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Yingdong Lu

Publications and source records attributed to Yingdong Lu.

At least 19 recordsLinked to original sources
arXiv2026

Counting Triangles of Graphs via Randomized Trace Estimation with Incomplete Matrix-Vector Products

Counting triangles in graphs is a fundamental operation in network analysis, underpinning metrics such as clustering coefficients and serving as a signal for community detection, link prediction, and anomaly detection. The standard approach computes the trace of the cube of the adjacency matrix, but explicitly forming $\mathbf{A}^3$ is infeasible for large graphs. Hutchinson randomized trace estimator offers an efficient alternative by approximating the trace through stochastic averaging of quadratic forms, requiring only matrix vector products with $\mathbf{A}$. However, in distributed and heterogeneous computing environments, observing all entries of these products can be costly due to communication overhead and straggler effects. To address this, we propose a new variant of Hutchinson estimator that operates under partial observation constraints, where both the number and identities of observed entries are random. We provide theoretical guarantees on unbiasedness, variance bounds, and sample complexity, and demonstrate through experiments on synthetic and real world graphs that our method achieves accurate triangle count estimates while reducing synchronization costs. This work highlights the adaptability of randomized algorithms to modern computational architectures and opens avenues for efficient motif counting in large scale network analytics.

math.NA↗
arXiv2026

Analysis of Power Iteration Algorithm with Partially Observed Matrix-vector Products

We consider the problem of computing the dominant eigenvector of a symmetric matrix via the power iteration algorithm subject to constraints in the computation of matrix-vector pr ucts. In particular, we focus on scenarios where the entries of matrix-vector products with the input matrix are only partially observed. Such constraints frequently arise on cloud architectures implemented via the controller-worker model where the matrix-vector products are distributed across workers on remote servers. Instead of a prolonged delay incurred by waiting for the slowest workers to return their output to the controller, a phenomenon known as straggling, a set of pre-determined values can replace the values of the delayed workers and allow the power iteration to proceed to the next iteration. In this paper, we develop two algorithms whose expected approximation converges to the true dominant eigenvector. The first algorithm relies on a probabilistic switch between two different approaches to set the omitted entries: either set them to zero or to their previous recorded value. The second algorithm relies on averaging previously generated partial power iteration approximations obtained by ignoring a set of columns of the iteration matrix. several theoretical details are discussed while numerical experiments verify the effectiveness of the two proposed schemes and demonstrate their comparative performance advantage over current state-of-the-art.

math.NA↗
arXiv2026

Causal-Aware Foundation-Model for Bilevel Optimization in Discrete Choice Settings

We introduce a causal aware foundation-model framework for real time optimal decision making in discrete choice environments. We propose a constrained triple-head price optimization (C3PO) network to solve a bilevel decision problem in which a service provider selects an optimal assortment while heterogeneous users make personalized acceptance or rejection choices optimizing their own personalized preferences. C3PO integrates imitation learning of prices, multi-task learning of revenue responses, and in context learning of price elasticity to generate pricing recommendations while adhering to business constraints. During inference, frontier model prompting retrieves an enhanced elasticity prior for new products from behavioral economics literature, improving pricing effectiveness. We demonstrate strong in context learning performance using simulated, synthetic, and real-world datasets. C3PO is trained on simulated data generated from multiple classical discrete choice models in economics. The model is trained on data comprising simulated customer segments and counterfactual action and outcome pairs and evaluated on randomly generated choice environments with no access to the underlying preference structure. The trained model consistently improves the pricing KPIs, with gains increasing as customer price sensitivity increases. We also deploy the tuned foundation model for optimal pricing in real-world applications such as healthcare, tender pricing, airline ancillary pricing, and other domains, achieving substantial gains across multiple products, markets, and divisions.

cs.LG↗
arXiv2026

On Hamiltonian Monte Carlo for Gaussian Random Variables with Random Hamiltonians

We study a family of (multivariate-)Gaussian Hamiltonian Monte Carlo (GHMC) operators and prove that the family of Gaussian distributions and their mixtures are invariant under such operators. Furthermore, each such operator is a contraction on the space of parameters and an explicit formulae are derived. These results then enable us to analyze the dynamics and convergences of independent and identically distributed random sequences of such operators.

math.PR↗
arXiv2025

Optimality and NP-Hardness of Transformers in Learning Markovian Dynamical Functions

Transformer architectures can solve unseen tasks based on input-output pairs in a given prompt due to in-context learning (ICL). Existing theoretical studies on ICL have mainly focused on linear regression tasks, often with i.i.d. inputs. To understand how transformers express ICL when modeling dynamics-driven functions, we investigate Markovian function learning through a structured ICL setup, where we characterize the loss landscape to reveal underlying optimization behaviors. Specifically, we (1) provide the closed-form expression of the global minimizer (in an enlarged parameter space) for a single-layer linear self-attention (LSA) model; (2) prove that recovering transformer parameters that realize the optimal solution is NP-hard in general, revealing a fundamental limitation of one-layer LSA in representing structured dynamical functions; and (3) supply a novel interpretation of a multilayer LSA as performing preconditioned gradient descent to optimize multiple objectives beyond the square loss. These theoretical results are numerically validated using simplified transformers.

