When has an agent converged? Standard models of the reinforcement learning problem give rise to a straightforward definition of convergence: An agent converges when its behavior or performance in each environment state stops changing. However, as we shift the focus of our learning problem from the environment's state to the agent's state, the concept of an agent's convergence becomes significantly less clear. In this paper, we propose two complementary accounts of agent convergence in a framing of the reinforcement learning problem that centers around bounded agents. The first view says that a bounded agent has converged when the minimal number of states needed to describe the agent's future behavior cannot decrease. The second view says that a bounded agent has converged just when the agent's performance only changes if the agent's internal state changes. We establish basic properties of these two definitions, show that they accommodate typical views of convergence in standard settings, and prove several facts about their nature and relationship. We take these perspectives, definitions, and analysis to bring clarity to a central idea of the field.

This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on the agent's current state and an estimate of the macroscopic population state, given by a weighted average of the neighboring states. When the number of agents is large and the network is a complete graph (has all-to-all information access), the macroscopic behavior of the population can be well-approximated by a set of deterministic differential equations called a {\it mean-field approximation}. For incomplete networks such characterizations remained previously unclear, i.e., in general whether a suitable mean-field approximation exists for the macroscopic behavior of the population. The paper addresses this gap by establishing a generic theory describing when various mean-field approximations are accurate for \emph{arbitrary} interaction structures. Our results are threefold. Letting $W$ be the matrix describing agent interactions, we first show that a simple mean-field approximation that incorrectly assumes a homogeneous interaction structure is accurate provided $W$ has a large spectral gap. Second, we show that a more complex mean-field approximation which takes into account agent interactions is accurate as long as the Frobenius norm of $W$ is small. Finally, we compare the predictions of the two mean-field approximations through simulations, highlighting cases where using mean-field approximations that assume a homogeneous interaction structure can lead to inaccurate qualitative and quantitative predictions.

To improve the performance of multi-agent reinforcement learning under the constraint of wireless resources, we propose a message importance metric and design an importance-aware scheduling policy to effectively exchange messages. The key insight is spending the precious communication resources on important messages. The message importance depends not only on the messages themselves, but also on the needs of agents who receive them. Accordingly, we propose a query-message-based architecture, called QMNet. Agents generate queries and messages with the environment observation. Sharing queries can help calculate message importance. Exchanging messages can help agents cooperate better. Besides, we exploit the message importance to deal with random access collisions in decentralized systems. Furthermore, a message prediction mechanism is proposed to compensate for messages that are not transmitted. Finally, we evaluate the proposed schemes in a traffic junction environment, where only a fraction of agents can send messages due to limited wireless resources. Results show that QMNet can extract valuable information to guarantee the system performance even when only $30\%$ of agents can share messages. By exploiting message prediction, the system can further save $40\%$ of wireless resources. The importance-aware decentralized multi-access mechanism can effectively avoid collisions, achieving almost the same performance as centralized scheduling.

Robot swarms often exhibit emergent behaviors that are fascinating to observe; however, it is often difficult to predict what swarm behaviors can emerge under a given set of agent capabilities. We seek to efficiently leverage human input to automatically discover a taxonomy of collective behaviors that can emerge from a particular multi-agent system, without requiring the human to know beforehand what behaviors are interesting or even possible. Our proposed approach adapts to user preferences by learning a similarity space over swarm collective behaviors using self-supervised learning and human-in-the-loop queries. We combine our learned similarity metric with novelty search and clustering to explore and categorize the space of possible swarm behaviors. We also propose several general-purpose heuristics that improve the efficiency of our novelty search by prioritizing robot controllers that are likely to lead to interesting emergent behaviors. We test our approach in simulation on two robot capability models and show that our methods consistently discover a richer set of emergent behaviors than prior work. Code, videos, and datasets are available at https://sites.google.com/view/evolving-novel-swarms.

We consider a cooperative multi-agent system consisting of a team of agents with decentralized information. Our focus is on the design of symmetric (i.e. identical) strategies for the agents in order to optimize a finite horizon team objective. We start with a general information structure and then consider some special cases. The constraint of using symmetric strategies introduces new features and complications in the team problem. For example, we show in a simple example that randomized symmetric strategies may outperform deterministic symmetric strategies. We also discuss why some of the known approaches for reducing agents' private information in teams may not work under the constraint of symmetric strategies. We then adopt the common information approach for our problem and modify it to accommodate the use of symmetric strategies. This results in a common information based dynamic program where each step involves minimization over a single function from the space of an agent's private information to the space of probability distributions over actions. We present specialized models where private information can be reduced using simple dynamic program based arguments.

