arXiv subjects

Yue Guan

Publications and source records attributed to Yue Guan.

At least 55 records · Page 3Linked to original sources

arXiv2023

On the Adversarial Convex Body Chasing Problem

In this work, we extend the convex bodies chasing problem (CBC) to an adversarial setting, where an agent (the Player) is tasked with chasing a sequence of convex bodies generated adversarially by another agent (the Opponent). The Player aims to minimize the total cost associated with its own movements, while the Opponent tries to maximize the same cost. The set of feasible convex bodies is finite and known to both agents, which allows us to provide performance guarantees with max-min optimality. Under certain assumptions, we show the continuity of the optimal value function, and propose an algorithm to numerically approximate the optimal policies for both the Player and the Opponent within a guaranteed tolerance. Finally, the theoretical results are verified through numerical examples.

eess.SY↗

arXiv2022

Jump Law of Co-State in Optimal Control for State-Dependent Switched Systems and Applications

This paper presents the jump law of co-states in optimal control for state-dependent switched systems. The number of switches and the switching modes are assumed to be known a priori. A proposed jump law is rigorously derived by theoretical analysis and illustrated by simulation results. An algorithm is then proposed to solve optimal control for state-dependent hybrid systems. Through numerical simulations, we further show that the proposed approach is more efficient than existing methods in solving optimal control for state-dependent switched systems.

math.OC↗

arXiv2022

Hierarchical Decompositions of Stochastic Pursuit-Evasion Games

In this work we present a hierarchical framework for solving discrete stochastic pursuit-evasion games (PEGs) in large grid worlds. With a partition of the grid world into superstates (e.g., "rooms"), the proposed approach creates a two-resolution decision-making process, which consists of a set of local PEGs at the original state level and an aggregated PEG at the superstate level. Having much smaller cardinality, both the local games and the aggregated game can be easily solved to a Nash equilibrium. To connect the decision-making at the two resolutions, we use the Nash values of the local PEGs as the rewards for the aggregated game. Through numerical simulations, we show that the proposed hierarchical framework significantly reduces the computation overhead, while still maintaining a satisfactory level of performance when competing against the flat Nash policies.

cs.MA↗

arXiv2022

Shaping Large Population Agent Behaviors Through Entropy-Regularized Mean-Field Games

Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time setting. We show that entropy regularization provides the necessary regularity conditions, that are lacking in the standard finite mean field games. Such regularity conditions enable us to design fixed-point iteration algorithms to find the unique mean-field equilibrium (MFE). Furthermore, the reference policy used in the regularization provides an extra parameter, through which one can control the behavior of the population. We first consider a stochastic game with a large population of $N$ homogeneous agents. We establish conditions for the existence of a Nash equilibrium in the limiting case as $N$ tends to infinity, and we demonstrate that the Nash equilibrium for the infinite population case is also an $ε$-Nash equilibrium for the $N$-agent system, where the sub-optimality $ε$ is of order $\mathcal{O}\big(1/\sqrt{N}\big)$. Finally, we verify the theoretical guarantees through a resource allocation example and demonstrate the efficacy of using a reference policy to control the behavior of a large population.

cs.GT↗

arXiv2022

Block-Skim: Efficient Question Answering for Transformer

Transformer models have achieved promising results on natural language processing (NLP) tasks including extractive question answering (QA). Common Transformer encoders used in NLP tasks process the hidden states of all input tokens in the context paragraph throughout all layers. However, different from other tasks such as sequence classification, answering the raised question does not necessarily need all the tokens in the context paragraph. Following this motivation, we propose Block-skim, which learns to skim unnecessary context in higher hidden layers to improve and accelerate the Transformer performance. The key idea of Block-Skim is to identify the context that must be further processed and those that could be safely discarded early on during inference. Critically, we find that such information could be sufficiently derived from the self-attention weights inside the Transformer model. We further prune the hidden states corresponding to the unnecessary positions early in lower layers, achieving significant inference-time speedup. To our surprise, we observe that models pruned in this way outperform their full-size counterparts. Block-Skim improves QA models' accuracy on different datasets and achieves 3 times speedup on BERT-base model.

