arXiv subjects

Guannan Qu

Publications and source records attributed to Guannan Qu.

At least 37 records · Page 2Linked to original sources

arXiv2026

Polynomial Convergence of Riemannian Diffusion Models

Diffusion models have demonstrated remarkable empirical success in the recent years and are considered one of the state-of-the-art generative models in modern AI. These models consist of a forward process, which gradually diffuses the data distribution to a noise distribution spanning the whole space, and a backward process, which inverts this transformation to recover the data distribution from noise. Most of the existing literature assumes that the underlying space is Euclidean. However, in many practical applications, the data are constrained to lie on a submanifold of Euclidean space. Addressing this setting, De Bortoli et al. (2022) introduced Riemannian diffusion models and proved that using an exponentially small step size yields a small sampling error in the Wasserstein distance, provided the data distribution is smooth and strictly positive, and the score estimate is $L_\infty$-accurate. In this paper, we greatly strengthen this theory by establishing that, under $L_2$-accurate score estimate, a {\em polynomially small stepsize} suffices to guarantee small sampling error in the total variation distance, without requiring smoothness or positivity of the data distribution. Our analysis only requires mild and standard curvature assumptions on the underlying manifold. The main ingredients in our analysis are Li-Yau estimate for the log-gradient of heat kernel, and Minakshisundaram-Pleijel parametrix expansion of the perturbed heat equation. Our approach opens the door to a sharper analysis of diffusion models on non-Euclidean spaces.

cs.LG↗

arXiv2025

Predictive Control and Regret Analysis of Non-Stationary MDP with Look-ahead Information

Policy design in non-stationary Markov Decision Processes (MDPs) is inherently challenging due to the complexities introduced by time-varying system transition and reward, which make it difficult for learners to determine the optimal actions for maximizing cumulative future rewards. Fortunately, in many practical applications, such as energy systems, look-ahead predictions are available, including forecasts for renewable energy generation and demand. In this paper, we leverage these look-ahead predictions and propose an algorithm designed to achieve low regret in non-stationary MDPs by incorporating such predictions. Our theoretical analysis demonstrates that, under certain assumptions, the regret decreases exponentially as the look-ahead window expands. When the system prediction is subject to error, the regret does not explode even if the prediction error grows sub-exponentially as a function of the prediction horizon. We validate our approach through simulations, confirming the efficacy of our algorithm in non-stationary environments.

cs.LG↗

arXiv2025

Mean-Field Sampling for Cooperative Multi-Agent Reinforcement Learning

Designing efficient algorithms for multi-agent reinforcement learning (MARL) is fundamentally challenging because the size of the joint state and action spaces grows exponentially in the number of agents. These difficulties are exacerbated when balancing sequential global decision-making with local agent interactions. In this work, we propose a new algorithm $\texttt{SUBSAMPLE-MFQ}$ ($\textbf{Subsample}$-$\textbf{M}$ean-$\textbf{F}$ield-$\textbf{Q}$-learning) and a decentralized randomized policy for a system with $n$ agents. For any $k\leq n$, our algorithm learns a policy for the system in time polynomial in $k$. We prove that this learned policy converges to the optimal policy on the order of $\tilde{O}(1/\sqrt{k})$ as the number of subsampled agents $k$ increases. In particular, this bound is independent of the number of agents $n$.

cs.LG↗

arXiv2025

Cyber-Resilient System Identification for Power Grid through Bayesian Integration

Power grids increasingly need real-time situational awareness under the ever-evolving cyberthreat landscape. Advances in snapshot-based system identification approaches have enabled accurately estimating states and topology from a snapshot of measurement data, under random bad data and topology errors. However, modern interactive, targeted false data can stay undetectable to these methods, and significantly compromise estimation accuracy. This work advances system identification that combines snapshot-based method with time-series model via Bayesian Integration, to advance cyber resiliency against both random and targeted false data. Using a distance-based time-series model, this work can leverage historical data of different distributions induced by changes in grid topology and other settings. The normal system behavior captured from historical data is integrated into system identification through a Bayesian treatment, to make solutions robust to targeted false data. We experiment on mixed random anomalies (bad data, topology error) and targeted false data injection attack (FDIA) to demonstrate our method's 1) cyber resilience: achieving over 70% reduction in estimation error under FDIA; 2) anomalous data identification: being able to alarm and locate anomalous data; 3) almost linear scalability: achieving comparable speed with the snapshot-based baseline, both taking <1min per time tick on the large 2,383-bus system using a laptop CPU.

