Dynamic games can be an effective approach for modeling interactive behavior between multiple competitive agents in autonomous racing and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In this work, we propose DG-SQP, a numerical method for the solution of local generalized Nash equilibria (GNE) for open-loop general-sum dynamic games for agents with nonlinear dynamics and constraints. In particular, we formulate a sequential quadratic programming (SQP) approach which requires only the solution of a single convex quadratic program at each iteration. The three key elements of the method are a non-monotonic line search for solving the associated KKT equations, a merit function to handle zero sum costs, and a decaying regularization scheme for SQP step selection. We show that our method achieves linear convergence in the neighborhood of local GNE and demonstrate the effectiveness of the approach in the context of head-to-head car racing, where we show significant improvement in solver success rate when comparing against the state-of-the-art PATH solver for dynamic games. An implementation of our solver can be found at https://github.com/zhu-edward/DGSQP.

An exciting frontier in robotic manipulation is the use of multiple arms at once. However, planning concurrent motions is a challenging task using current methods. The high-dimensional composite state space renders many well-known motion planning algorithms intractable. Recently, Multi-Agent Path-Finding (MAPF) algorithms have shown promise in discrete 2D domains, providing rigorous guarantees. However, widely used conflict-based methods in MAPF assume an efficient single-agent motion planner. This poses challenges in adapting them to manipulation cases where this assumption does not hold, due to the high dimensionality of configuration spaces and the computational bottlenecks associated with collision checking. To this end, we propose an approach for accelerating conflict-based search algorithms by leveraging their repetitive and incremental nature -- making them tractable for use in complex scenarios involving multi-arm coordination in obstacle-laden environments. We show that our method preserves completeness and bounded sub-optimality guarantees, and demonstrate its practical efficacy through a set of experiments with up to 10 robotic arms.

We consider online no-regret learning in unknown games with bandit feedback, where each player can only observe its reward at each time -- determined by all players' current joint action -- rather than its gradient. We focus on the class of \textit{smooth and strongly monotone} games and study optimal no-regret learning therein. Leveraging self-concordant barrier functions, we first construct a new bandit learning algorithm and show that it achieves the single-agent optimal regret of $\tilde{\Theta}(n\sqrt{T})$ under smooth and strongly concave reward functions ($n \geq 1$ is the problem dimension). We then show that if each player applies this no-regret learning algorithm in strongly monotone games, the joint action converges in the \textit{last iterate} to the unique Nash equilibrium at a rate of $\tilde{\Theta}(nT^{-1/2})$. Prior to our work, the best-known convergence rate in the same class of games is $\tilde{O}(n^{2/3}T^{-1/3})$ (achieved by a different algorithm), thus leaving open the problem of optimal no-regret learning algorithms (since the known lower bound is $\Omega(nT^{-1/2})$). Our results thus settle this open problem and contribute to the broad landscape of bandit game-theoretical learning by identifying the first doubly optimal bandit learning algorithm, in that it achieves (up to log factors) both optimal regret in the single-agent learning and optimal last-iterate convergence rate in the multi-agent learning. We also present preliminary numerical results on several application problems to demonstrate the efficacy of our algorithm in terms of iteration count.

Effective agent coordination is crucial in cooperative Multi-Agent Reinforcement Learning (MARL). While agent cooperation can be represented by graph structures, prevailing graph learning methods in MARL are limited. They rely solely on one-step observations, neglecting crucial historical experiences, leading to deficient graphs that foster redundant or detrimental information exchanges. Additionally, high computational demands for action-pair calculations in dense graphs impede scalability. To address these challenges, we propose inferring a Latent Temporal Sparse Coordination Graph (LTS-CG) for MARL. The LTS-CG leverages agents' historical observations to calculate an agent-pair probability matrix, where a sparse graph is sampled from and used for knowledge exchange between agents, thereby simultaneously capturing agent dependencies and relation uncertainty. The computational complexity of this procedure is only related to the number of agents. This graph learning process is further augmented by two innovative characteristics: Predict-Future, which enables agents to foresee upcoming observations, and Infer-Present, ensuring a thorough grasp of the environmental context from limited data. These features allow LTS-CG to construct temporal graphs from historical and real-time information, promoting knowledge exchange during policy learning and effective collaboration. Graph learning and agent training occur simultaneously in an end-to-end manner. Our demonstrated results on the StarCraft II benchmark underscore LTS-CG's superior performance.

Robotic access monitoring of multiple target areas has applications including checkpoint enforcement, surveillance and containment of fire and flood hazards. Monitoring access for a single target region has been successfully modeled as a minimum-cut problem. We generalize this model to support multiple target areas using two approaches: iterating on individual targets and examining the collections of targets holistically. Through simulation we measure the performance of each approach on different scenarios.

Investors and regulators can greatly benefit from a realistic market simulator that enables them to anticipate the consequences of their decisions in real markets. However, traditional rule-based market simulators often fall short in accurately capturing the dynamic behavior of market participants, particularly in response to external market impact events or changes in the behavior of other participants. In this study, we explore an agent-based simulation framework employing reinforcement learning (RL) agents. We present the implementation details of these RL agents and demonstrate that the simulated market exhibits realistic stylized facts observed in real-world markets. Furthermore, we investigate the behavior of RL agents when confronted with external market impacts, such as a flash crash. Our findings shed light on the effectiveness and adaptability of RL-based agents within the simulation, offering insights into their response to significant market events.

