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We consider an Anonymous Multi-Agent Path-Finding (AMAPF) problem where the set of agents is confined to a graph, a set of goal vertices is given and each of these vertices has to be reached by some agent. The problem is to find an assignment of the goals to the agents as well as the collision-free paths, and we are interested in finding the solution with the optimal makespan. A well-established approach to solve this problem is to reduce it to a special type of a graph search problem, i.e. to the problem of finding a maximum flow on an auxiliary graph induced by the input one. The size of the former graph may be very large and the search on it may become a bottleneck. To this end, we suggest a specific search algorithm that leverages the idea of exploring the search space not through considering separate search states but rather bulks of them simultaneously. That is, we implicitly compress, store and expand bulks of the search states as single states, which results in high reduction in runtime and memory. Empirically, the resultant AMAPF solver demonstrates superior performance compared to the state-of-the-art competitor and is able to solve all publicly available MAPF instances from the well-known MovingAI benchmark in less than 30 seconds.
While decentralized training is attractive in multi-agent reinforcement learning (MARL) for its excellent scalability and robustness, its inherent coordination challenges in collaborative tasks result in numerous interactions for agents to learn good policies. To alleviate this problem, action advising methods make experienced agents share their knowledge about what to do, while less experienced agents strictly follow the received advice. However, this method of sharing and utilizing knowledge may hinder the team's exploration of better states, as agents can be unduly influenced by suboptimal or even adverse advice, especially in the early stages of learning. Inspired by the fact that humans can learn not only from the success but also from the failure of others, this paper proposes a novel knowledge sharing framework called Cautiously-Optimistic kNowledge Sharing (CONS). CONS enables each agent to share both positive and negative knowledge and cautiously assimilate knowledge from others, thereby enhancing the efficiency of early-stage exploration and the agents' robustness to adverse advice. Moreover, considering the continuous improvement of policies, agents value negative knowledge more in the early stages of learning and shift their focus to positive knowledge in the later stages. Our framework can be easily integrated into existing Q-learning based methods without introducing additional training costs. We evaluate CONS in several challenging multi-agent tasks and find it excels in environments where optimal behavioral patterns are difficult to discover, surpassing the baselines in terms of convergence rate and final performance.
Strategies synthesized using formal methods can be complex and often require infinite memory, which does not correspond to the expected behavior when trying to model Multi-Agent Systems (MAS). To capture such behaviors, natural strategies are a recently proposed framework striking a balance between the ability of agents to strategize with memory and the complexity of the model-checking problem, but until now has been restricted to fully deterministic settings. For the first time, we consider the probabilistic temporal logics PATL and PATL∗ under natural strategies (NatPATL and NatPATL∗). As main result we show that, in stochastic MAS, NatPATL model-checking is NP-complete when the active coalition is restricted to deterministic strategies. We also give a 2NEXPTIME complexity result for NatPATL∗ with the same restriction. In the unrestricted case, we give an EXPSPACE complexity for NatPATL and 3EXPSPACE complexity for NatPATL*.
Alternating-time temporal logic (ATL*) is a well-established framework for formal reasoning about multi-agent systems. However, while ATL* can reason about the strategic ability of agents (e.g., some coalition A can ensure that a goal is reached eventually), we cannot compare multiple strategic interactions, nor can we require multiple agents to follow the same strategy. For example, we cannot state that coalition A can reach a goal sooner (or more often) than some other coalition A'. In this paper, we propose HyperATL*_S, an extension of ATL* in which we can (1) compare the outcome of multiple strategic interactions w.r.t. a hyperproperty, i.e., a property that refers to multiple paths at the same time, and (2) enforce that some agents share the same strategy. We show that HyperATL*_S is a rich specification language that captures important AI-related properties that were out of reach of existing logics. We prove that model checking of HyperATL*_S on concurrent game structures is decidable. We implement our model-checking algorithm in a tool we call HyMASMC and evaluate it on a range of benchmarks.
