arXiv subjects

Yuxiang Guan

Publications and source records attributed to Yuxiang Guan.

10 recordsLinked to original sources

arXiv2026

Best Response Dynamics for Zero-Sum Dynamic Games with Partial-Asymmetric Information

This work studies a class of zero-sum stochastic linear quadratic dynamic games (LQDGs) under partial and asymmetric information. Information asymmetry introduces fundamental challenges related to \textit{belief representation} and \textit{theory of mind}, where players must impute belief states and estimates of other players to inform their strategies. Existing work highlights the difficulty of applying dynamic programming-like decomposition approach to these problems. An alternative approach based on \textit{best response dynamics} is proposed, which provides insights into belief representation and theory of mind challenges. Explicit expressions for each player's best response within the class of pure linear dynamic output feedback control strategies are derived, where the internal state dimension of each control is an integer multiple of the system state dimension. As players iteratively update their best responses, they form increasingly higher-order belief states, leading to infinite-dimensional internal states. However, numerical results reveal that the game's value converges after only a few iterations, suggesting that higher-order belief states provide vanishing benefit. This work further conducts numerical experiments to analyze the impact of asymmetric beliefs, belief orders, relative controllability and observability, and direct feed-through on a linear quadratic pursuit-evasion game's value.

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arXiv2026

Forward-Backward Dynamic Programming for LQG Dynamic Games with Partial and Asymmetric Information

We formulate and study a class of two-player zero-sum stochastic dynamic games with partial and asymmetric information. Information asymmetry introduces fundamental challenges involving \emph{belief representation} and \emph{theory of mind} issues, where agents must impute belief states and estimates of other agents to inform their own strategy. To avoid an infinite regress of higher-order beliefs amongst agents and obtain computationally implementable results, we focus on a linear quadratic Gaussian (LQG) model and consider strategies with limited internal state dimension. We present a novel iterative forward-backward algorithm to jointly compute belief states and equilibrium strategies and value functions for a finite-horizon problem. We also present a value iteration-like algorithm to jointly compute stationary belief states and equilibrium strategies for an average-cost infinite-horizon problem. An open-source implementation of the algorithms is provided, and we demonstrate the effectiveness of the proposed algorithms in numerical experiments.

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arXiv2025

Best Response Convergence for Zero-sum Stochastic Dynamic Games with Partial and Asymmetric Information

We analyze best response dynamics for finding a Nash equilibrium of an infinite horizon zero-sum stochastic linear quadratic dynamic game (LQDG) with partial and asymmetric information. We derive explicit expressions for each player's best response within the class of pure linear dynamic output feedback control strategies where the internal state dimension of each control strategy is an integer multiple of the system state dimension. With each best response, the players form increasingly higher-order belief states, leading to infinite-dimensional internal states. However, we observe in extensive numerical experiments that the game's value converges after just a few iterations, suggesting that strategies associated with increasingly higher-order belief states eventually provide no benefit. To help explain this convergence, our numerical analysis reveals rapid decay of the controllability and observability Gramian eigenvalues and Hankel singular values in higher-order belief dynamics, indicating that the higher-order belief dynamics become increasingly difficult for both players to control and observe. Consequently, the higher-order belief dynamics can be closely approximated by low-order belief dynamics with bounded error, and thus feedback strategies with limited internal state dimension can closely approximate a Nash equilibrium.

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arXiv2025

A Guide to Misinformation Detection Data and Evaluation

Misinformation is a complex societal issue, and mitigating solutions are difficult to create due to data deficiencies. To address this, we have curated the largest collection of (mis)information datasets in the literature, totaling 75. From these, we evaluated the quality of 36 datasets that consist of statements or claims, as well as the 9 datasets that consist of data in purely paragraph form. We assess these datasets to identify those with solid foundations for empirical work and those with flaws that could result in misleading and non-generalizable results, such as spurious correlations, or examples that are ambiguous or otherwise impossible to assess for veracity. We find the latter issue is particularly severe and affects most datasets in the literature. We further provide state-of-the-art baselines on all these datasets, but show that regardless of label quality, categorical labels may no longer give an accurate evaluation of detection model performance. Finally, we propose and highlight Evaluation Quality Assurance (EQA) as a tool to guide the field toward systemic solutions rather than inadvertently propagating issues in evaluation. Overall, this guide aims to provide a roadmap for higher quality data and better grounded evaluations, ultimately improving research in misinformation detection. All datasets and other artifacts are available at https://misinfo-datasets.complexdatalab.com/.

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arXiv2025

From Intuition to Understanding: Using AI Peers to Overcome Physics Misconceptions

Generative AI has the potential to transform personalization and accessibility of education. However, it raises serious concerns about accuracy and helping students become independent critical thinkers. In this study, we designed a helpful AI "Peer" to help students correct fundamental physics misconceptions related to Newtonian mechanic concepts. In contrast to approaches that seek near-perfect accuracy to create an authoritative AI tutor or teacher, we directly inform students that this AI can answer up to 40% of questions incorrectly. In a randomized controlled trial with 165 students, those who engaged in targeted dialogue with the AI Peer achieved post-test scores that were, on average, 10.5 percentage points higher - with over 20 percentage points higher normalized gain - than a control group that discussed physics history. Qualitative feedback indicated that 91% of the treatment group's AI interactions were rated as helpful. Furthermore, by comparing student performance on pre- and post-test questions about the same concept, along with experts' annotations of the AI interactions, we find initial evidence suggesting the improvement in performance does not depend on the correctness of the AI. With further research, the AI Peer paradigm described here could open new possibilities for how we learn, adapt to, and grow with AI.