eess.SY↗

arXiv2025

Distributed Truncated Predictive Control for Networked Systems under Uncertainty: Stability and Near-Optimality Guarantee

We study the problem of distributed online control of networked systems with time-varying cost functions and disturbances, where each node only has local information of the states and forecasts of the costs and disturbances. We develop a distributed truncated predictive control (DTPC) algorithm, where each node solves a ``truncated'' predictive optimal control problem with horizon $k$, but only involving nodes in a $κ$-hop neighborhood (ignoring nodes outside). We show that the DTPC algorithm satisfies input-to-state stability (ISS) bounds and has regret decaying exponentially in $k$ and $κ$, meaning a short predictive horizon $k$ and a small truncation radius $κ$ is sufficient to achieve near-optimal performance. Furthermore, we show that when the future costs and disturbances are not exactly known, the regret has exponentially decaying sensitivity to the forecast errors in terms of predictive horizon, meaning near-term forecast errors play a much more important role than longer-term forecasts.

math.OC↗

arXiv2025

Recovery of UAV Swarm-enabled Collaborative Beamforming in Low-altitude Wireless Networks under Wind Field Disturbances

Unmanned aerial vehicle (UAV) swarms utilizing collaborative beamforming (CB) in low-altitude wireless networks (LAWN) demonstrate significant potential for enhanced communication range, energy efficiency, and signal directivity through the formation of virtual antenna arrays (VAA). However, environmental disturbances, particularly wind fields, significantly degrade CB performance by introducing positional errors that disrupt beam patterns, thereby compromising transmission reliability. This paper investigates the critical challenge of maintaining CB performance in UAV-based VAAs operating in LAWN under wind field disturbances. We propose a comprehensive framework that models the impact of three distinct wind conditions (constant, shear, and turbulent) on UAV array performance, and formulate a long-term real-time optimization problem to maximize directivity while minimizing maximum sidelobe levels through adaptive excitation current weight adjustments. To address the inherent complexity of this problem, we propose a novel proximal policy optimization algorithm with long short-term memory (LSTM) structure and adaptive learning rate (PPO-LA), which effectively captures temporal patterns in wind field disturbances and enables real-time adaptation without requiring extensive prior training for specific wind conditions. Our simulation results demonstrate that the proposed PPO-LA algorithm successfully recovers degraded CB performance across various wind scenarios, and thus significantly outperforming benchmark algorithms.

cs.NI↗

arXiv2025

A Theoretical Study of (Hyper) Self-Attention through the Lens of Interactions: Representation, Training, Generalization

Self-attention has emerged as a core component of modern neural architectures, yet its theoretical underpinnings remain elusive. In this paper, we study self-attention through the lens of interacting entities, ranging from agents in multi-agent reinforcement learning to alleles in genetic sequences, and show that a single layer linear self-attention can efficiently represent, learn, and generalize functions capturing pairwise interactions, including out-of-distribution scenarios. Our analysis reveals that self-attention acts as a mutual interaction learner under minimal assumptions on the diversity of interaction patterns observed during training, thereby encompassing a wide variety of real-world domains. In addition, we validate our theoretical insights through experiments demonstrating that self-attention learns interaction functions and generalizes across both population distributions and out-of-distribution scenarios. Building on our theories, we introduce HyperFeatureAttention, a novel neural network module designed to learn couplings of different feature-level interactions between entities. Furthermore, we propose HyperAttention, a new module that extends beyond pairwise interactions to capture multi-entity dependencies, such as three-way, four-way, or general n-way interactions.

cs.LG↗

arXiv2025

Thinking Beyond Visibility: A Near-Optimal Policy Framework for Locally Interdependent Multi-Agent MDPs

Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) are known to be NEXP-Complete and intractable to solve. However, for problems such as cooperative navigation, obstacle avoidance, and formation control, basic assumptions can be made about local visibility and local dependencies. The work DeWeese and Qu 2024 formalized these assumptions in the construction of the Locally Interdependent Multi-Agent MDP. In this setting, it establishes three closed-form policies that are tractable to compute in various situations and are exponentially close to optimal with respect to visibility. However, it is also shown that these solutions can have poor performance when the visibility is small and fixed, often getting stuck during simulations due to the so called "Penalty Jittering" phenomenon. In this work, we establish the Extended Cutoff Policy Class which is, to the best of our knowledge, the first non-trivial class of near optimal closed-form partially observable policies that are exponentially close to optimal with respect to the visibility for any Locally Interdependent Multi-Agent MDP. These policies are able to remember agents beyond their visibilities which allows them to perform significantly better in many small and fixed visibility settings, resolve Penalty Jittering occurrences, and under certain circumstances guarantee fully observable joint optimal behavior despite the partial observability. We also propose a generalized form of the Locally Interdependent Multi-Agent MDP that allows for transition dependence and extended reward dependence, then replicate our theoretical results in this setting.

cs.MA↗

arXiv2025

ASAP: Aligning Simulation and Real-World Physics for Learning Agile Humanoid Whole-Body Skills

Humanoid robots hold the potential for unparalleled versatility in performing human-like, whole-body skills. However, achieving agile and coordinated whole-body motions remains a significant challenge due to the dynamics mismatch between simulation and the real world. Existing approaches, such as system identification (SysID) and domain randomization (DR) methods, often rely on labor-intensive parameter tuning or result in overly conservative policies that sacrifice agility. In this paper, we present ASAP (Aligning Simulation and Real-World Physics), a two-stage framework designed to tackle the dynamics mismatch and enable agile humanoid whole-body skills. In the first stage, we pre-train motion tracking policies in simulation using retargeted human motion data. In the second stage, we deploy the policies in the real world and collect real-world data to train a delta (residual) action model that compensates for the dynamics mismatch. Then, ASAP fine-tunes pre-trained policies with the delta action model integrated into the simulator to align effectively with real-world dynamics. We evaluate ASAP across three transfer scenarios: IsaacGym to IsaacSim, IsaacGym to Genesis, and IsaacGym to the real-world Unitree G1 humanoid robot. Our approach significantly improves agility and whole-body coordination across various dynamic motions, reducing tracking error compared to SysID, DR, and delta dynamics learning baselines. ASAP enables highly agile motions that were previously difficult to achieve, demonstrating the potential of delta action learning in bridging simulation and real-world dynamics. These results suggest a promising sim-to-real direction for developing more expressive and agile humanoids.

cs.RO↗

arXiv2025

Natural Policy Gradient for Average Reward Non-Stationary RL

We consider the problem of non-stationary reinforcement learning (RL) in the infinite-horizon average-reward setting. We model it by a Markov Decision Process with time-varying rewards and transition probabilities, with a variation budget of $Δ_T$. Existing non-stationary RL algorithms focus on model-based and model-free value-based methods. Policy-based methods despite their flexibility in practice are not theoretically well understood in non-stationary RL. We propose and analyze the first model-free policy-based algorithm, Non-Stationary Natural Actor-Critic (NS-NAC), a policy gradient method with a restart based exploration for change and a novel interpretation of learning rates as adapting factors. Further, we present a bandit-over-RL based parameter-free algorithm BORL-NS-NAC that does not require prior knowledge of the variation budget $Δ_T$. We present a dynamic regret of $\tilde{\mathscr O}(|S|^{1/2}|A|^{1/2}Δ_T^{1/6}T^{5/6})$ for both algorithms, where $T$ is the time horizon, and $|S|$, $|A|$ are the sizes of the state and action spaces. The regret analysis leverages a novel adaptation of the Lyapunov function analysis of NAC to dynamic environments and characterizes the effects of simultaneous updates in policy, value function estimate and changes in the environment.