Communication is crucial for solving cooperative Multi-Agent Reinforcement Learning tasks in partially observable Markov Decision Processes. Existing works often rely on black-box methods to encode local information/features into messages shared with other agents, leading to the generation of continuous messages with high communication overhead and poor interpretability. Prior attempts at discrete communication methods generate one-hot vectors trained as part of agents' actions and use the Gumbel softmax operation for calculating message gradients, which are all heuristic designs that do not provide any quantitative guarantees on the expected return. This paper establishes an upper bound on the return gap between an ideal policy with full observability and an optimal partially observable policy with discrete communication. This result enables us to recast multi-agent communication into a novel online clustering problem over the local observations at each agent, with messages as cluster labels and the upper bound on the return gap as clustering loss. To minimize the return gap, we propose the Return-Gap-Minimization Communication (RGMComm) algorithm, which is a surprisingly simple design of discrete message generation functions and is integrated with reinforcement learning through the utilization of a novel Regularized Information Maximization loss function, which incorporates cosine-distance as the clustering metric. Evaluations show that RGMComm significantly outperforms state-of-the-art multi-agent communication baselines and can achieve nearly optimal returns with few-bit messages that are naturally interpretable.
Centralized Training with Decentralized Execution (CTDE) has been proven to be an effective paradigm in cooperative multi-agent reinforcement learning (MARL). One of the major challenges is credit assignment, which aims to credit agents by their contributions. They lack the functionality to model complicated relations of the delayed global reward in the temporal dimension and suffer from inefficiencies. To tackle this, we introduce Spatial-Temporal Attention with Shapley (STAS), a novel method that learns credit assignment in both temporal and spatial dimensions. It first decomposes the global return back to each time step, then utilizes the Shapley Value to redistribute the individual payoff from the decomposed global reward. To mitigate the computational complexity of the Shapley Value, we introduce an approximation of marginal contribution and utilize Monte Carlo sampling to estimate it. We evaluate our method on an Alice & Bob example and MPE environments across different scenarios. Our results demonstrate that our method effectively assigns spatial-temporal credit, outperforming all state-of-the-art baselines.
Efficient communication learning among agents has been shown crucial for cooperative multi-agent reinforcement learning (MARL), as it can promote the action coordination of agents and ultimately improve performance. Graph neural network (GNN) provide a general paradigm for communication learning, which consider agents and communication channels as nodes and edges in a graph, with the action selection corresponding to node labeling. Under such paradigm, an agent aggregates information from neighbor agents, which can reduce uncertainty in local decision-making and induce implicit action coordination. However, this communication paradigm is vulnerable to adversarial attacks and noise, and how to learn robust and efficient communication under perturbations has largely not been studied. To this end, this paper introduces a novel Multi-Agent communication mechanism via Graph Information bottleneck (MAGI), which can optimally balance the robustness and expressiveness of the message representation learned by agents. This communication mechanism is aim at learning the minimal sufficient message representation for an agent by maximizing the mutual information (MI) between the message representation and the selected action, and simultaneously constraining the MI between the message representation and the agent feature. Empirical results demonstrate that MAGI is more robust and efficient than state-of-the-art GNN-based MARL methods.
Information sharing through communication is essential for tackling complex multi-agent reinforcement learning tasks. Many existing multi-agent communication protocols can be viewed as instances of message passing graph neural networks (GNNs). However, due to the significantly limited expressive ability of the standard GNN method, the agent feature representations remain similar and indistinguishable even though the agents have different neighborhood structures. This further results in the homogenization of agent behaviors and reduces the capability to solve tasks effectively. In this paper, we propose a multi-agent communication protocol via identity-aware learning (IDEAL), which explicitly enhances the distinguishability of agent feature representations to break the diversity bottleneck. Specifically, IDEAL extends existing multi-agent communication protocols by inductively considering the agents' identities during the message passing process. To obtain expressive feature representations for a given agent, IDEAL first extracts the ego network centered around that agent and then performs multiple rounds of heterogeneous message passing, where different parameter sets are applied to the central agent and the other surrounding agents within the ego network. IDEAL fosters expressive communication between agents and generates distinguishable feature representations, which promotes action diversity and individuality emergence. Experimental results on various benchmarks demonstrate IDEAL can be flexibly integrated into various multi-agent communication methods and enhances the corresponding performance.