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arXiv2025

Primitive-Planner: An Ultra Lightweight Quadrotor Planner with Time-optimal Primitives

It is a significant requirement for a quadrotor trajectory planner to simultaneously guarantee trajectory quality and system lightweight. Many researchers focus on this problem, but there's still a gap between their performance and our common wish. In this paper, we propose an ultra lightweight quadrotor planner with time-optimal primitives. Firstly, a novel motion primitive library is proposed to generate time-optimal and dynamical feasible trajectories offline. Secondly, we propose a fast collision checking method with a deterministic time consumption, independent of the sampling resolution of the primitives. Finally, we select the minimum cost trajectory to execute among the safe primitives based on user-defined requirements. The propsed transformation relation between the local trajectories ensures the smoothness of the global trajectory. The planner reduces unnecessary online computing power consumption as much as possible, while ensuring a high-quality trajectory. Benchmark comparisons show that our method can generate the shortest flight time and distance of trajectory with the lowest computation overload. Challenging real-world experiments validate the robustness of our method.

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arXiv2025

Primitive-Swarm: An Ultra-lightweight and Scalable Planner for Large-scale Aerial Swarms

Achieving large-scale aerial swarms is challenging due to the inherent contradictions in balancing computational efficiency and scalability. This paper introduces Primitive-Swarm, an ultra-lightweight and scalable planner designed specifically for large-scale autonomous aerial swarms. The proposed approach adopts a decentralized and asynchronous replanning strategy. Within it is a novel motion primitive library consisting of time-optimal and dynamically feasible trajectories. They are generated utlizing a novel time-optimial path parameterization algorithm based on reachability analysis (TOPP-RA). Then, a rapid collision checking mechanism is developed by associating the motion primitives with the discrete surrounding space according to conflicts. By considering both spatial and temporal conflicts, the mechanism handles robot-obstacle and robot-robot collisions simultaneously. Then, during a replanning process, each robot selects the safe and minimum cost trajectory from the library based on user-defined requirements. Both the time-optimal motion primitive library and the occupancy information are computed offline, turning a time-consuming optimization problem into a linear-complexity selection problem. This enables the planner to comprehensively explore the non-convex, discontinuous 3-D safe space filled with numerous obstacles and robots, effectively identifying the best hidden path. Benchmark comparisons demonstrate that our method achieves the shortest flight time and traveled distance with a computation time of less than 1 ms in dense environments. Super large-scale swarm simulations, involving up to 1000 robots, running in real-time, verify the scalability of our method. Real-world experiments validate the feasibility and robustness of our approach. The code will be released to foster community collaboration.

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arXiv2024

Lie Theory Based Optimization for Unified State Planning of Mobile Manipulators

Mobile manipulators are finding use in numerous practical applications. The current issues with mobile manipulation are the large state space owing to the mobile base and the challenge of modeling high degree of freedom systems. It is critical to devise fast and accurate algorithms that generate smooth motion plans for such mobile manipulators. Existing techniques attempt to solve this problem but focus on separating the motion of the base and manipulator. We propose an approach using Lie theory to find the inverse kinematic constraints by converting the kinematic model, created using screw coordinates, between its Lie group and vector representation. An optimization function is devised to solve for the desired joint states of the entire mobile manipulator. This allows the motion of the mobile base and manipulator to be planned and applied in unison resulting in a smooth and accurate motion plan. The performance of the proposed state planner is validated on simulated mobile manipulators in an analytical experiment. Our solver is available with further derivations and results at https://github.com/peleito/slithers.

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arXiv2024

A Policy Iteration Algorithm for N-player General-Sum Linear Quadratic Dynamic Games

We present a policy iteration algorithm for the infinite-horizon N-player general-sum deterministic linear quadratic dynamic games and compare it to policy gradient methods. We demonstrate that the proposed policy iteration algorithm is distinct from the Gauss-Newton policy gradient method in the N-player game setting, in contrast to the single-player setting where under suitable choice of step size they are equivalent. We illustrate in numerical experiments that the convergence rate of the proposed policy iteration algorithm significantly surpasses that of the Gauss-Newton policy gradient method and other policy gradient variations. Furthermore, our numerical results indicate that, compared to policy gradient methods, the convergence performance of the proposed policy iteration algorithm is less sensitive to the initial policy and changes in the number of players.

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arXiv2023

FlowMap: Path Generation for Automated Vehicles in Open Space Using Traffic Flow

There is extensive literature on perceiving road structures by fusing various sensor inputs such as lidar point clouds and camera images using deep neural nets. Leveraging the latest advance of neural architects (such as transformers) and bird-eye-view (BEV) representation, the road cognition accuracy keeps improving. However, how to cognize the ``road'' for automated vehicles where there is no well-defined ``roads'' remains an open problem. For example, how to find paths inside intersections without HD maps is hard since there is neither an explicit definition for ``roads'' nor explicit features such as lane markings. The idea of this paper comes from a proverb: it becomes a way when people walk on it. Although there are no ``roads'' from sensor readings, there are ``roads'' from tracks of other vehicles. In this paper, we propose FlowMap, a path generation framework for automated vehicles based on traffic flows. FlowMap is built by extending our previous work RoadMap, a light-weight semantic map, with an additional traffic flow layer. A path generation algorithm on traffic flow fields (TFFs) is proposed to generate human-like paths. The proposed framework is validated using real-world driving data and is amenable to generating paths for super complicated intersections without using HD maps.

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