Best-Response Multiagent Learning in Non-Stationary Environments

Learning in multi-agent settings has recently garnered much interest, the result of which has been the development of somewhat effective multi-agent learning (MAL) algorithms for repeated normal-form games. However, general-purpose MAL algorithms for richer environments, such as general-sum repeated stochastic (Markov) games (RSGs), are less advanced. Indeed, previously created MAL algorithms for RSGs are typically successful only when the behavior of associates meets specific game theoretic assumptions and when the game is of a particular class (such as zero-sum games). In this paper, we present a new algorithm, called Pepper, that can be used to extend MAL algorithms designed for repeated normal-form games to RSGs. We demonstrate that Pepper creates a family of new algorithms, each of whose asymptotic performance in RSGs is reminiscent of its asymptotic performance in related repeated normal-form games. We also show that some algorithms formed with Pepper outperform existing algorithms in an interesting RSG.

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.

In this paper, we investigate multi-agent learning (MAL) in a multi-agent resource selection problem (MARS) in which a large group of agents are competing for common resources. Since agents in such a setting are self-interested, MAL in MARS domains typically focuses on the convergence to a set of non-cooperative equilibria. As seen in the example of prisoner's dilemma, however, selfish equilibria are not necessarily optimal with respect to the natural objective function of a target problem, e.g., resource utilization in the case of MARS. Conversely, a centrally administered optimization of physically distributed agents is infeasible in many real-life applications such as transportation traffic problems. In order to explore the possibility for a middle ground solution, we analyze two types of costs for evaluating MAL algorithms in this context. The quality loss of a selfish algorithm can be quantitatively measured by the price of anarchy, i.e., the ratio of the objective function value of a selfish solution to that of an optimal solution. Analogously, we introduce the price of monarchy of a learning algorithm to quantify the practical cost of coordination in terms of communication cost. We then introduce a multi-agent social learning approach named A Few Good Agents (AFGA) that motivates self-interested agents to cooperate with one another to reduce the price of anarchy, while bounding the price of monarchy at the same time. A preliminary set of experiments on the El Farol bar problem, a simple example of MARS, show promising results.

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.

Two multi-agent policy iteration learning algorithms are proposed in this work. The two proposed algorithms use the exponential moving average approach along with the Q-learning algorithm as a basis to update the policy for the learning agent so that the agent's policy converges to a Nash equilibrium policy. The first proposed algorithm uses a constant learning rate when updating the policy of the learning agent, while the second proposed algorithm uses two different decaying learning rates. These two decaying learning rates are updated based on either the Win-or-Learn-Fast (WoLF) mechanism or the Win-or-Learn-Slow (WoLS) mechanism. The WoLS mechanism is introduced in this article to make the algorithm learn fast when it is winning and learn slowly when it is losing. The second proposed algorithm uses the rewards received by the learning agent to decide which mechanism (WoLF mechanism or WoLS mechanism) to use for the game being learned. The proposed algorithms have been theoretically analyzed and a mathematical proof of convergence to pure Nash equilibrium is provided for each algorithm. In the case of games with mixed Nash equilibrium, our mathematical analysis shows that the second proposed algorithm converges to an equilibrium. Although our mathematical analysis does not explicitly show that the second proposed algorithm converges to a Nash equilibrium, our simulation results indicate that the second proposed algorithm does converge to Nash equilibrium. The proposed algorithms are examined on a variety of matrix and stochastic games. Simulation results show that the second proposed algorithm converges in a wider variety of situations than state-of-the-art multi-agent reinforcement learning algorithms.

An agent must learn and adapt quickly when playing against other agents. This process is challenging in particular when playing in stochastic environments against other learning agents. In this paper, we introduce a fast and adaptive learning algorithm for repeated stochastic games (FAL-SG). FAL-SG utilizes lossy game abstraction to reduce the state space of the game and facilitate learning and adapting rapidly. We analyze FAL-SG's performance by proving bounds on the abstraction loss and prediction mistakes and show that FAL-SG satisfies three criteria prescribed for multiagent learning algorithms. We successfully establish the robustness and scalability of FAL-SG with extensive theoretical and experimental results.

Highly accurate sensor measurements are crucial in order for power plants to effectively operate, as well as to predict and subsequently prevent any potentially catastrophic failures. As the cost of sensors decreases while their power increases, distributed sensor networks become a more attractive option for implementation in power plants. In this work, we investi- gate the use of a distributed sensor network to achieve highly accurate measurements. We apply shaped rewards to local components and use a simple learning algorithm at each sen- sor in order to maximize those rewards. Our results show that the measurements from a sensor network trained us- ing shaped rewards are up to two orders of magnitude more accurate than a sensor network trained with a traditional global reward. Further, the algorithm proposed scales well to large networks, and is robust to measurement noise and sensor failures.

