We study a new class of Markov games (MGs), \textit{Multi-player Zero-sum Markov Games} with {\it Networked separable interactions} (MZNMGs), to model the local interaction structure in non-cooperative multi-agent sequential decision-making. We define an MZNMG as a model where {the payoffs of the auxiliary games associated with each state are zero-sum and} have some separable (i.e., polymatrix) structure across the neighbors over some interaction network. We first identify the necessary and sufficient conditions under which an MG can be presented as an MZNMG, and show that the set of Markov coarse correlated equilibrium (CCE) collapses to the set of Markov Nash equilibrium (NE) in these games, in that the {product of} per-state marginalization of the former for all players yields the latter. Furthermore, we show that finding approximate Markov \emph{stationary} CCE in infinite-horizon discounted MZNMGs is \texttt{PPAD}-hard, unless the underlying network has a ``star topology''. Then, we propose fictitious-play-type dynamics, the classical learning dynamics in normal-form games, for MZNMGs, and establish convergence guarantees to Markov stationary NE under a star-shaped network structure. Finally, in light of the hardness result, we focus on computing a Markov \emph{non-stationary} NE and provide finite-iteration guarantees for a series of value-iteration-based algorithms. We also provide numerical experiments to corroborate our theoretical results.

This paper proposes a novel multi-agent reinforcement learning (MARL) method to learn multiple coordinated agents under directed acyclic graph (DAG) constraints. Unlike existing MARL approaches, our method explicitly exploits the DAG structure between agents to achieve more effective learning performance. Theoretically, we propose a novel surrogate value function based on a MARL model with synthetic rewards (MARLM-SR) and prove that it serves as a lower bound of the optimal value function. Computationally, we propose a practical training algorithm that exploits new notion of leader agent and reward generator and distributor agent to guide the decomposed follower agents to better explore the parameter space in environments with DAG constraints. Empirically, we exploit four DAG environments including a real-world scheduling for one of Intel's high volume packaging and test factory to benchmark our methods and show it outperforms the other non-DAG approaches.

Off-policy evaluation (OPE) aims to estimate the benefit of following a counterfactual sequence of actions, given data collected from executed sequences. However, existing OPE estimators often exhibit high bias and high variance in problems involving large, combinatorial action spaces. We investigate how to mitigate this issue using factored action spaces i.e. expressing each action as a combination of independent sub-actions from smaller action spaces. This approach facilitates a finer-grained analysis of how actions differ in their effects. In this work, we propose a new family of "decomposed" importance sampling (IS) estimators based on factored action spaces. Given certain assumptions on the underlying problem structure, we prove that the decomposed IS estimators have less variance than their original non-decomposed versions, while preserving the property of zero bias. Through simulations, we empirically verify our theoretical results, probing the validity of various assumptions. Provided with a technique that can derive the action space factorisation for a given problem, our work shows that OPE can be improved "for free" by utilising this inherent problem structure.

In this paper we present a layered approach for multi-agent control problem, decomposed into three stages, each building upon the results of the previous one. First, a high-level plan for a coarse abstraction of the system is computed, relying on parametric timed automata augmented with stopwatches as they allow to efficiently model simplified dynamics of such systems. In the second stage, the high-level plan, based on SMT-formulation, mainly handles the combinatorial aspects of the problem, provides a more dynamically accurate solution. These stages are collectively referred to as the SWA-SMT solver. They are correct by construction but lack a crucial feature: they cannot be executed in real time. To overcome this, we use SWA-SMT solutions as the initial training dataset for our last stage, which aims at obtaining a neural network control policy. We use reinforcement learning to train the policy, and show that the initial dataset is crucial for the overall success of the method.

The integrated development of city clusters has given rise to an increasing demand for intercity travel. Intercity ride-pooling service exhibits considerable potential in upgrading traditional intercity bus services by implementing demand-responsive enhancements. Nevertheless, its online operations suffer the inherent complexities due to the coupling of vehicle resource allocation among cities and pooled-ride vehicle routing. To tackle these challenges, this study proposes a two-level framework designed to facilitate online fleet management. Specifically, a novel multi-agent feudal reinforcement learning model is proposed at the upper level of the framework to cooperatively assign idle vehicles to different intercity lines, while the lower level updates the routes of vehicles using an adaptive large neighborhood search heuristic. Numerical studies based on the realistic dataset of Xiamen and its surrounding cities in China show that the proposed framework effectively mitigates the supply and demand imbalances, and achieves significant improvement in both the average daily system profit and order fulfillment ratio.

