can be executed simultaneously and distributedly. The convergence proof is given, while the resulting learning algorithm is tested against the state of the arts. We found that the proposed bi-level actor-critic algorithm successfully converged to the Stackelberg equilibria in matrix games and find a asymmetric solution in a highway merge environment.

With the development of unmanned combat air vehicles (UCAVs) and artificial intelligence (AI), within visual range (WVR) air combat confrontations utilizing intelligent UCAVs are expected to be widely used in future air combats. As controlling highly dynamic and uncertain WVR air combats from the ground stations of the UCAV is not feasible, it is necessary to develop an algorithm that can generate highly intelligent air combat strategies in order to enable UCAV to independently complete air combat missions. In this paper, a 1-vs.-1 WVR air combat strategy generation algorithm is proposed using the multi-agent deep deterministic policy gradient (MADDPG). A 1-vs.-1 WVR air combat is modeled as a two-player zero-sum Markov game (ZSMG). A method for predicting the position of the target is introduced into the model in order to enable the UCAV to predict the target’s actions and position. Moreover, to ensure that the UCAV is not limited by the constraints of the basic fighter maneuver (BFM) library, the action space is considered to be a continuous one. At the same time, a potential-based reward shaping method is proposed in order to improve the efficiency of the air combat strategy generation algorithm. Finally, the efficiency of the air combat strategy generation algorithm and the intelligence level of the resulting strategy is verified through simulation experiments. The results show that an air combat strategy using target position prediction is superior to the one that does not use target position prediction.

Self-play (SP) is a popular multi-agent reinforcement learning (MARL) framework for solving competitive games, where each agent optimizes policy by treating others as part of the environment. Despite the empirical successes, the theoretical properties of SP-based methods are limited to two-player zero-sum games. However, for mixed cooperative-competitive games where agents on the same team need to cooperate with each other, we can show a simple counter-example where SP-based methods cannot converge to a global Nash equilibrium (NE) with high probability. Alternatively, Policy-Space Response Oracles (PSRO) is an iterative framework for learning NE, where the best responses w.r.t. previous policies are learned in each iteration. PSRO can be directly extended to mixed cooperative-competitive settings by jointly learning team best responses with all convergence properties unchanged. However, PSRO requires repeatedly training joint policies from scratch till convergence, which makes it hard to scale to complex games. In this work, we develop a novel algorithm, Fictitious Cross-Play (FXP), which inherits the benefits from both frameworks. FXP simultaneously trains an SP-based main policy and a counter population of best response policies. The main policy is trained by fictitious self-play and cross-play against the counter population, while the counter policies are trained as the best responses to the main policy's past versions. We validate our method in matrix games and show that FXP converges to global NEs while SP methods fail. We also conduct experiments in a gridworld domain, where FXP achieves higher Elo ratings and lower exploitabilities than baselines, and a more challenging football game, where FXP defeats SOTA models with over 94% win rate.

As cyber threats become increasingly automated and sophisticated, novel solutions must be introduced to improve defense of enterprise networks. Deep reinforcement learning (DRL) has demonstrated potential in mitigating these advanced threats. Single DRL agents have proven utility toward execution of autonomous cyber defense. Despite the success of employing single DRL agents, this approach presents significant limitations, especially regarding scalability within large enterprise networks. An attractive alternative to the single‐agent approach is the use of multi‐agent reinforcement learning (MARL). However, developing MARL agents is costly with few options for examining MARL cyber defense techniques against adversarial agents. This paper presents a MARL network security environment, the fourth iteration of the cyber autonomy gym for experimentation (CAGE) challenges. This challenge was specifically designed to test the efficacy of MARL algorithms in an enterprise network. Our work aims to evaluate the potential of MARL as a robust and scalable solution for autonomous network defense.

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p498.pdf **Abstract:** In multiagent systems, the complex interaction of fixed incentives can lead agents to outcomes that are poor (\emph{inefficient}) not only for the group, but also for each individual. Price of anarchy is a technical, game-theoretic definition that quantifies the inefficiency arising in these scenarios\textemdash it compares the welfare that can be achieved through perfect coordination against that achieved by self-interested agents at a Nash equilibrium. We derive a differentiable, upper bound on a price of anarchy that agents can cheaply estimate during learning. Equipped with this estimator, agents can adjust their incentives in a way that improves the efficiency incurred at a Nash equilibrium. Agents do so by learning to mix their reward (equiv. negative loss) with that of other agents by following the gradient of our derived upper bound. We refer to this approach as D3C. In the case where agent incentives are differentiable, D3C resembles the celebrated Win-Stay, Lose-Shift strategy from behavioral game theory, thereby establishing a connection between the global goal of maximum welfare and an established agent-centric learning rule. In the non-differentiable setting, as is common in multiagent reinforcement learning, we show the upper bound can be reduced via evolutionary strategies, until a compromise is reached in a distributed fashion. We demonstrate that D3C improves outcomes for each agent and the group as a whole on several social dilemmas including a traffic network exhibiting Braess’s paradox, a prisoner’s dilemma, and several multiagent domains.

Automated clash resolution for reinforcement steel design in concrete frames via Q-learning and Building Information Modeling

This paper investigates the error accumulation problem in centralized training and decentralized execution (CTDE) policy‐based multi‐agent reinforcement learning (MARL) algorithms, which arises from local observation inaccuracies. To address this issue, we propose a novel MARL algorithm that incorporates imitation learning using local observations. Firstly, by analysing the multi‐agent proximal policy optimization algorithm and examining the problems arising when global states are replaced with local observations, it is proved that insufficient observations can lead to information loss, thereby introducing errors of advantage function, and it is demonstrated that the generalized advantage estimation method accumulates errors during the training process. Then, imitation learning is introduced and a novel training framework that combines reinforcement learning and imitation learning is proposed. During the reinforcement learning phase, an MARL agent trained with global observations acts as an expert. Subsequently, imitation learning is applied to train another agent that mimics the expert's decisions using only local observations. Finally, the effectiveness of this algorithm is verified in some commonly used multi‐agent environments, which demonstrates its superior performance compared to traditional multi‐agent reinforcement learning algorithms.

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.

Mobile edge computing (MEC) has appeared as a promising solution to fill the gap between the growing computationally intensive applications and limited computation capability of mobile devices by providing powerful computing services at the edge of the wireless access network. To use the services provided by the MEC more effectively, making efficient and reasonable offloading decisions is crucial. In this paper, we study the computation offloading of tasks from multiple users to a single-cell edge server under a dynamic environment. We consider a practical case wherein a group of mobile users with random mobility patterns use a common set of time-varying stochastic transmission channels to perform computation offloading, and the number of active users in the system randomly changes. To reduce the mutual interference among users when accessing the wireless channels, we adopt game theory to formulate the users’ computation offloading decision process as a stochastic game model. Next, we prove the existence of the Nash Equilibrium (NE) for the proposed game model by showing its equivalency to a weighted potential game which has at least one pure-strategy NE point. Then, we present distributed computation offloading algorithms by adopting a payoff-based multi-agent reinforcement learning (MARL) approach to reach the NE of the game. Finally, through simulation, we validate the effectiveness of the proposed algorithms by comparing them with the results obtained from other previously studied multi-agent learning algorithms as well as conventional Q-learning and deep Q-learning algorithms.