Multi-agent learning is a crucial method to control or find solutions for systems, in which more than one entity needs to be adaptive. In today's interconnected world, such systems are ubiquitous in many domains, including auctions in economics, swarm robotics in computer science, and politics in social sciences. Multi-agent learning is inherently more complex than single-agent learning and has a relatively thin theoretical framework supporting it. Recently, multi-agent learning dynamics have been linked to evolutionary game theory, allowing the interpretation of learning as an evolution of competing policies in the mind of the learning agents. The dynamical system from evolutionary game theory that has been linked to Q-learning predicts the expected behavior of the learning agents. Closer analysis however allows for two interesting observations: the predicted behavior is not always the same as the actual behavior, and in case of deviation, the predicted behavior is more desirable. This discrepancy is elucidated in this article, and based on these new insights Frequency Adjusted Q- (FAQ-) learning is proposed. This variation of Q-learning perfectly adheres to the predictions of the evolutionary model for an arbitrarily large part of the policy space. In addition to the theoretical discussion, experiments in the three classes of two-agent two-action games illustrate the superiority of FAQ-learning.

In this paper we develop a Bayesian policy search approach for Multi-Agent RL (MARL), which is model-free and allows for priors on policy parameters. We present a novel optimization algorithm based on hybrid MCMC, which leverages both the prior and gradient information estimated from trajectories. Our experiments demonstrate the automatic discovery of roles through reinforcement learning in a real-time strategy game.

Solving complex but structured problems in a decentralized manner via multiagent collaboration has received much attention in recent years. This is natural, as on one hand, multiagent systems usually possess a structure that determines the allowable interactions among the agents; and on the other hand, the single most pressing need in a cooperative multiagent system is to coordinate the local policies of autonomous agents with restricted capabilities to serve a system-wide goal. The presence of uncertainty makes this even more challenging, as the agents face the additional need to learn the unknown environment parameters while forming (and following) local policies in an online fashion. In this paper, we provide the first Bayesian reinforcement learning (BRL) approach for distributed coordination and learning in a cooperative multiagent system by devising two solutions to this type of problem. More specifically, we show how the Value of Perfect Information (VPI) can be used to perform efficient decentralised exploration in both model-based and model-free BRL, and in the latter case, provide a closed form solution for VPI, correcting a decade old result by Dearden, Friedman and Russell. To evaluate these solutions, we present experimental results comparing their relative merits, and demonstrate empirically that both solutions outperform an existing multiagent learning method, representative of the state-of-the-art.

Due to the non-stationary environment, learning in multi-agent systems is a challenging problem. This paper first introduces a new gradient-based learning algorithm, augmenting the basic gradient ascent approach with policy prediction. We prove that this augmentation results in a stronger notion of convergence than the basic gradient ascent, that is, strategies converge to a Nash equilibrium within a restricted class of iterated games. Motivated by this augmentation, we then propose a new practical multi-agent reinforcement learning (MARL) algorithm exploiting approximate policy prediction. Empirical results show that it converges faster and in a wider variety of situations than state-of-the-art MARL algorithms.

**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.

Q-learning is a very popular reinforcement learning algorithm being proven to converge to optimal policies in Markov decision processes. However, Q-learning shows artifacts if the optimal action is played with a low probability, a situation that may arise due to wrong initialization of Q-values or due to convergence to an almost pure policy after which a change in the environment makes another action optimal. These artifacts was resolved in literature by the variant Frequency Adjusted Q-learning (FAQL). However, FAQL also suffered from practical concerns that limited the policy subspace for which the behavior was improved. Here, we introduce the Repeated Update Q-learning (RUQL), a variant of Q-learning that resolves the undesirable artifacts of Q-learning without the practical concerns of FAQL. We show (both theoretically and experimentally) the similarities and differences between RUQL and FAQL (the closest state-of-the-art). Experimental results verify the theoretical insights and show how RUQL outperforms FAQL and QL in non-stationary environments.

The paper gives novel approach Multiagent Cooperative Reinforcement Learning by Expert Agents (MCRLEA) for dynamic decision making in the retail application. Furthermore, it put up different cooperation schemes for multiagent cooperative reinforcement learning i.e. EQ learning, EGroup, EDynamic, EGoal driven and Expert agents scheme. Implementation outcome includes a demonstration of recommended cooperation schemes that are competent enough to speedup the collection of agents that achieve excellent action policies. Accordingly this approach presents three retailer stores in the retail market place. Retailers can help to each other and can obtain profit from cooperation knowledge through learning their own strategies that just stand for their aims and benefit. The vendors are the knowledgeable agents in the hypothesis to employ cooperative learning to train in the circumstances. Assuming significant hypothesis on the vendor’s stock policy, restock period, arrival process of the consumers, the approach is formed as Markov decision process model that makes it possible to design learning algorithms. The proposed algorithms noticeably learn dynamic consumer performance. Moreover, the paper illustrates results of Cooperative Reinforcement Learning Algorithms of three shop agents for the period of one year sale duration and then demonstrated the results using proposed approach for three shop agents for the period of one year sale duration. The results obtained by the proposed expert agent based cooperation approach show that such methods can put into a quick convergence of agents in the dynamic environment.

Despite much research in recent years, newly created multiagent learning (MAL) algorithms continue to have one or more fatal weaknesses. These weaknesses include slow learning rates, failure to learn non-myopic solutions, and inability to scale up to domains with many actions, states, and associates. To overcome these weaknesses, we argue that fundamentally different approaches to MAL should be developed. One possibility is to develop methods that allow people to teach learning agents. To begin to determine the usefulness of this approach, we explore the effectiveness of learning by demonstration (LbD) in repeated stochastic games.