arXiv subjects

Weijian Li

Publications and source records attributed to Weijian Li.

At least 19 recordsLinked to original sources

arXiv2026

Safe Distributed Generalized Nash Equilibrium Seeking via Control Barrier Functions

In this paper, we consider generalized Nash equilibrium (GNE) seeking in non-cooperative games with coupled constraint sets. Specifically, we aim to enforce safety for distributed GNE seeking, whereby the safety specifications are encoded in the coupled constraint set. To achieve this, we introduce the control barrier function (CBF) in the design of the GNE seeking dynamics. We design the dynamics for both full- and partial-information setting, where each player has knowledge of the decision information of all other players or only neighboring players, respectively. We justify the proposed dynamics by showing that the coupled constraint set is forward invariant, the equilibrium of the dynamics coincides with the exact GNE of the game, and the dynamics is asymptotically stable. Furthermore, we extend the approach to games where the agents are multi-integrators. Numerical simulations are provided to verify our results.

math.OC↗

arXiv2026

Hopformer: Homogeneity-Pursuit Transformer for Time Series Forecasting

Forecasting multiple time-series with high-dimensional covariates presents a core challenge: unifying common temporal patterns while retaining meaningful series-specific information. We introduce Hopformer (Homogeneity-Pursuit Transformer), a two-stage framework that addresses this challenge. In the first stage, we perform a Sparsity Pattern Aggregation (SPA) scheme extracting a common low-variance trend that incorporates the covariates. This acts as a homogenization layer. In the second stage, a LoRA-fine-tuned Transformer models the remaining complex dependencies in the residual. Our method is theoretically grounded. We prove that SPA achieves a near-optimal bias-variance trade-off via an oracle inequality. We also provide generalization bounds for the second stage under dependent time series data. Hopformer sets a new state of the art, improving MASE by an average of 6.56% across synthetic and real-world forecasting benchmarks.

stat.ML↗

arXiv2026

Data-Driven Linear Quadratic Control Using Output-Feedback via Non-Minimal Realization

In this paper, we investigate a continuous-time linear quadratic control problem for systems with unknown matrices, where only input-output data are available. We propose an output-feedback learning framework based on a canonical nonminimal realization constructed through Kreisselmeier's adaptive filter. The filter admits an observer interpretation, which leads to an augmented system that preserves the input-output response of the realization and provides accessible state trajectories. We show that the optimal gain of this augmented system explicitly recovers the optimal gain associated with the canonical non-minimal realization, and hence achieves the optimal state-feedback solution of the original plant. Exploiting this relation and the known structure of the augmented input matrix, we develop a data-driven value iteration algorithm within the adaptive dynamic programming framework. The resulting controller is implementable from input-output data, and its performance is validated via simulations.

math.OC↗

arXiv2026

PhyPrompt: RL-based Prompt Refinement for Physically Plausible Text-to-Video Generation

State-of-the-art text-to-video (T2V) generators frequently violate physical laws despite high visual quality. We show this stems from insufficient physical constraints in prompts rather than model limitations: manually adding physics details reliably produces physically plausible videos, but requires expertise and does not scale. We present PhyPrompt, a two-stage reinforcement learning framework that automatically refines prompts for physically realistic generation. First, we fine-tune a large language model on a physics-focused Chain-of-Thought dataset to integrate principles like object motion and force interactions while preserving user intent. Second, we apply Group Relative Policy Optimization with a dynamic reward curriculum that initially prioritizes semantic fidelity, then progressively shifts toward physical commonsense. This curriculum achieves synergistic optimization: PhyPrompt-7B reaches 40.8\% joint success on VideoPhy2 (8.6pp gain), improving physical commonsense by 11pp (55.8\% to 66.8\%) while simultaneously increasing semantic adherence by 4.4pp (43.4\% to 47.8\%). Remarkably, our curriculum exceeds single-objective training on both metrics, demonstrating compositional prompt discovery beyond conventional multi-objective trade-offs. PhyPrompt outperforms GPT-4o (+3.8\% joint) and DeepSeek-V3 (+2.2\%, 100$\times$ larger) using only 7B parameters. The approach transfers zero-shot across diverse T2V architectures (Lavie, VideoCrafter2, CogVideoX-5B) with up to 16.8\% improvement, establishing that domain-specialized reinforcement learning with compositional curricula surpasses general-purpose scaling for physics-aware generation.

