We introduce a system called Amorphous Fortress -- an abstract, yet spatial, open-ended artificial life simulation. In this environment, the agents are represented as finite-state machines (FSMs) which allow for multi-agent interaction within a constrained space. These agents are created by randomly generating and evolving the FSMs; sampling from pre-defined states and transitions. This environment was designed to explore the emergent AI behaviors found implicitly in simulation games such as Dwarf Fortress or The Sims. We apply the hill-climber evolutionary search algorithm to this environment to explore the various levels of depth and interaction from the generated FSMs.

Centralised training with decentralised execution (CT-DE) serves as the foundation of many leading multi-agent reinforcement learning (MARL) algorithms. Despite its popularity, it suffers from a critical drawback due to its reliance on learning from a single sample of the joint-action at a given state. As agents explore and update their policies during training, these single samples may poorly represent the actual joint-policy of the system of agents leading to high variance gradient estimates that hinder learning. To address this problem, we propose an enhancement tool that accommodates any actor-critic MARL method. Our framework, Performance Enhancing Reinforcement Learning Apparatus (PERLA), introduces a sampling technique of the agents' joint-policy into the critics while the agents train. This leads to TD updates that closely approximate the true expected value under the current joint-policy rather than estimates from a single sample of the joint-action at a given state. This produces low variance and precise estimates of expected returns, minimising the variance in the critic estimators which typically hinders learning. Moreover, as we demonstrate, by eliminating much of the critic variance from the single sampling of the joint policy, PERLA enables CT-DE methods to scale more efficiently with the number of agents. Theoretically, we prove that PERLA reduces variance in value estimates similar to that of decentralised training while maintaining the benefits of centralised training. Empirically, we demonstrate PERLA's superior performance and ability to reduce estimator variance in a range of benchmarks including Multi-agent Mujoco, and StarCraft II Multi-agent Challenge.

The emergent behavior of a distributed system is conditioned by the information available to the local decision-makers. Therefore, one may expect that providing decision-makers with more information will improve system performance; in this work, we find that this is not necessarily the case. In multi-agent maximum coverage problems, we find that even when agents' objectives are aligned with the global welfare, informing agents about the realization of the resource's random values can reduce equilibrium performance by a factor of 1/2. This affirms an important aspect of designing distributed systems: information need be shared carefully. We further this understanding by providing lower and upper bounds on the ratio of system welfare when information is (fully or partially) revealed and when it is not, termed the value-of-informing. We then identify a trade-off that emerges when optimizing the performance of the best-case and worst-case equilibrium.

In cooperative Multi-Agent Reinforcement Learning (MARL) agents are required to learn behaviours as a team to achieve a common goal. However, while learning a task, some agents may end up learning sub-optimal policies, not contributing to the objective of the team. Such agents are called lazy agents due to their non-cooperative behaviours that may arise from failing to understand whether they caused the rewards. As a consequence, we observe that the emergence of cooperative behaviours is not necessarily a byproduct of being able to solve a task as a team. In this paper, we investigate the applications of causality in MARL and how it can be applied in MARL to penalise these lazy agents. We observe that causality estimations can be used to improve the credit assignment to the agents and show how it can be leveraged to improve independent learning in MARL. Furthermore, we investigate how Amortized Causal Discovery can be used to automate causality detection within MARL environments. The results demonstrate that causality relations between individual observations and the team reward can be used to detect and punish lazy agents, making them develop more intelligent behaviours. This results in improvements not only in the overall performances of the team but also in their individual capabilities. In addition, results show that Amortized Causal Discovery can be used efficiently to find causal relations in MARL.

Cooperative multi-agent reinforcement learning (MARL) for navigation enables agents to cooperate to achieve their navigation goals. Using emergent communication, agents learn a communication protocol to coordinate and share information that is needed to achieve their navigation tasks. In emergent communication, symbols with no pre-specified usage rules are exchanged, in which the meaning and syntax emerge through training. Learning a navigation policy along with a communication protocol in a MARL environment is highly complex due to the huge state space to be explored. To cope with this complexity, this work proposes a novel neural network architecture, for jointly learning an adaptive state space abstraction and a communication protocol among agents participating in navigation tasks. The goal is to come up with an adaptive abstractor that significantly reduces the size of the state space to be explored, without degradation in the policy performance. Simulation results show that the proposed method reaches a better policy, in terms of achievable rewards, resulting in fewer training iterations compared to the case where raw states or fixed state abstraction are used. Moreover, it is shown that a communication protocol emerges during training which enables the agents to learn better policies within fewer training iterations.

