Many real-world multi-agent reinforcement learning applications require agents to communicate, assisted by a communication protocol. These applications face a common and critical issue of communication's limited bandwidth that constrains agents' ability to cooperate successfully. In this paper, rather than proposing a fixed communication protocol, we develop an Informative Multi-Agent Communication (IMAC) method to learn efficient communication protocols. Our contributions are threefold. First, we notice a fact that a limited bandwidth translates into a constraint on the communicated message entropy, thus paving the way of controlling the bandwidth. Second, we introduce a customized batch-norm layer, which controls the messages' entropy to simulate the limited bandwidth constraint. Third, we apply the information bottleneck method to discover the optimal communication protocol, which can satisfy a bandwidth constraint via training with the prior distribution in the method. To demonstrate the efficacy of our method, we conduct extensive experiments in various cooperative and competitive multi-agent tasks across two dimensions: the number of agents and different bandwidths. We show that IMAC converges fast, and leads to efficient communication among agents under the limited-bandwidth constraint as compared to many baseline methods.

This paper investigates the convergence of learning dynamics in Stackelberg games. In the class of games we consider, there is a hierarchical game being played between a leader and a follower with continuous action spaces. We establish a number of connections between the Nash and Stackelberg equilibrium concepts and characterize conditions under which attracting critical points of simultaneous gradient descent are Stackelberg equilibria in zero-sum games. Moreover, we show that the only stable critical points of the Stackelberg gradient dynamics are Stackelberg equilibria in zero-sum games. Using this insight, we develop a gradient-based update for the leader while the follower employs a best response strategy for which each stable critical point is guaranteed to be a Stackelberg equilibrium in zero-sum games. As a result, the learning rule provably converges to a Stackelberg equilibria given an initialization in the region of attraction of a stable critical point. We then consider a follower employing a gradient-play update rule instead of a best response strategy and propose a two-timescale algorithm with similar asymptotic convergence guarantees. For this algorithm, we also provide finite-time high probability bounds for local convergence to a neighborhood of a stable Stackelberg equilibrium in general-sum games. Finally, we present extensive numerical results that validate our theory, provide insights into the optimization landscape of generative adversarial networks, and demonstrate that the learning dynamics we propose can effectively train generative adversarial networks.

The idea of experience sharing between cooperative agents naturally emerges from our understanding of how humans learn. Our evolution as a species is tightly linked to the ability to exchange learned knowledge with one another. It follows that experience sharing (ES) between autonomous and independent agents could become the key to accelerate learning in cooperative multiagent settings. We investigate if randomly selecting experiences to share can increase the performance of deep reinforcement learning agents, and propose three new methods for selecting experiences to accelerate the learning process. Firstly, we introduce Focused ES, which prioritizes unexplored regions of the state space. Secondly, we present Prioritized ES, in which temporal-difference error is used as a measure of priority. Finally, we devise Focused Prioritized ES, which combines both previous approaches. The methods are empirically validated in a control problem. While sharing randomly selected experiences between two Deep Q-Network agents shows no improvement over a single agent baseline, we show that the proposed ES methods can successfully outperform the baseline. In particular, the Focused ES accelerates learning by a factor of 2, reducing by 51% the number of episodes required to complete the task.

The goal of coordinated multi-robot exploration tasks is to employ a team of autonomous robots to explore an unknown environment as quickly as possible. Compared with human-designed methods, which began with heuristic and rule-based approaches, learning-based methods enable individual robots to learn sophisticated and hard-to-design cooperation strategies through deep reinforcement learning technologies. However, in decentralized multi-robot exploration tasks, learning-based algorithms are still far from being universally applicable to the continuous space due to the difficulties associated with area calculation and reward function designing; moreover, existing learning-based methods encounter problems when attempting to balance the historical trajectory issue and target area conflict problem. Furthermore, the scalability of these methods to a large number of agents is poor because of the exponential explosion problem of state space. Accordingly, this paper proposes a novel approach - Multi-head Attention-based Multi-robot Exploration in Continuous Space (MAMECS) - aimed at reducing the state space and automatically learning the cooperation strategies required for decentralized multi-robot exploration tasks in continuous space. Computational geometry knowledge is applied to describe the environment in continuous space and to design an improved reward function to ensure a superior exploration rate. Moreover, the multi-head attention mechanism employed helps to solve the historical trajectory issue in the decentralized multi-robot exploration task, as well as to reduce the quadratic increase of action space.