Learning to collaborate has witnessed significant progress in multi-agent reinforcement learning (MARL). However, promoting coordination among agents and enhancing exploration capabilities remain challenges. In multi-agent environments, interactions between agents are limited in specific situations. Effective collaboration between agents thus requires a nuanced understanding of when and how agents' actions influence others.To this end, in this paper, we propose a novel MARL algorithm named Situation-Dependent Causal Influence-Based Cooperative Multi-agent Reinforcement Learning (SCIC), which incorporates a novel Intrinsic reward mechanism based on a new cooperation criterion measured by situation-dependent causal influence among agents.Our approach aims to detect inter-agent causal influences in specific situations based on the criterion using causal intervention and conditional mutual information. This effectively assists agents in exploring states that can positively impact other agents, thus promoting cooperation between agents.The resulting update links coordinated exploration and intrinsic reward distribution, which enhance overall collaboration and performance.Experimental results on various MARL benchmarks demonstrate the superiority of our method compared to state-of-the-art approaches.
The study of emergent communication has been dedicated to interactive artificial intelligence. While existing work focuses on communication about single objects or complex image scenes, we argue that communicating relationships between multiple objects is important in more realistic tasks, but understudied. In this paper, we try to fill this gap and focus on emergent communication about positional relationships between two objects. We train agents in the referential game where observations contain two objects, and find that generalization is the major problem when the positional relationship is involved. The key factor affecting the generalization ability of the emergent language is the input variation between Speaker and Listener, which is realized by a random image generator in our work. Further, we find that the learned language can generalize well in a new multi-step MDP task where the positional relationship describes the goal, and performs better than raw-pixel images as well as pre-trained image features, verifying the strong generalization ability of discrete sequences. We also show that language transfer from the referential game performs better in the new task than learning language directly in this task, implying the potential benefits of pre-training in referential games. All in all, our experiments demonstrate the viability and merit of having agents learn to communicate positional relationships between multiple objects through emergent communication.
In the Multiagent Path Finding (MAPF for short) problem, we focus on efficiently finding non-colliding paths for a set of k agents on a given graph G, where each agent seeks a path from its source vertex to a target. An important measure of the quality of the solution is the length of the proposed schedule l, that is, the length of a longest path (including the waiting time). In this work, we propose a systematic study under the parameterized complexity framework. The hardness results we provide align with many heuristics used for this problem, whose running time could potentially be improved based on our Fixed-Parameter Tractability (FPT) results. We show that MAPF is W[1]-hard with respect to k (even if k is combined with the maximum degree of the input graph). The problem remains NP-hard in planar graphs even if the maximum degree and the makespan l are fixed constants. On the positive side, we show an FPT algorithm for k+l. As we continue, the structure of G comes into play. We give an FPT algorithm for parameter k plus the diameter of the graph G. The MAPF problem is W[1]-hard for cliquewidth of G plus l while it is FPT for treewidth of G plus l.
Information diffusion models on networks are at the forefront of AI research. The dynamics of such models typically follow stochastic models from epidemiology, used to model not only infections but various phenomena, including the behavior of computer viruses and viral marketing campaigns. A core question in this setting is how to efficiently detect the most influential vertices in the host graph such that the infection survives the longest. In processes that incorporate re-infection of the vertices, such as the SIS process, theoretical studies identify parameter thresholds where the survival time of the process rapidly transitions from logarithmic to super-polynomial. These results contradict the intuition that the starting configuration is relevant, since the process will always either die out fast or survive almost indefinitely. A shortcoming of these results is that models incorporating short-term immunity (or creative advertisement fatigue) have not been subjected to such a theoretical analysis so far. We reduce this gap in the literature by studying the SIRS process, a more realistic model, which besides re-infection additionally incorporates short-term immunity. On complex network models, we identify parameter regimes for which the process survives exponentially long, and we get a tight threshold for random graphs. Underlying these results is our main technical contribution, showing a threshold behavior for the survival time of the SIRS process on graphs with large expander subgraphs, such as social network models.