cs.LG↗

arXiv2025

Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions

We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances \textit{"consistency"}, which measures the competitive ratio when predictions are accurate, and \textit{"robustness"}, which bounds the competitive ratio when predictions are inaccurate. We propose a novel $λ$-confident policy and provide a competitive ratio upper bound that depends on a trust parameter $λ\in [0,1]$ set based on the confidence in the predictions and some prediction error $\varepsilon$. Motivated by online learning methods, we design a self-tuning policy that adaptively learns the trust parameter $λ$ with a competitive ratio that depends on $\varepsilon$ and the variation of system perturbations and predictions. We show that its competitive ratio is bounded from above by $ 1+{O(\varepsilon)}/({Θ(1)+Θ(\varepsilon)})+O(μ_{\mathsf{Var}})$ where $μ_\mathsf{Var}$ measures the variation of perturbations and predictions. It implies that when the variations of perturbations and predictions are small, by automatically adjusting the trust parameter online, the self-tuning scheme ensures a competitive ratio that does not scale up with the prediction error $\varepsilon$.

eess.SY↗

arXiv2025

Stabilizing Linear Systems under Partial Observability: Sample Complexity and Fundamental Limits

We study the problem of stabilizing an unknown partially observable linear time-invariant (LTI) system. For fully observable systems, leveraging an unstable/stable subspace decomposition approach, state-of-art sample complexity is independent from system dimension $n$ and only scales with respect to the dimension of the unstable subspace. However, it remains open whether such sample complexity can be achieved for partially observable systems because such systems do not admit a uniquely identifiable unstable subspace. In this paper, we propose LTS-P, a novel technique that leverages compressed singular value decomposition (SVD) on the ''lifted'' Hankel matrix to estimate the unstable subsystem up to an unknown transformation. Then, we design a stabilizing controller that integrates a robust stabilizing controller for the unstable mode and a small-gain-type assumption on the stable subspace. We show that LTS-P stabilizes unknown partially observable LTI systems with state-of-the-art sample complexity that is dimension-free and only scales with the number of unstable modes, which significantly reduces data requirements for high-dimensional systems with many stable modes.

eess.SY↗

arXiv2024

Efficient Reinforcement Learning for Global Decision Making in the Presence of Local Agents at Scale

We study reinforcement learning for global decision-making in the presence of local agents, where the global decision-maker makes decisions affecting all local agents, and the objective is to learn a policy that maximizes the joint rewards of all the agents. Such problems find many applications, e.g. demand response, EV charging, queueing, etc. In this setting, scalability has been a long-standing challenge due to the size of the state space which can be exponential in the number of agents. This work proposes the \texttt{SUBSAMPLE-Q} algorithm where the global agent subsamples $k\leq n$ local agents to compute a policy in time that is polynomial in $k$. We show that this learned policy converges to the optimal policy in the order of $\tilde{O}(1/\sqrt{k}+ε_{k,m})$ as the number of sub-sampled agents $k$ increases, where $ε_{k,m}$ is the Bellman noise. Finally, we validate the theory through numerical simulations in a demand-response setting and a queueing setting.

cs.LG↗

arXiv2024

Full-Order Sampling-Based MPC for Torque-Level Locomotion Control via Diffusion-Style Annealing

Due to high dimensionality and non-convexity, real-time optimal control using full-order dynamics models for legged robots is challenging. Therefore, Nonlinear Model Predictive Control (NMPC) approaches are often limited to reduced-order models. Sampling-based MPC has shown potential in nonconvex even discontinuous problems, but often yields suboptimal solutions with high variance, which limits its applications in high-dimensional locomotion. This work introduces DIAL-MPC (Diffusion-Inspired Annealing for Legged MPC), a sampling-based MPC framework with a novel diffusion-style annealing process. Such an annealing process is supported by the theoretical landscape analysis of Model Predictive Path Integral Control (MPPI) and the connection between MPPI and single-step diffusion. Algorithmically, DIAL-MPC iteratively refines solutions online and achieves both global coverage and local convergence. In quadrupedal torque-level control tasks, DIAL-MPC reduces the tracking error of standard MPPI by $13.4$ times and outperforms reinforcement learning (RL) policies by $50\%$ in challenging climbing tasks without any training. In particular, DIAL-MPC enables precise real-world quadrupedal jumping with payload. To the best of our knowledge, DIAL-MPC is the first training-free method that optimizes over full-order quadruped dynamics in real-time.

cs.RO↗

arXiv2024

Locally Interdependent Multi-Agent MDP: Theoretical Framework for Decentralized Agents with Dynamic Dependencies