cs.LG↗
arXiv2025

Fast Linear Solvers via AI-Tuned Markov Chain Monte Carlo-based Matrix Inversion

Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for ill-conditioned matrices, so practical deployments usually require preconditioners. Markov chain Monte Carlo (MCMC)-based matrix inversion can generate such preconditioners and accelerate Krylov iterations, but its effectiveness depends on parameters whose optima vary across matrices; manual or grid search is costly. We present an AI-driven framework recommending MCMC parameters for a given linear system. A graph neural surrogate predicts preconditioning speed from $A$ and MCMC parameters. A Bayesian acquisition function then chooses the parameter sets most likely to minimise iterations. On a previously unseen ill-conditioned system, the framework achieves better preconditioning with 50\% of the search budget of conventional methods, yielding about a 10\% reduction in iterations to convergence. These results suggest a route for incorporating MCMC-based preconditioners into large-scale systems.

cs.LG↗
arXiv2025

Stackelberg Coupling of Online Representation Learning and Reinforcement Learning

Deep Q-learning jointly learns representations and values within monolithic networks, promising beneficial co-adaptation between features and value estimates. Although this architecture has attained substantial success, the coupling between representation and value learning creates instability as representations must constantly adapt to non-stationary value targets, while value estimates depend on these shifting representations. This is compounded by high variance in bootstrapped targets, which causes bias in value estimation in off-policy methods. We introduce Stackelberg Coupled Representation and Reinforcement Learning (SCORER), a framework for value-based RL that views representation and Q-learning as two strategic agents in a hierarchical game. SCORER models the Q-function as the leader, which commits to its strategy by updating less frequently, while the perception network (encoder) acts as the follower, adapting more frequently to learn representations that minimize Bellman error variance given the leader's committed strategy. Through this division of labor, the Q-function minimizes MSBE while perception minimizes its variance, thereby reducing bias accordingly, with asymmetric updates allowing stable co-adaptation, unlike simultaneous parameter updates in monolithic solutions. Our proposed SCORER framework leads to a bi-level optimization problem whose solution is approximated by a two-timescale algorithm that creates an asymmetric learning dynamic between the two players. Extensive experiments on DQN and its variants demonstrate that gains stem from algorithmic insight rather than model complexity.

cs.LG↗
arXiv2025

In-Context Reinforcement Learning via Communicative World Models

Reinforcement learning (RL) agents often struggle to generalize to new tasks and contexts without updating their parameters, mainly because their learned representations and policies are overfit to the specifics of their training environments. To boost agents' in-context RL (ICRL) ability, this work formulates ICRL as a two-agent emergent communication problem and introduces CORAL (Communicative Representation for Adaptive RL), a framework that learns a transferable communicative context by functionally separating latent representation learning from control. In CORAL, an Information Agent (IA) is pre-trained as a world model on a diverse distribution of tasks. Its objective is not direct return maximization, but world modeling and distilling its understanding into concise messages. The emergent communication protocol is shaped by a novel Causal Influence Loss, which measures the effect that the message has on the next action. During deployment, the previously trained IA serves as a fixed contextualizer for a new Control Agent (CA), which learns to solve tasks by interpreting the provided communicative context. Our experiments demonstrate that this approach enables the CA to achieve significant gains in sample efficiency and successfully perform zero-shot adaptation with the help of pre-trained IA in diverse online and offline environments, validating the efficacy of learning a transferable communicative representation.

cs.LG↗
arXiv2025

SPRIG: Stackelberg Perception-Reinforcement Learning with Internal Game Dynamics

Deep reinforcement learning agents often face challenges to effectively coordinate perception and decision-making components, particularly in environments with high-dimensional sensory inputs where feature relevance varies. This work introduces SPRIG (Stackelberg Perception-Reinforcement learning with Internal Game dynamics), a framework that models the internal perception-policy interaction within a single agent as a cooperative Stackelberg game. In SPRIG, the perception module acts as a leader, strategically processing raw sensory states, while the policy module follows, making decisions based on extracted features. SPRIG provides theoretical guarantees through a modified Bellman operator while preserving the benefits of modern policy optimization. Experimental results on the Atari BeamRider environment demonstrate SPRIG's effectiveness, achieving around 30% higher returns than standard PPO through its game-theoretical balance of feature extraction and decision-making.

cs.AI↗
arXiv2024

Dynamical Behaviors of the Gradient Flows for In-Context Learning

We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances, including identifying its invariants, optimum, and saddle points. This understanding allows us to quantify the behavior of the two gradient flows under the full generality of parameters and data.