Learning in games considers how multiple agents maximize their own rewards through repeated games. Memory, an ability that an agent changes his/her action depending on the history of actions in previous games, is often introduced into learning to explore more clever strategies and discuss the decision-making of real agents like humans. However, such games with memory are hard to analyze because they exhibit complex phenomena like chaotic dynamics or divergence from Nash equilibrium. In particular, how asymmetry in memory capacities between agents affects learning in games is still unclear. In response, this study formulates a gradient ascent algorithm in games with asymmetry memory capacities. To obtain theoretical insights into learning dynamics, we first consider a simple case of zero-sum games. We observe complex behavior, where learning dynamics draw a heteroclinic connection from unstable fixed points to stable ones. Despite this complexity, we analyze learning dynamics and prove local convergence to these stable fixed points, i.e., the Nash equilibria. We identify the mechanism driving this convergence: an agent with a longer memory learns to exploit the other, which in turn endows the other's utility function with strict concavity. We further numerically observe such convergence in various initial strategies, action numbers, and memory lengths. This study reveals a novel phenomenon due to memory asymmetry, providing fundamental strides in learning in games and new insights into computing equilibria.
In centralized multi-agent systems, often modeled as multi-agent partially observable Markov decision processes (MPOMDPs), the action and observation spaces grow exponentially with the number of agents, making the value and belief estimation of single-agent online planning ineffective. Prior work partially tackles value estimation by exploiting the inherent structure of multi-agent settings via so-called coordination graphs. Additionally, belief estimation methods have been improved by incorporating the likelihood of observations into the approximation. However, the challenges of value estimation and belief estimation have only been tackled individually, which prevents existing methods from scaling to settings with many agents. Therefore, we address these challenges simultaneously. First, we introduce weighted particle filtering to a sample-based online planner for MPOMDPs. Second, we present a scalable approximation of the belief. Third, we bring an approach that exploits the typical locality of agent interactions to novel online planning algorithms for MPOMDPs operating on a so-called sparse particle filter tree. Our experimental evaluation against several state-of-the-art baselines shows that our methods (1) are competitive in settings with only a few agents and (2) improve over the baselines in the presence of many agents.
Given a specification of Linear-time Temporal Logic interpreted over finite traces (LTLf), the reactive synthesis problem asks to find a finitely-representable, terminating controller that reacts to the uncontrollable actions of an environment in order to enforce a desired system specification. In this paper we study, for the first time, the foundations of reactive synthesis for DECLARE, a well-established declarative, pattern-based business process modelling language grounded in LTLf. We provide a threefold contribution. First, we define a reactive synthesis problem for DECLARE. Second, we show how an arbitrary DECLARE specification can be polynomially encoded into an equivalent pure-past one in LTLf, and exploit this to define an EXPTIME algorithm for DECLARE synthesis. Third, we derive a symbolic version of this algorithm, by introducing a novel translation of pure-past temporal formulas into symbolic deterministic finite automata.
We study a ubiquitous learning challenge in online principal-agent problems during which the principal learns the agent's private information from the agent's revealed preferences in historical interactions. This paradigm includes important special cases such as pricing and contract design, which have been widely studied in recent literature. However, existing work considers the case where the principal can only choose a single strategy at every round to interact with the agent and then observe the agent's revealed preference through their actions. In this paper, we extend this line of study to allow the principal to offer a menu of strategies to the agent and learn additionally from observing the agent's selection from the menu. We provide a thorough investigation of several online principal-agent problem settings and characterize their sample complexities, accompanied by the corresponding algorithms we have developed. We instantiate this paradigm to several important design problems — including Stackelberg (security) games, contract design, and information design. Finally, we also explore the connection between our findings and existing results about online learning in Stackelberg games, and we offer a solution that can overcome a key hard instance of previous work.
The behaviour of multi agent learning in competitive network games is often studied within the context of zero sum games, in which convergence guarantees may be obtained. However, outside of this class the behaviour of learning is known to display complex behaviours and convergence cannot be always guaranteed. Nonetheless, in order to develop a complete picture of the behaviour of multi agent learning in competitive settings, the zero sum assumption must be lifted. Motivated by this we study the Q Learning dynamics, a popular model of exploration and exploitation in multi agent learning, in competitive network games. We determine how the degree of competition, exploration rate and network connectivity impact the convergence of Q Learning. To study generic competitive games, we parameterise network games in terms of correlations between agent payoffs and study the average behaviour of the Q Learning dynamics across all games drawn from a choice of this parameter. This statistical approach establishes choices of parameters for which Q Learning dynamics converge to a stable fixed point. Differently to previous works, we find that the stability of Q Learning is explicitly dependent only on the network connectivity rather than the total number of agents. Our experiments validate these findings and show that, under certain network structures, the total number of agents can be increased without increasing the likelihood of unstable or chaotic behaviours.