cs.CV↗

arXiv2026

Towards Sparse Video Understanding and Reasoning

We present \revise (\underline{Re}asoning with \underline{Vi}deo \underline{S}parsity), a multi-round agent for video question answering (VQA). Instead of uniformly sampling frames, \revise selects a small set of informative frames, maintains a summary-as-state across rounds, and stops early when confident. It supports proprietary vision-language models (VLMs) in a ``plug-and-play'' setting and enables reinforcement fine-tuning for open-source models. For fine-tuning, we introduce EAGER (Evidence-Adjusted Gain for Efficient Reasoning), an annotation-free reward with three terms: (1) Confidence gain: after new frames are added, we reward the increase in the log-odds gap between the correct option and the strongest alternative; (2) Summary sufficiency: at answer time we re-ask using only the last committed summary and reward success; (3) Correct-and-early stop: answering correctly within a small turn budget is rewarded. Across multiple VQA benchmarks, \revise improves accuracy while reducing frames, rounds, and prompt tokens, demonstrating practical sparse video reasoning.

cs.CV↗

arXiv2026

Primal-dual algorithm for distributed optimization: A dissipativity-based perspective

We study a continuous-time primal-dual algorithm for distributed optimization with nonconvex local cost functions over weight-unbalanced digraphs, and analyze its performance from a dissipativity-based perspective. We first reformulate the algorithm as a Lure type system, consisting of a linear subsystem that relies on the communication topology and the algorithm gains, and a static nonlinear gradient feedback. We then show that the linear subsystem is dissipative with respect to a suitable supply rate, while the nonlinear feedback is not passive. Finally, we establish that, by properly selecting the gains or appropriately designing the communication network, this algorithm converges to an equilibrium at an exponential rate, and thus, achieves an optimal solution to the distributed problem. This work provides new insights into the roles of the network topology, algorithm gains, and cost functions in the performance of a distributed algorithm, and complements existing results from a different viewpoint.

math.OC↗

arXiv2025

Dynamic Nash Equilibrium Seeking for a Class of Nonlinear Uncertain Multi-agent Systems

We consider seeking a Nash equilibrium (NE) of a monotone game, played by dynamic agents which are modeled as a class of lower-triangular nonlinear uncertain dynamics with external disturbances. We establish a general framework that converts the problem into a distributed robust stabilization problem of an appropriately augmented system. To be specific, we construct a virtual single-integrator multi-agent system, as a reference signal generator, to compute an NE in a fully distributed manner. By introducing internal models to tackle the disturbances, as well as embedding the virtual system, we derive an augmented system. Following that, we show that the outputs of all agents reach an NE of the game if the augmented system can be stabilized by a control law. Finally, resorting to a backstepping procedure, we design a distributed state-feedback controller to stabilize the augmented system semi-globally.

math.OC↗

arXiv2025

Actor-Critic Learning for Risk-Constrained Linear Quadratic Regulation

In this paper, we investigate the infinite-horizon risk-constrained linear quadratic regulator problem (RC-QR), which augments the classical LQR formulation with a statistical constraint on the variability of the system state to incorporate risk awareness, a key requirement in safety-critical control applications. We propose an actor-critic learning algorithm that jointly performs policy evaluation and policy improvement in a model-free and online manner. The RC-QR problem is first reformulated as a max-min optimization problem, from which we develop a multi-time-scale stochastic approximation scheme. The critic employs temporal-difference learning to estimate the action-value function, the actor updates the policy parameters via a policy gradient step, and the dual variable is adapted through gradient ascent to enforce the risk constraint.

math.OC↗

arXiv2025

StarEmbed: Benchmarking Time Series Foundation Models on Astronomical Observations of Variable Stars

Current time series foundation model (TSFM) training corpora largely omit data with certain complexities like irregular temporal sampling. Astronomical time series of stellar fluxes (light curves) are available in immense quantities and exhibit irregular sampling, multiple variates, and heteroskedasticity. We introduce StarEmbed, the first public benchmark for light curves comprised of real observations of ~40,000 stars expert-labeled across seven classes and evaluations in clustering, classification, and out-of-distribution (OOD) source detection. We benchmark TSFMs with differing architecture and training strategies as well as domain-specific transformers. Our results demonstrate that the Chronos family, despite being pre-trained on regularly sampled non-astronomical data, yields state-of-the-art (SOTA) performance in light curve clustering and OOD detection. While no TSFM strictly surpasses the classification performance of the long-established domain baseline, they do demonstrate excellent generalization abilities. StarEmbed marks a step toward universal light curve embeddings and improved TSFM performance on challenging data.