Efficient exploration is critical in cooperative deep Multi-Agent Reinforcement Learning (MARL). In this work, we propose an exploration method that effectively encourages cooperative exploration based on the idea of sequential action-computation scheme. The high-level intuition is that to perform optimism-based exploration, agents would explore cooperative strategies if each agent's optimism estimate captures a structured dependency relationship with other agents. Assuming agents compute actions following a sequential order at \textit{each environment timestep}, we provide a perspective to view MARL as tree search iterations by considering agents as nodes at different depths of the search tree. Inspired by the theoretically justified tree search algorithm UCT (Upper Confidence bounds applied to Trees), we develop a method called Conditionally Optimistic Exploration (COE). COE augments each agent's state-action value estimate with an action-conditioned optimistic bonus derived from the visitation count of the global state and joint actions of preceding agents. COE is performed during training and disabled at deployment, making it compatible with any value decomposition method for centralized training with decentralized execution. Experiments across various cooperative MARL benchmarks show that COE outperforms current state-of-the-art exploration methods on hard-exploration tasks.

In the intrinsically motivated skills acquisition problem, the agent is set in an environment without any pre-defined goals and needs to acquire an open-ended repertoire of skills. To do so the agent needs to be autotelic (deriving from the Greek auto (self) and telos (end goal)): it needs to generate goals and learn to achieve them following its own intrinsic motivation rather than external supervision. Autotelic agents have so far been considered in isolation. But many applications of open-ended learning entail groups of agents. Multi-agent environments pose an additional challenge for autotelic agents: to discover and master goals that require cooperation agents must pursue them simultaneously, but they have low chances of doing so if they sample them independently. In this work, we propose a new learning paradigm for modeling such settings, the Decentralized Intrinsically Motivated Skills Acquisition Problem (Dec-IMSAP), and employ it to solve cooperative navigation tasks. First, we show that agents setting their goals independently fail to master the full diversity of goals. Then, we show that a sufficient condition for achieving this is to ensure that a group aligns its goals, i.e., the agents pursue the same cooperative goal. Our empirical analysis shows that alignment enables specialization, an efficient strategy for cooperation. Finally, we introduce the Goal-coordination game, a fully-decentralized emergent communication algorithm, where goal alignment emerges from the maximization of individual rewards in multi-goal cooperative environments and show that it is able to reach equal performance to a centralized training baseline that guarantees aligned goals. To our knowledge, this is the first contribution addressing the problem of intrinsically motivated multi-agent goal exploration in a decentralized training paradigm.

We study a fair resource sharing problem, where a set of resources are to be shared among a group of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, who share the same resource with them. Clearly, the strong notion of envy-freeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even deciding the existence of such a strongly envy-free assignment is an intractable problem. Hence, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envyfreeness, can be achieved. Under this relaxed notion, an agent envies another only when they envy both the resource and the mates of the other agent. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dormmates. We show that when the capacity of each dorm is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment. Nevertheless, the result breaks immediately when the capacity increases to 3, in which case even Pareto envyfreeness cannot be guaranteed. In addition to the existential results, we also investigate the utility guarantees of (Pareto) envy-free assignments in our model.

Time is a crucial factor in modelling dynamic behaviours of intelligent agents: activities have a determined temporal duration in a real-world environment, and previous actions influence agents' behaviour. In this paper, we propose a language for modelling concurrent interaction between agents that also allows the specification of temporal intervals in which particular actions occur. Such a language exploits a timed version of Abstract Argumentation Frameworks to realise a shared memory used by the agents to communicate and reason on the acceptability of their beliefs with respect to a given time interval. An interleaving model on a single processor is used for basic computation steps, with maximum parallelism for time elapsing. Following this approach, only one of the enabled agents is executed at each moment. To demonstrate the capabilities of language, we also show how it can be used to model interactions such as debates and dialogue games taking place between intelligent agents. Lastly, we present an implementation of the language that can be accessed via a web interface. Under consideration in Theory and Practice of Logic Programming (TPLP).

Order execution is a fundamental task in quantitative finance, aiming at finishing acquisition or liquidation for a number of trading orders of the specific assets. Recent advance in model-free reinforcement learning (RL) provides a data-driven solution to the order execution problem. However, the existing works always optimize execution for an individual order, overlooking the practice that multiple orders are specified to execute simultaneously, resulting in suboptimality and bias. In this paper, we first present a multi-agent RL (MARL) method for multi-order execution considering practical constraints. Specifically, we treat every agent as an individual operator to trade one specific order, while keeping communicating with each other and collaborating for maximizing the overall profits. Nevertheless, the existing MARL algorithms often incorporate communication among agents by exchanging only the information of their partial observations, which is inefficient in complicated financial market. To improve collaboration, we then propose a learnable multi-round communication protocol, for the agents communicating the intended actions with each other and refining accordingly. It is optimized through a novel action value attribution method which is provably consistent with the original learning objective yet more efficient. The experiments on the data from two real-world markets have illustrated superior performance with significantly better collaboration effectiveness achieved by our method.