Exploration in decentralized cooperative multi-agent reinforcement learning faces two challenges. One is that the novelty of global states is unavailable, while the novelty of local observations is biased. The other is how agents can explore in a coordinated way. To address these challenges, we propose MACE, a simple yet effective multi-agent coordinated exploration method. By communicating only local novelty, agents can take into account other agents' local novelty to approximate the global novelty. Further, we newly introduce weighted mutual information to measure the influence of one agent's action on other agents' accumulated novelty. We convert it as an intrinsic reward in hindsight to encourage agents to exert more influence on other agents' exploration and boost coordinated exploration. Empirically, we show that MACE achieves superior performance in three multi-agent environments with sparse rewards.
In cooperative multi-agent reinforcement learning, decentralized agents hold the promise of overcoming the combinatorial explosion of joint action space and enabling greater scalability. However, they are susceptible to a game-theoretic pathology called relative overgeneralization that shadows the optimal joint action. Although recent value-decomposition algorithms guide decentralized agents by learning a factored global action value function, the representational limitation and the inaccurate sampling of optimal joint actions during the learning process make this problem still. To address this limitation, this paper proposes a novel algorithm called Optimistic Value Instructors (OVI). The main idea behind OVI is to introduce multiple optimistic instructors into the value-decomposition paradigm, which are capable of suggesting potentially optimal joint actions and rectifying the factored global action value function to recover these optimal actions. Specifically, the instructors maintain optimistic value estimations of per-agent local actions and thus eliminate the negative effects caused by other agents' exploratory or sub-optimal non-cooperation, enabling accurate identification and suggestion of optimal joint actions. Based on the instructors' suggestions, the paper further presents two instructive constraints to rectify the factored global action value function to recover these optimal joint actions, thus overcoming the RO problem. Experimental evaluation of OVI on various cooperative multi-agent tasks demonstrates its superior performance against multiple baselines, highlighting its effectiveness.
Value function factorization has achieved great success in multi-agent reinforcement learning by optimizing joint action-value functions through the maximization of factorized per-agent utilities. To ensure Individual-Global-Maximum property, existing works often focus on value factorization using monotonic functions, which are known to result in restricted representation expressiveness. In this paper, we analyze the limitations of monotonic factorization and present ConcaveQ, a novel non-monotonic value function factorization approach that goes beyond monotonic mixing functions and employs neural network representations of concave mixing functions. Leveraging the concave property in factorization, an iterative action selection scheme is developed to obtain optimal joint actions during training. It is used to update agents’ local policy networks, enabling fully decentralized execution. The effectiveness of the proposed ConcaveQ is validated across scenarios involving multi-agent predator-prey environment and StarCraft II micromanagement tasks. Empirical results exhibit significant improvement of ConcaveQ over state-of-the-art multi-agent reinforcement learning approaches.
Many real-world scenarios including fleet management and Ad auctions can be modeled as Stackelberg mean-field games (SMFGs) where a leader aims to incentivize a large number of homogeneous self-interested followers to maximize her utility. Existing works focus on cases with a small number of heterogeneous followers, e.g., 5-10, and suffer from scalability issue when the number of followers increases. There are three major challenges in solving large-scale SMFGs: i) classical methods based on solving differential equations fail as they require exact dynamics parameters, ii) learning by interacting with environment is data-inefficient, and iii) complex interaction between the leader and followers makes the learning performance unstable. We address these challenges through transition-informed reinforcement learning. Our main contributions are threefold: i) we first propose an RL framework, the Stackelberg mean-field update, to learn the leader's policy without priors of the environment, ii) to improve the data efficiency and accelerate the learning process, we then propose the Transition-Informed Reinforcement Learning (TIRL) by leveraging the instantiated empirical Fokker-Planck equation, and iii) we develop a regularized TIRL by employing various regularizers to alleviate the sensitivity of the learning performance to the initialization of the leader's policy. Extensive experiments on fleet management and food gathering demonstrate that our approach can scale up to 100,000 followers and significantly outperform existing baselines.