Many multi-agent systems in practice are decentralized and have dynamically varying dependencies. There has been a lack of attempts in the literature to analyze these systems theoretically. In this paper, we propose and theoretically analyze a decentralized model with dynamically varying dependencies called the Locally Interdependent Multi-Agent MDP. This model can represent problems in many disparate domains such as cooperative navigation, obstacle avoidance, and formation control. Despite the intractability that general partially observable multi-agent systems suffer from, we propose three closed-form policies that are theoretically near-optimal in this setting and can be scalable to compute and store. Consequentially, we reveal a fundamental property of Locally Interdependent Multi-Agent MDP's that the partially observable decentralized solution is exponentially close to the fully observable solution with respect to the visibility radius. We then discuss extensions of our closed-form policies to further improve tractability. We conclude by providing simulations to investigate some long horizon behaviors of our closed-form policies.

cs.LG↗

arXiv2024

Learning to Stabilize Unknown LTI Systems on a Single Trajectory under Stochastic Noise

We study the problem of learning to stabilize unknown noisy Linear Time-Invariant (LTI) systems on a single trajectory. It is well known in the literature that the learn-to-stabilize problem suffers from exponential blow-up in which the state norm blows up in the order of $Θ(2^n)$ where $n$ is the state space dimension. This blow-up is due to the open-loop instability when exploring the $n$-dimensional state space. To address this issue, we develop a novel algorithm that decouples the unstable subspace of the LTI system from the stable subspace, based on which the algorithm only explores and stabilizes the unstable subspace, the dimension of which can be much smaller than $n$. With a new singular-value-decomposition(SVD)-based analytical framework, we prove that the system is stabilized before the state norm reaches $2^{O(k \log n)}$, where $k$ is the dimension of the unstable subspace. Critically, this bound avoids exponential blow-up in state dimension in the order of $Θ(2^n)$ as in the previous works, and to the best of our knowledge, this is the first paper to avoid exponential blow-up in dimension for stabilizing LTI systems with noise.

cs.LG↗

arXiv2024

Model-Based Diffusion for Trajectory Optimization

Recent advances in diffusion models have demonstrated their strong capabilities in generating high-fidelity samples from complex distributions through an iterative refinement process. Despite the empirical success of diffusion models in motion planning and control, the model-free nature of these methods does not leverage readily available model information and limits their generalization to new scenarios beyond the training data (e.g., new robots with different dynamics). In this work, we introduce Model-Based Diffusion (MBD), an optimization approach using the diffusion process to solve trajectory optimization (TO) problems without data. The key idea is to explicitly compute the score function by leveraging the model information in TO problems, which is why we refer to our approach as model-based diffusion. Moreover, although MBD does not require external data, it can be naturally integrated with data of diverse qualities to steer the diffusion process. We also reveal that MBD has interesting connections to sampling-based optimization. Empirical evaluations show that MBD outperforms state-of-the-art reinforcement learning and sampling-based TO methods in challenging contact-rich tasks. Additionally, MBD's ability to integrate with data enhances its versatility and practical applicability, even with imperfect and infeasible data (e.g., partial-state demonstrations for high-dimensional humanoids), beyond the scope of standard diffusion models.

cs.RO↗

arXiv2024

Efficient Reinforcement Learning for Routing Jobs in Heterogeneous Queueing Systems

We consider the problem of efficiently routing jobs that arrive into a central queue to a system of heterogeneous servers. Unlike homogeneous systems, a threshold policy, that routes jobs to the slow server(s) when the queue length exceeds a certain threshold, is known to be optimal for the one-fast-one-slow two-server system. But an optimal policy for the multi-server system is unknown and non-trivial to find. While Reinforcement Learning (RL) has been recognized to have great potential for learning policies in such cases, our problem has an exponentially large state space size, rendering standard RL inefficient. In this work, we propose ACHQ, an efficient policy gradient based algorithm with a low dimensional soft threshold policy parameterization that leverages the underlying queueing structure. We provide stationary-point convergence guarantees for the general case and despite the low-dimensional parameterization prove that ACHQ converges to an approximate global optimum for the special case of two servers. Simulations demonstrate an improvement in expected response time of up to ~30% over the greedy policy that routes to the fastest available server.

cs.LG↗