In multi-agent reinforcement learning, the use of a global objective is a powerful tool for incentivising cooperation. Unfortunately, it is not sample-efficient to train individual agents with a global reward, because it does not necessarily correlate with an agent's individual actions. This problem can be solved by factorising the global value function into local value functions. Early work in this domain performed factorisation by conditioning local value functions purely on local information. Recently, it has been shown that providing both local information and an encoding of the global state can promote cooperative behaviour. In this paper we propose QGNN, the first value factorisation method to use a graph neural network (GNN) based model. The multi-layer message passing architecture of QGNN provides more representational complexity than models in prior work, allowing it to produce a more effective factorisation. QGNN also introduces a permutation invariant mixer which is able to match the performance of other methods, even with significantly fewer parameters. We evaluate our method against several baselines, including QMIX-Att, GraphMIX, QMIX, VDN, and hybrid architectures. Our experiments include Starcraft, the standard benchmark for credit assignment; Estimate Game, a custom environment that explicitly models inter-agent dependencies; and Coalition Structure Generation, a foundational problem with real-world applications. The results show that QGNN outperforms state-of-the-art value factorisation baselines consistently.

Before taking actions in an environment with more than one intelligent agent, an autonomous agent may benefit from reasoning about the other agents and utilizing a notion of a guarantee or confidence about the behavior of the system. In this article, we propose a novel multi-agent reinforcement learning (MARL) algorithm CAMMARL, which involves modeling the actions of other agents in different situations in the form of confident sets, i.e., sets containing their true actions with a high probability. We then use these estimates to inform an agent's decision-making. For estimating such sets, we use the concept of conformal predictions, by means of which, we not only obtain an estimate of the most probable outcome but get to quantify the operable uncertainty as well. For instance, we can predict a set that provably covers the true predictions with high probabilities (e.g., 95%). Through several experiments in two fully cooperative multi-agent tasks, we show that CAMMARL elevates the capabilities of an autonomous agent in MARL by modeling conformal prediction sets over the behavior of other agents in the environment and utilizing such estimates to enhance its policy learning. All developed codes can be found here: https://github.com/Nikunj-Gupta/conformal-agent-modelling.

As a unifying concept in economics, game theory, and operations research, even in the Robotics and AI field, the utility is used to evaluate the level of individual needs, preferences, and interests. Especially for decision-making and learning in multi-agent/robot systems (MAS/MRS), a suitable utility model can guide agents in choosing reasonable strategies to achieve their current needs and learning to cooperate and organize their behaviors, optimizing the system's utility, building stable and reliable relationships, and guaranteeing each group member's sustainable development, similar to the human society. Although these systems' complex, large-scale, and long-term behaviors are strongly determined by the fundamental characteristics of the underlying relationships, there has been less discussion on the theoretical aspects of mechanisms and the fields of applications in Robotics and AI. This paper introduces a utility-orient needs paradigm to describe and evaluate inter and outer relationships among agents' interactions. Then, we survey existing literature in relevant fields to support it and propose several promising research directions along with some open problems deemed necessary for further investigations.

This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the problem of classifying a stream of unlabeled data in a distributed manner. We consider two kinds of classification tasks with limited observations in the prediction phase, namely, the statistical classification task and the single-sample classification task. For each task, we describe the distributed learning rule and analyze the probability of error accordingly. To do so, we first introduce a stronger consistent training condition that involves the margin distributions generated by the trained classifiers. Based on this condition, we derive an upper bound on the probability of error for both tasks, which depends on the statistical properties of the data and the combination policy used to combine the distributed classifiers. For the statistical classification problem, we employ the geometric social learning rule and conduct a non-asymptotic performance analysis. An exponential decay of the probability of error with respect to the number of unlabeled samples is observed in the upper bound. For the single-sample classification task, a distributed learning rule that functions as an ensemble classifier is constructed. An upper bound on the probability of error of this ensemble classifier is established.

The majority of Multi-Agent Reinforcement Learning (MARL) literature equates the cooperation of self-interested agents in mixed environments to the problem of social welfare maximization, allowing agents to arbitrarily share rewards and private information. This results in agents that forgo their individual goals in favour of social good, which can potentially be exploited by selfish defectors. We argue that cooperation also requires agents' identities and boundaries to be respected by making sure that the emergent behaviour is an equilibrium, i.e., a convention that no agent can deviate from and receive higher individual payoffs. Inspired by advances in mechanism design, we propose to solve the problem of cooperation, defined as finding socially beneficial equilibrium, by using mediators. A mediator is a benevolent entity that may act on behalf of agents, but only for the agents that agree to it. We show how a mediator can be trained alongside agents with policy gradient to maximize social welfare subject to constraints that encourage agents to cooperate through the mediator. Our experiments in matrix and iterative games highlight the potential power of applying mediators in MARL.