astro-ph.SR↗

arXiv2025

Robust Accelerated Dynamics for Subnetwork Bilinear Zero-Sum Games with Distributed Restarting

In this paper, we investigate distributed Nash equilibrium seeking for a class of two-subnetwork zero-sum games characterized by bilinear coupling. We present a distributed primal-dual accelerated mirror-descent algorithm with convergence guarantees. However, we demonstrate that this time-varying algorithm is not robust, as it fails to converge under arbitrarily small disturbances. To address this limitation, we introduce a distributed accelerated algorithm that incorporates a coordinated restarting mechanism. We model this new algorithm as a hybrid dynamical system and establish its structural robustness.

math.OC↗

arXiv2025

On the Robustness of Derivative-free Methods for Linear Quadratic Regulator

Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing the robustness of derivative-free methods for solving an infinite-horizon LQR problem. To be specific, we estimate policy gradients by cost values, and study the effect of perturbations on the estimations, where the perturbations may arise from function approximations, measurement noises, etc. We show that under sufficiently small perturbations, the derivative-free methods converge to any pre-specified neighborhood of the optimal policy. Furthermore, we establish explicit bounds on the perturbations, and provide the sample complexity for the perturbed derivative-free methods.

math.OC↗

arXiv2025

Adaptive Batch Size Schedules for Distributed Training of Language Models with Data and Model Parallelism

An appropriate choice of batch sizes in large-scale model training is crucial, yet it involves an intrinsic yet inevitable dilemma: large-batch training improves training efficiency in terms of memory utilization, while generalization performance often deteriorates due to small amounts of gradient noise. Despite this dilemma, the common practice of choosing batch sizes in language model training often prioritizes training efficiency -- employing either constant large sizes with data parallelism or implementing batch size warmup schedules. However, such batch size schedule designs remain heuristic and often fail to adapt to training dynamics, presenting the challenge of designing adaptive batch size schedules. Given the abundance of available datasets and the data-hungry nature of language models, data parallelism has become an indispensable distributed training paradigm, enabling the use of larger batch sizes for gradient computation. However, vanilla data parallelism requires replicas of model parameters, gradients, and optimizer states at each worker, which prohibits training larger models with billions of parameters. To optimize memory usage, more advanced parallelism strategies must be employed. In this work, we propose general-purpose and theoretically principled adaptive batch size schedules compatible with data parallelism and model parallelism. We develop a practical implementation with PyTorch Fully Sharded Data Parallel, facilitating the pretraining of language models of different sizes. We empirically demonstrate that our proposed approaches outperform constant batch sizes and heuristic batch size warmup schedules in the pretraining of models in the Llama 2 family, with particular focus on smaller models with up to 3 billion parameters. We also establish theoretical convergence guarantees for such adaptive batch size schedules with Adam for general smooth nonconvex objectives.

cs.LG↗

arXiv2024

CRTRE: Causal Rule Generation with Target Trial Emulation Framework

Causal inference and model interpretability are gaining increasing attention, particularly in the biomedical domain. Despite recent advance, decorrelating features in nonlinear environments with human-interpretable representations remains underexplored. In this study, we introduce a novel method called causal rule generation with target trial emulation framework (CRTRE), which applies randomize trial design principles to estimate the causal effect of association rules. We then incorporate such association rules for the downstream applications such as prediction of disease onsets. Extensive experiments on six healthcare datasets, including synthetic data, real-world disease collections, and MIMIC-III/IV, demonstrate the model's superior performance. Specifically, our method achieved a $β$ error of 0.907, outperforming DWR (1.024) and SVM (1.141). On real-world datasets, our model achieved accuracies of 0.789, 0.920, and 0.300 for Esophageal Cancer, Heart Disease, and Cauda Equina Syndrome prediction task, respectively, consistently surpassing baseline models. On the ICD code prediction tasks, it achieved AUC Macro scores of 92.8 on MIMIC-III and 96.7 on MIMIC-IV, outperforming the state-of-the-art models KEPT and MSMN. Expert evaluations further validate the model's effectiveness, causality, and interpretability.

cs.LG↗

arXiv2024

Communication-Efficient Adaptive Batch Size Strategies for Distributed Local Gradient Methods