We consider decentralized gradient-free optimization of minimizing Lipschitz continuous functions that satisfy neither smoothness nor convexity assumption. We propose two novel gradient-free algorithms, the Decentralized Gradient-Free Method (DGFM) and its variant, the Decentralized Gradient-Free Method+ (DGFM+). Based on the techniques of randomized smoothing and gradient tracking, DGFM requires the computation of the zeroth-order oracle of a single sample in each iteration, making it less demanding in terms of computational resources for individual computing nodes. Theoretically, DGFM achieves a complexity of O(d^(3/2)δ^(-1)ε^(-4)) for obtaining a (δ,ε)-Goldstein stationary point. DGFM+, an advanced version of DGFM, incorporates variance reduction to further improve the convergence behavior. It samples a mini-batch at each iteration and periodically draws a larger batch of data, which improves the complexity to O(d^(3/2)δ^(-1)ε^(-3)). Moreover, experimental results underscore the empirical advantages of our proposed algorithms when applied to real-world datasets.
Effective exploration is crucial to discovering optimal strategies for multi-agent reinforcement learning (MARL) in complex coordination tasks. Existing methods mainly utilize intrinsic rewards to enable committed exploration or use role-based learning for decomposing joint action spaces instead of directly conducting a collective search in the entire action-observation space. However, they often face challenges obtaining specific joint action sequences to reach successful states in long-horizon tasks. To address this limitation, we propose Imagine, Initialize, and Explore (IIE), a novel method that offers a promising solution for efficient multi-agent exploration in complex scenarios. IIE employs a transformer model to imagine how the agents reach a critical state that can influence each other's transition functions. Then, we initialize the environment at this state using a simulator before the exploration phase. We formulate the imagination as a sequence modeling problem, where the states, observations, prompts, actions, and rewards are predicted autoregressively. The prompt consists of timestep-to-go, return-to-go, influence value, and one-shot demonstration, specifying the desired state and trajectory as well as guiding the action generation. By initializing agents at the critical states, IIE significantly increases the likelihood of discovering potentially important under-explored regions. Despite its simplicity, empirical results demonstrate that our method outperforms multi-agent exploration baselines on the StarCraft Multi-Agent Challenge (SMAC) and SMACv2 environments. Particularly, IIE shows improved performance in the sparse-reward SMAC tasks and produces more effective curricula over the initialized states than other generative methods, such as CVAE-GAN and diffusion models.
Multi-Agent Policy Gradient (MAPG) has made significant progress in recent years. However, centralized critics in state-of-the-art MAPG methods still face the centralized-decentralized mismatch (CDM) issue, which means sub-optimal actions by some agents will affect other agent's policy learning. While using individual critics for policy updates can avoid this issue, they severely limit cooperation among agents. To address this issue, we propose an agent topology framework, which decides whether other agents should be considered in policy gradient and achieves compromise between facilitating cooperation and alleviating the CDM issue. The agent topology allows agents to use coalition utility as learning objective instead of global utility by centralized critics or local utility by individual critics. To constitute the agent topology, various models are studied. We propose Topology-based multi-Agent Policy gradiEnt (TAPE) for both stochastic and deterministic MAPG methods. We prove the policy improvement theorem for stochastic TAPE and give a theoretical explanation for the improved cooperation among agents. Experiment results on several benchmarks show the agent topology is able to facilitate agent cooperation and alleviate CDM issue respectively to improve performance of TAPE. Finally, multiple ablation studies and a heuristic graph search algorithm are devised to show the efficacy of the agent topology.
Communication plays a crucial role in information sharing within the field of multi-agent reinforcement learning (MARL). However, how to transmit information that meets individual needs remains a long-standing challenge. Some existing work focus on using a common channel for information transfer, which limits the capability for local communication. Meanwhile, other work attempt to establish peer-to-peer communication topologies but suffer from quadratic complexity. In this paper, we propose Personalized Multi-Agent Communication (PMAC), which enables the formation of peer-to-peer communication topologies, personalized message sending, and personalized message receiving. All these modules in PMAC are performed using only multilayer perceptrons (MLPs) with linear computational complexity. Empirically, we show the strength of personalized communication in a variety of cooperative scenarios. Our approach exhibits competitive performance compared to existing methods while maintaining notable computational efficiency.