Understanding the characteristics of swarming autonomous agents is critical for defense and security applications. This article presents a study on using supervised neural network time series classification (NN TSC) to predict key attributes and tactics of swarming autonomous agents for military contexts. Specifically, NN TSC is applied to infer two binary attributes - communication and proportional navigation - which combine to define four mutually exclusive swarm tactics. We identify a gap in literature on using NNs for swarm classification and demonstrate the effectiveness of NN TSC in rapidly deducing intelligence about attacking swarms to inform counter-maneuvers. Through simulated swarm-vs-swarm engagements, we evaluate NN TSC performance in terms of observation window requirements, noise robustness, and scalability to swarm size. Key findings show NNs can predict swarm behaviors with 97% accuracy using short observation windows of 20 time steps, while also demonstrating graceful degradation down to 80% accuracy under 50% noise, as well as excellent scalability to swarm sizes from 10 to 100 agents. These capabilities are promising for real-time decision-making support in defense scenarios by rapidly inferring insights about swarm behavior.

We consider a setting in which $N$ agents aim to speedup a common Stochastic Approximation (SA) problem by acting in parallel and communicating with a central server. We assume that the up-link transmissions to the server are subject to asynchronous and potentially unbounded time-varying delays. To mitigate the effect of delays and stragglers while reaping the benefits of distributed computation, we propose \texttt{DASA}, a Delay-Adaptive algorithm for multi-agent Stochastic Approximation. We provide a finite-time analysis of \texttt{DASA} assuming that the agents' stochastic observation processes are independent Markov chains. Significantly advancing existing results, \texttt{DASA} is the first algorithm whose convergence rate depends only on the mixing time $\tau_{mix}$ and on the average delay $\tau_{avg}$ while jointly achieving an $N$-fold convergence speedup under Markovian sampling. Our work is relevant for various SA applications, including multi-agent and distributed temporal difference (TD) learning, Q-learning and stochastic optimization with correlated data.

Navigating multi-robot systems in complex terrains has always been a challenging task. This is due to the inherent limitations of traditional robots in collision avoidance, adaptation to unknown environments, and sustained energy efficiency. In order to overcome these limitations, this research proposes a solution by integrating living insects with miniature electronic controllers to enable robotic-like programmable control, and proposing a novel control algorithm for swarming. Although these creatures, called cyborg insects, have the ability to instinctively avoid collisions with neighbors and obstacles while adapting to complex terrains, there is a lack of literature on the control of multi-cyborg systems. This research gap is due to the difficulty in coordinating the movements of a cyborg system under the presence of insects' inherent individual variability in their reactions to control input. In response to this issue, we propose a novel swarm navigation algorithm addressing these challenges. The effectiveness of the algorithm is demonstrated through an experimental validation in which a cyborg swarm was successfully navigated through an unknown sandy field with obstacles and hills. This research contributes to the domain of swarm robotics and showcases the potential of integrating biological organisms with robotics and control theory to create more intelligent autonomous systems with real-world applications.

University of Sussex, School of Engineering and Informatics, Chichester I, CI-128, Falmer, Brighton, BN1 9RH, United Kingdom Acknowledgement This work was supported by a European Research Council Grant (XSCAPE) ERC-2020-SyG 951631 Abstract Legal autonomy -- the lawful activity of artificial intelligence agents -- can be achieved in one of two ways. It can be achieved either by imposing constraints on AI actors such as developers, deployers and users, and on AI resources such as data, or by imposing constraints on the range and scope of the impact that AI agents can have on the environment. The latter approach involves encoding extant rules concerning AI driven devices into the software of AI agents controlling those devices (e.g., encoding rules about limitations on zones of operations into the agent software of an autonomous drone device). This is a challenge since the effectivity of such an approach requires a method of extracting, loading, transforming and computing legal information that would be both explainable and legally interoperable, and that would enable AI agents to "reason" about the law. In this paper, we sketch a proof of principle for such a method using large language models (LLMs), expert legal systems known as legal decision paths, and Bayesian networks. We then show how the proposed method could be applied to extant regulation in matters of autonomous cars, such as the California Vehicle Code. Keywords Legal Reasoning; Large Language Models; Expert System; Bayesian Network; Explanability; Interoperability; Autonomous Vehicles 1. Two paths towards legal autonomy What does it mean to regulate artificial intelligence (AI), and how should we go about it? To answer this question, one must first be clear on what artificial intelligence is--at least, for the purposes of the law-- and then ask whether existing laws are sufficient for its regulation. This consensus is that the term "AI" refers to software (i) that is developed using computational techniques, (ii) that is able to make decisions that influence an environment, (iii) that is able to make such decisions autonomously, or partly autonomously, and (iv) that makes those decisions to align with a set of human defined objectives. In AI research, decision-making typically involves the ability to evaluate options, predict outcomes, and select an optimal or satisfactory course of action based on the data available and predefined objectives. This process is crucial in distinguishing AI systems from simple automated systems that operate based on a fixed set of rules without variation or learning ((Friedman & Frank, 1983; Gupta et al., 2022). Autonomy in AI is characterized by goal-oriented behaviour, where the system is not just reacting to inputs based on fixed rules but is actively pursuing objectives.