cs.CL↗

arXiv2022

Transkimmer: Transformer Learns to Layer-wise Skim

Transformer architecture has become the de-facto model for many machine learning tasks from natural language processing and computer vision. As such, improving its computational efficiency becomes paramount. One of the major computational inefficiency of Transformer-based models is that they spend the identical amount of computation throughout all layers. Prior works have proposed to augment the Transformer model with the capability of skimming tokens to improve its computational efficiency. However, they suffer from not having effectual and end-to-end optimization of the discrete skimming predictor. To address the above limitations, we propose the Transkimmer architecture, which learns to identify hidden state tokens that are not required by each layer. The skimmed tokens are then forwarded directly to the final output, thus reducing the computation of the successive layers. The key idea in Transkimmer is to add a parameterized predictor before each layer that learns to make the skimming decision. We also propose to adopt reparameterization trick and add skim loss for the end-to-end training of Transkimmer. Transkimmer achieves 10.97x average speedup on GLUE benchmark compared with vanilla BERT-base baseline with less than 1% accuracy degradation.

cs.CL↗

arXiv2021

Dynamic Defender-Attacker Blotto Game

This work studies a dynamic, adversarial resource allocation problem in environments modeled as graphs. A blue team of defender robots are deployed in the environment to protect the nodes from a red team of attacker robots. We formulate the engagement as a discrete-time dynamic game, where the robots can move at most one hop in each time step. The game terminates with the attacker's win if any location has more attacker robots than defender robots at any time. The goal is to identify dynamic resource allocation strategies, as well as the conditions that determines the winner: graph structure, available resources, and initial conditions. We analyze the problem using reachable sets and show how the outdegree of the underlying graph directly influences the difficulty of the defending task. Furthermore, we provide algorithms that identify sufficiency of attacker's victory.

eess.SY↗

arXiv2021

PointManifoldCut: Point-wise Augmentation in the Manifold for Point Clouds

Mixed-based point cloud augmentation is a popular solution to the problem of limited availability of large-scale public datasets. But the mismatch between mixed points and corresponding semantic labels hinders the further application in point-wise tasks such as part segmentation. This paper proposes a point cloud augmentation approach, PointManifoldCut(PMC), which replaces the neural network embedded points, rather than the Euclidean space coordinates. This approach takes the advantage that points at the higher levels of the neural network are already trained to embed its neighbors relations and mixing these representation will not mingle the relation between itself and its label. We set up a spatial transform module after PointManifoldCut operation to align the new instances in the embedded space. The effects of different hidden layers and methods of replacing points are also discussed in this paper. The experiments show that our proposed approach can enhance the performance of point cloud classification as well as segmentation networks, and brings them additional robustness to attacks and geometric transformations. The code of this paper is available at: https://github.com/fun0515/PointManifoldCut.

cs.CV↗

arXiv2021

Meshfree implementation of the cardiac monodomain model through the Fragile Points Method

Meshfree methods for in silico modelling and simulation of cardiac electrophysiology are gaining more and more popularity. These methods do not require a mesh and are more suitable than the Finite Element Method (FEM) to simulate the activity of complex geometrical structures like the human heart. However, challenges such as numerical integration accuracy and time efficiency remain and limit their applicability. Recently, the Fragile Points Method (FPM) has been introduced in the meshfree methods family. It uses local, simple, polynomial, discontinuous functions to construct trial and test functions in the Galerkin weak form. This allows for accurate integration and improved efficiency while enabling the imposition of essential and natural boundary conditions as in the FEM. In this work, we consider the application of FPM for cardiac electrophysiology simulation. We derive the cardiac monodomain model using the FPM formulation and we solve several benchmark problems in 2D and 3D. We show that FPM leads to solutions of similar accuracy and efficiency with FEM while alleviating the need for a mesh. Additionally, FPM demonstrates better convergence than FEM in the considered benchmarks.

math.NA↗

arXiv2021

Joint Optical Neuroimaging Denoising with Semantic Tasks

Optical neuroimaging is a vital tool for understanding the brain structure and the connection between regions and nuclei. However, the image noise introduced in the sample preparation and the imaging system hinders the extraction of the possible knowlege from the dataset, thus denoising for the optical neuroimaging is usually necessary. The supervised denoisng methods often outperform the unsupervised ones, but the training of the supervised denoising models needs the corresponding clean labels, which is not always avaiable due to the high labeling cost. On the other hand, those semantic labels, such as the located soma positions, the reconstructed neuronal fibers, and the nuclei segmentation result, are generally available and accumulated from everyday neuroscience research. This work connects a supervised denoising and a semantic segmentation model together to form a end-to-end model, which can make use of the semantic labels while still provides a denoised image as an intermediate product. We use both the supervised and the self-supervised models for the denoising and introduce a new cost term for the joint denoising and the segmentation setup. We test the proposed approach on both the synthetic data and the real-world data, including the optical neuroimaing dataset and the electron microscope dataset. The result shows that the joint denoising result outperforms the one using the denoising method alone and the joint model benefits the segmentation and other downstream task as well.