Modern deep neural networks often require distributed training with many workers due to their large size. As the number of workers increases, communication overheads become the main bottleneck in data-parallel minibatch stochastic gradient methods with per-iteration gradient synchronization. Local gradient methods like Local SGD reduce communication by only synchronizing model parameters and/or gradients after several local steps. Despite an understanding of their convergence and the importance of batch sizes for training efficiency and generalization, optimal batch sizes for local gradient methods are difficult to determine. We introduce adaptive batch size strategies for local gradient methods that increase batch sizes adaptively to reduce minibatch gradient variance. We provide convergence guarantees under homogeneous data conditions and support our claims with image classification and language modeling experiments, demonstrating the effectiveness of our strategies for both training efficiency and generalization.

stat.ML↗

arXiv2024

Primal-dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems

We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent dynamics. It deals with constraints such as simplices and convex set constraints effectively, and converges with a rate of $O(1/t^2)$. Furthermore, we employ the acceleration scheme to constrained distributed optimization and bilinear zero-sum games, and obtain two variants of distributed accelerated algorithms.

math.OC↗

arXiv2024

Incorporating Gradients to Rules: Towards Lightweight, Adaptive Provenance-based Intrusion Detection

As cyber attacks grow increasingly sophisticated and stealthy, it becomes more imperative and challenging to detect intrusion from normal behaviors. Through fine-grained causality analysis, provenance-based intrusion detection systems (PIDS) demonstrated a promising capacity to distinguish benign and malicious behaviors, attracting widespread attention from both industry and academia. Among diverse approaches, rule-based PIDS stands out due to its lightweight overhead, real-time capabilities, and explainability. However, existing rule-based systems suffer low detection accuracy, especially the high false alarms, due to the lack of fine-grained rules and environment-specific configurations. In this paper, we propose CAPTAIN, a rule-based PIDS capable of automatically adapting to diverse environments. Specifically, we propose three adaptive parameters to adjust the detection configuration with respect to nodes, edges, and alarm generation thresholds. We build a differentiable tag propagation framework and utilize the gradient descent algorithm to optimize these adaptive parameters based on the training data. We evaluate our system using data from DARPA Engagements and simulated environments. The evaluation results demonstrate that CAPTAIN enhances rule-based PIDS with learning capabilities, resulting in improved detection accuracy, reduced detection latency, lower runtime overhead, and more interpretable detection procedures and results compared to the state-of-the-art (SOTA) PIDS.

cs.CR↗

arXiv2024

Passivity-based Gradient-Play Dynamics for Distributed Generalized Nash Equilibrium Seeking

We consider seeking generalized Nash equilibria (GNE) for noncooperative games with coupled nonlinear constraints over networks. We first revisit a well-known gradientplay dynamics from a passivity-based perspective, and address that the strict monotonicity on pseudo-gradients is a critical assumption to ensure the exact convergence of the dynamics. Then we propose two novel passivity-based gradient-play dynamics by introducing parallel feedforward compensators (PFCs) and output feedback compensators (OFCs). We show that the proposed dynamics can reach exact GNEs in merely monotone regimes if the PFCs are strictly passive or the OFCs are output strictly passive. Following that, resorting to passivity, we develop a unifying framework to generalize the gradient-play dynamics, and moreover, design a class of explicit passive-based dynamics with convergence guarantees. In addition, we explore the relation between the proposed dynamics and some existing methods, and extend our results to partial-decision information settings.

math.OC↗

arXiv2024

BiSHop: Bi-Directional Cellular Learning for Tabular Data with Generalized Sparse Modern Hopfield Model

We introduce the \textbf{B}i-Directional \textbf{S}parse \textbf{Hop}field Network (\textbf{BiSHop}), a novel end-to-end framework for deep tabular learning. BiSHop handles the two major challenges of deep tabular learning: non-rotationally invariant data structure and feature sparsity in tabular data. Our key motivation comes from the recent established connection between associative memory and attention mechanisms. Consequently, BiSHop uses a dual-component approach, sequentially processing data both column-wise and row-wise through two interconnected directional learning modules. Computationally, these modules house layers of generalized sparse modern Hopfield layers, a sparse extension of the modern Hopfield model with adaptable sparsity. Methodologically, BiSHop facilitates multi-scale representation learning, capturing both intra-feature and inter-feature interactions, with adaptive sparsity at each scale. Empirically, through experiments on diverse real-world datasets, we demonstrate that BiSHop surpasses current SOTA methods with significantly less HPO runs, marking it a robust solution for deep tabular learning.

cs.LG↗