Making decisions in the presence of a strategic opponent requires one to take into account the opponent's ability to actively mask its intended objective. To describe such strategic situations, we introduce the non-cooperative inverse reinforcement learning (N-CIRL) formalism. The N-CIRL formalism consists of two agents with completely misaligned objectives, where only one of the agents knows the true objective function. Formally, we model the N-CIRL formalism as a zero-sum Markov game with one-sided incomplete information. Through interacting with the more informed player, the less informed player attempts to both infer, and act according to, the true objective function. As a result of the one-sided incomplete information, the multi-stage game can be decomposed into a sequence of single-stage games expressed by a recursive formula. Solving this recursive formula yields the value of the N-CIRL game and the more informed player's equilibrium strategy. Another recursive formula, constructed by forming an auxiliary game, termed the dual game, yields the less informed player's strategy. Building upon these two recursive formulas, we develop a computationally tractable algorithm to approximately solve for the equilibrium strategies. Finally, we demonstrate the benefits of our N-CIRL formalism over the existing multi-agent IRL formalism via extensive numerical simulation in a novel cyber security setting.

W e present an approach to generating natural language justifications of decisions derived from norm-based reasoning. Assuming an agent which maximally satisfies a set of rules specified in an object-oriented temporal logic, the user can ask factual questions (about the agent's rules, actions, and the extent to which the agent violated the rules) as well as "why" questions that require the agent comparing actual behavior to counterfactual trajectories with respect to these rules. To produce natural-sounding explanations, we focus on the subproblem of producing natural language clauses from statements in a fragment of temporal logic, and then describe how to embed these clauses into explanatory sentences. W e use a human judgment evaluation on a testbed task to compare our approach to variants in terms of intelligibility, mental model and perceived trust.

Single-agent deep reinforcement learning has achieved impressive performance in many domains, including playing Go [1, 2] and Atari games [3, 4]. However, many real world problems, such as traffic congestion reduction [5, 6], antenna tilt control [7], and dynamic resource allocation [8] are more naturally modeled as multi-agent systems. Unfortunately, directly deploying single-agent reinforcement learning to each agent in a multi-agent system does not result in satisfying performance [9, 10]. Particularly, in multi-agent reinforcement learning [8, 10-19], estimating the value function is challenging, because the environment is non-stationary from the perspective of an individual agent [10, 11]. To alleviate the issue, recently, multi-agent deep deterministic policy gradient (MADDPG) [10] proposed a centralized critic whose input is the concatenation of all agents' observations and actions.

A shield is attached to a system to guarantee safety by correcting the system's behavior at runtime. Existing methods that employ design-time synthesis of shields do not scale to multi-agent systems. Moreover, such shields are typically implemented in a centralized manner, requiring global information on the state of all agents in the system. We address these limitations through a new approach where the shields are synthesized at runtime and do not require global information. There is a shield onboard every agent, which can only modify the behavior of the corresponding agent. In this approach, which is fundamentally decentralized, the shield on every agent has two components: a pathfinder that corrects the behavior of the agent and an ordering mechanism that dynamically modifies the priority of the agent. The current priority determines if the shield uses the pathfinder to modify behavior of the agent. We derive an upper bound on the maximum deviation for any agent from its original behavior. We prove that the worst-case synthesis time is quadratic in the number of agents at runtime as opposed to exponential at design-time for existing methods. We test the performance of the decentralized, runtime shield synthesis approach on a collision-avoidance problem. For 50 agents in a 50x50 grid, the synthesis at runtime requires a few seconds per agent whenever a potential collision is detected. In contrast, the centralized design-time synthesis of shields for a similar setting is intractable beyond 4 agents in a 5x5 grid.

Deep reinforcement learning (DRL) is a booming area of artificial intelligence. Many practical applications of DRL naturally involve more than one collaborative learners, making it important to study DRL in a multi-agent context. Previous research showed that effective learning in complex multi-agent systems demands for highly coordinated environment exploration among all the participating agents. Many researchers attempted to cope with this challenge through learning centralized value functions. However, the common strategy for every agent to learn their local policies directly often fail to nurture strong inter-agent collaboration and can be sample inefficient whenever agents alter their communication channels. To address these issues, we propose a new framework known as centralized training and exploration with decentralized execution via policy distillation. Guided by this framework and the maximum-entropy learning technique, we will first train agents' policies with shared global component to foster coordinated and effective learning. Locally executable policies will be derived subsequently from the trained global policies via policy distillation. Experiments show that our new framework and algorithm can achieve significantly better performance and higher sample efficiency than a cutting-edge baseline on several multi-agent DRL benchmarks.

In a multi-agent system, an agent's optimal policy will typically depend on the policies chosen by others. Therefore, a key issue in multi-agent systems research is that of predicting the behaviours of others, and responding promptly to changes in such behaviours. One obvious possibility is for each agent to broadcast their current intention, for example, the currently executed option in a hierarchical reinforcement learning framework. However, this approach results in inflexibility of agents if options have an extended duration and are dynamic. While adjusting the executed option at each step improves flexibility from a single-agent perspective, frequent changes in options can induce inconsistency between an agent's actual behaviour and its broadcast intention. In order to balance flexibility and predictability, we propose a dynamic termination Bellman equation that allows the agents to flexibly terminate their options. We evaluate our model empirically on a set of multi-agent pursuit and taxi tasks, and show that our agents learn to adapt flexibly across scenarios that require different termination behaviours.