eess.IV↗

arXiv2021

Learning Nash Equilibria in Zero-Sum Stochastic Games via Entropy-Regularized Policy Approximation

We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to approximate the Nash policy during the Q-function updates. We prove that under certain conditions, by updating the regularized Q-function, the algorithm converges to a Nash equilibrium. We also demonstrate the proposed algorithm's ability to transfer previous training experiences, enabling the agents to adapt quickly to new environments. We provide a dynamic hyper-parameter scheduling scheme to further expedite convergence. Empirical results applied to a number of stochastic games verify that the proposed algorithm converges to the Nash equilibrium, while exhibiting a major speed-up over existing algorithms.

cs.LG↗

arXiv2021

Sensitivity Analysis of Passenger Behavioral Model for Dynamic Pricing of Shared Mobility on Demand

This paper provides a framework to quantify the sensitivity associated with behavioral models based on Cumulative Prospect Theory (CPT). These are used to design dynamic pricing strategies aimed at maximizing performance metrics of the Shared Mobility On-Demand Service (SMoDS), as solutions to a constrained nonlinear optimization problem. We analyze the sensitivity of both the optimal tariff as well as the optimal objective function with respect to CPT model parameters. In addition to deriving analytical solutions under certain assumptions, more general numerical results are obtained via computational experiments and simulations to analyze the sensitivity. We find that the model is relatively robust for small to moderate parameter perturbations. Although some of the trends in sensitivity are fairly general, the exact nature of variations in many cases depends heavily on the specific travel scenarios and modes being considered. This is primarily due to the complex nonlinearities in the problem, as well as the significant heterogeneity in passenger preferences across different types of trips.

math.OC↗

arXiv2021

Meshless Fragile Points Methods Based on Petrov-Galerkin Weak-Forms for Transient Heat Conduction Problems in Complex Anisotropic Nonhomogeneous Media

Three kinds of Fragile Points Methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up of the previous study on the original FPM based on a symmetric Galerkin weak-form. The trial function is piecewise-continuous, written as local Taylor expansions at the Fragile Points. A modified Radial Basis Function-based Differential Quadrature (RBF-DQ) method is employed for establishing the local approximation. The Dirac delta function, Heaviside step function, and the local fundamental solution of the governing equation are alternatively used as test functions. Vanishing or pure contour integral formulation in subdomains or on local boundaries can be obtained. Extensive numerical examples in 2D and 3D are provided as validations. The collocation method (PG-FPM-1) is superior in transient analysis with arbitrary point distribution and domain partition. The finite volume method (PG-FPM-2) shows the best efficiency, saving 25% to 50% computational time comparing with the Galerkin FPM. The singular solution method (PG-FPM-3) is highly efficient in steady-state analysis. The anisotropy and nonhomogeneity give rise to no difficulties in all the methods. The proposed PG-FPM approaches represent an improvement to the original Galerkin FPM, as well as to other meshless methods in earlier literature.

math.NA↗

arXiv2020

How Far Does BERT Look At:Distance-based Clustering and Analysis of BERT$'$s Attention

Recent research on the multi-head attention mechanism, especially that in pre-trained models such as BERT, has shown us heuristics and clues in analyzing various aspects of the mechanism. As most of the research focus on probing tasks or hidden states, previous works have found some primitive patterns of attention head behavior by heuristic analytical methods, but a more systematic analysis specific on the attention patterns still remains primitive. In this work, we clearly cluster the attention heatmaps into significantly different patterns through unsupervised clustering on top of a set of proposed features, which corroborates with previous observations. We further study their corresponding functions through analytical study. In addition, our proposed features can be used to explain and calibrate different attention heads in Transformer models.

cs.CL↗

arXiv2020

A New Meshless Fragile Points Method (FPM) With Minimum Unknowns at Each Point, For Flexoelectric Analysis Under Two Theories with Crack Propagation. Part I: Theory and Implementation