math.DS↗
arXiv2024

Federated Learning for Discrete Optimal Transport with Large Population under Incomplete Information

Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this work, we introduce a discrete optimal transport framework designed to handle large-scale, heterogeneous target populations, characterized by type distributions. We address two scenarios: one where the type distribution of targets is known, and one where it is unknown. For the known distribution, we propose a fully distributed algorithm to achieve optimal resource allocation. In the case of unknown distribution, we develop a federated learning-based approach that enables efficient computation of the optimal transport scheme while preserving privacy. Case studies are provided to evaluate the performance of our learning algorithm.

cs.AI↗
arXiv2024

Mean Field Control by Stochastic Koopman Operator via a Spectral Method

Mean field control provides a robust framework for coordinating large-scale populations with complex interactions and has wide applications across diverse fields. However, the inherent nonlinearity and the presence of unknown system dynamics pose significant challenges for developing effective analytic or numerical solutions. There is a pressing need for data-driven methodologies to construct accurate models and facilitate efficient planning and control. To this end, we leverage Koopman operator theory to advance solution methods for mean field control problems. Our approach involves exploring stochastic Koopman operators using spectral analysis techniques. Through Koopman decomposition, we derive a linear model for mean field control problems in a data-driven fashion. Finally, we develop a model predictive control framework to achieve robust control and reduce the computational complexity for mean field control problems, thereby enhancing the efficacy and applicability of mean field control solutions in various domains.

math.OC↗
arXiv2024

On The Variance of Schatten $p$-Norm Estimation with Gaussian Sketching Matrices

Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the quality of such estimators is to consider the variance over the total number of observations. In this paper we present a procedure to compute the variance of the estimator proposed by Kong and Valiant [Ann. Statist. 45 (5), pp. 2218 - 2247] for the case of Gaussian random vectors and provide a sharper bound than previously available.

math.ST↗
arXiv2024

On the iterations of some random functions with Lipschitz number one

For the iterations of $x\mapsto |x-\theta|$ random functions with Lipschitz number one, we represent the dynamics as a Markov chain and prove its convergence under mild conditions. We also demonstrate that the Wasserstein metric of any two measures will not increase after the corresponding induced iterations for measures and identify conditions under which a polynomial convergence rate can be achieved in this metric. We also consider an associated nonlinear operator on the space of probability measures and identify its fixed points through an detailed analysis of their characteristic functions.

math.PR↗
arXiv2024

Regenerative Ulam-von Neumann Algorithm: An Innovative Markov chain Monte Carlo Method for Matrix Inversion

This paper presents a regenerative variant of the classical Ulam-von Neumann Markov chain Monte Carlo algorithm for the approximation of the matrix inverse. The algorithm presented in this paper, termed regenerative Ulam-von Neumann algorithm, utilizes the regenerative structure of classical, non-truncated Neumann series defined by a non-singular matrix and produces an estimator of the matrix inverse via ratios of unbiased estimators of the regenerative quantities. The accuracy of the proposed algorithm depends on a single parameter that controls the total number of simulated Markov transitions, thus avoiding the challenge of balancing between the total number of Markov chain replications and their length as in the classical Ulam-von Neumann algorithm. To efficiently utilize Markov chain transition samples in the calculation of the regenerative variables, the proposed algorithm automatically quantifies the contribution of each Markov transition to all regenerative quantities by a carefully designed updating scheme that utilized three separate matrices containing the current weights, total weights, and regenerative cycle count, respectively. A probabilistic analysis of the performance of the algorithm, including the variance of the estimator, is provided. Finally, numerical experiments verify the effectiveness of the proposed scheme.

math.NA↗
arXiv2024

On Convergence of the Alternating Directions SGHMC Algorithm

We study convergence rates of Hamiltonian Monte Carlo (HMC) algorithms with leapfrog integration under mild conditions on stochastic gradient oracle for the target distribution (SGHMC). Our method extends standard HMC by allowing the use of general auxiliary distributions, which is achieved by a novel procedure of Alternating Directions. The convergence analysis is based on the investigations of the Dirichlet forms associated with the underlying Markov chain driving the algorithms. For this purpose, we provide a detailed analysis on the error of the leapfrog integrator for Hamiltonian motions with both the kinetic and potential energy functions in general form. We characterize the explicit dependence of the convergence rates on key parameters such as the problem dimension, functional properties of both the target and auxiliary distributions, and the quality of the oracle.

math.ST↗
arXiv2024

Relative Error of Scaled Poisson Approximation via Stein's Method

We study the accuracy of a scaled Poisson approximation to the weighted sum of independent Poisson random variables, focusing on in particular the relative error of the tail distribution. A bound on the relative approximation error is established using a modified Stein-Chen method.

math.PR↗