Heading towards navigational autonomy in unmanned surface vehicles (USVs) in the maritime sector can fundamentally lead towards safer waters as well as reduced operating costs, while also providing a range of exciting new capabilities for oceanic research, exploration and monitoring. However, achieving such a goal is challenging. USV control systems must, safely and reliably, be able to adhere to the international regulations for preventing collisions at sea (COLREGs) in encounters with other vessels as they navigate to a given waypoint while being affected by realistic weather conditions, either during the day or at night. To deal with the multitude of possible scenarios, it is critical to have a virtual environment that is able to replicate the realistic operating conditions USVs will encounter, before they can be implemented in the real world. Such "digital twins" form the foundations upon which Deep Reinforcement Learning (DRL) and Computer Vision (CV) algorithms can be used to develop and guide USV control systems. In this paper we describe the novel development of a COLREG-compliant DRL-based collision avoidant navigational system with CV-based awareness in a realistic ocean simulation environment. The performance of the trained autonomous Agents resulting from this approach is evaluated in several successful navigations to set waypoints in both open sea and coastal encounters with other vessels. A binary executable version of the simulator with trained agents is available at https://github.com/aavek/Aeolus-Ocean

Decentralized learning algorithms are an essential tool for designing multi-agent systems, as they enable agents to autonomously learn from their experience and past interactions. In this work, we propose a theoretical and algorithmic framework for real-time identification of the learning dynamics that govern agent behavior using a short burst of a single system trajectory. Our method identifies agent dynamics through polynomial regression, where we compensate for limited data by incorporating side-information constraints that capture fundamental assumptions or expectations about agent behavior. These constraints are enforced computationally using sum-of-squares optimization, leading to a hierarchy of increasingly better approximations of the true agent dynamics. Extensive experiments demonstrated that our approach, using only 5 samples from a short run of a single trajectory, accurately recovers the true dynamics across various benchmarks, including equilibrium selection and prediction of chaotic systems up to 10 Lyapunov times. These findings suggest that our approach has significant potential to support effective policy and decision-making in strategic multi-agent systems.

Attention has become a common ingredient in deep learning architectures. It adds a dynamical selection of information on top of the static selection of information supported by weights. In the same way, we can imagine a higher-order informational filter built on top of attention: an Attention Schema (AS), namely, a descriptive and predictive model of attention. In cognitive neuroscience, Attention Schema Theory (AST) supports this idea of distinguishing attention from AS. A strong prediction of this theory is that an agent can use its own AS to also infer the states of other agents' attention and consequently enhance coordination with other agents. As such, multi-agent reinforcement learning would be an ideal setting to experimentally test the validity of AST. We explore different ways in which attention and AS interact with each other. Our preliminary results indicate that agents that implement the AS as a recurrent internal control achieve the best performance. In general, these exploratory experiments suggest that equipping artificial agents with a model of attention can enhance their social intelligence.

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 social choice theory, anonymity (all agents being treated equally) and neutrality (all alternatives being treated equally) are widely regarded as ``minimal demands'' and ``uncontroversial'' axioms of equity and fairness. However, the ANR impossibility -- there is no voting rule that satisfies anonymity, neutrality, and resolvability (always choosing one winner) -- holds even in the simple setting of two alternatives and two agents. How to design voting rules that optimally satisfy anonymity, neutrality, and resolvability remains an open question. We address the optimal design question for a wide range of preferences and decisions that include ranked lists and committees. Our conceptual contribution is a novel and strong notion of most equitable refinements that optimally preserves anonymity and neutrality for any irresolute rule that satisfies the two axioms. Our technical contributions are twofold. First, we characterize the conditions for the ANR impossibility to hold under general settings, especially when the number of agents is large. Second, we propose the most-favorable-permutation (MFP) tie-breaking to compute a most equitable refinement and design a polynomial-time algorithm to compute MFP when agents' preferences are full rankings.