Flexoelectricity refers to a phenomenon which involves a coupling of the mechanical strain gradient and electric polarization. In this study, a meshless Fragile Points Method (FPM), is presented for analyzing flexoelectric effects in dielectric solids. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless Differential Quadrature approximation of derivatives. Both primal and mixed FPM are developed, based on two alternate flexoelectric theories, with or without the electric gradient effect and Maxwell stress. In the present primal as well as mixed FPM, only the displacements and electric potential are retained as explicit unknown variables at each internal Fragile Point in the final algebraic equations. Thus the number of unknowns in the final system of algebraic equations is kept to be absolutely minimal. An algorithm for simulating crack initiation and propagation using the present FPM is presented, with classic stress-based criterion as well as a Bonding-Energy-Rate(BER)-based criterion for crack development. The present primal and mixed FPM approaches represent clear advantages as compared to the current methods for computational flexoelectric analyses, using primal as well as mixed Finite Element Methods, Element Free Galerkin (EFG) Methods, Meshless Local Petrov Galerkin (MLPG) Methods, and Isogeometric Analysis (IGA) Methods, because of the following new features: they are simpler Galerkin meshless methods using polynomial trial and test functions; minimal DoFs per Point make it very user-friendly; arbitrary polygonal subdomains make it flexible for modeling complex geometries; the numerical integration of the primal as well as mixed FPM weak forms is trivially simple; and FPM can be easily employed in crack development simulations without remeshing or trial function enhancement.

math.NA↗

arXiv2020

A New Meshless Fragile Points Method (FPM) With Minimum Unknowns at Each Point, For Flexoelectric Analysis Under Two Theories with Crack Propagation. Part II: Validation and discussion

In the first part of this two-paper series, a new Fragile Points Method (FPM), in both primal and mixed formulations, is presented for analyzing flexoelectric effects in 2D dielectric materials. In the present paper, a number of numerical results are provided as validations, including linear and quadratic patch tests, flexoelectric effects in continuous domains, and analyses of stationary cracks in dielectric materials. A discussion of the influence of the electroelastic stress is also given, showing that Maxwell stress could be significant and thus the full flexoelectric theory is recommended to be employed for nano-scale structures. The present primal as well as mixed FPMs also show their suitability and effectiveness in simulating crack initiation and propagation with flexoelectric effect. Flexoelectricity, coupled with piezoelectric effect, can help, hinder, or deflect the crack propagation paths and should not be neglected in nano-scale crack analysis. In FPM, no remeshing or trial function enhancement are required in modeling crack propagation. A new Bonding-Energy-Rate(BER)-based crack criterion as well as classic stress-based criterion are used for crack development simulations. Other complex problems such as dynamic crack developments, fracture, fragmentation and 3D flexoelectric analyses will be given in our future studies.

math.NA↗

arXiv2020

Accelerating Sparse DNN Models without Hardware-Support via Tile-Wise Sparsity

Network pruning can reduce the high computation cost of deep neural network (DNN) models. However, to maintain their accuracies, sparse models often carry randomly-distributed weights, leading to irregular computations. Consequently, sparse models cannot achieve meaningful speedup on commodity hardware (e.g., GPU) built for dense matrix computations. As such, prior works usually modify or design completely new sparsity-optimized architectures for exploiting sparsity. We propose an algorithm-software co-designed pruning method that achieves latency speedups on existing dense architectures. Our work builds upon the insight that the matrix multiplication generally breaks the large matrix into multiple smaller tiles for parallel execution. We propose a tiling-friendly "tile-wise" sparsity pattern, which maintains a regular pattern at the tile level for efficient execution but allows for irregular, arbitrary pruning at the global scale to maintain the high accuracy. We implement and evaluate the sparsity pattern on GPU tensor core, achieving a 1.95x speedup over the dense model.

cs.DC↗

arXiv2020

Towards Dynamic Pricing for Shared Mobility on Demand using Markov Decision Processes and Dynamic Programming

In a Shared Mobility on Demand Service (SMoDS), dynamic pricing plays an important role in the form of an incentive for the decision of the empowered passenger on the ride offer. Strategies for determining the dynamic tariff should be suitably designed so that the incurred demand and supply are balanced and therefore economic efficiency is achieved. In this manuscript, we formulate a discrete time Markov Decision Process (MDP) to determine the probability desired by the SMoDS platform corresponding to the acceptance rate of each empowered passenger at each state of the system. We use Estimated Waiting Time (EWT) as the metric for the balance between demand and supply, with the goal that EWT be regulated around a target value. We then develop a Dynamic Programming (DP) algorithm to derive the optimal policy of the MDP that regulates EWT around the target value. Computational experiments are conducted that demonstrate the regulation of EWT is effective, through various scenarios. The overall demonstration is carried out offline. The MDP formulation together with the DP algorithm can be utilized to an online determination of the dynamic tariff by integrating with our earlier works on Cumulative Prospect Theory based passenger behavioral modeling and the AltMin dynamic routing algorithm, and form the subject of future works.

math.OC↗