arXiv subjects

Tianjiao Li

Publications and source records attributed to Tianjiao Li.

32 records · Page 2Linked to original sources

arXiv2024

Accelerated stochastic approximation with state-dependent noise

We consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is assumed to be uniformly bounded, herein we assume that the variance of stochastic gradients is related to the "sub-optimality" of the approximate solutions delivered by the algorithm. Such problems naturally arise in a variety of applications, in particular, in the well-known generalized linear regression problem in statistics. However, to the best of our knowledge, none of the existing stochastic approximation algorithms for solving this class of problems attain optimality in terms of the dependence on accuracy, problem parameters, and mini-batch size. We discuss two non-Euclidean accelerated stochastic approximation routines--stochastic accelerated gradient descent (SAGD) and stochastic gradient extrapolation (SGE)--which carry a particular duality relationship. We show that both SAGD and SGE, under appropriate conditions, achieve the optimal convergence rate, attaining the optimal iteration and sample complexities simultaneously. However, corresponding assumptions for the SGE algorithm are more general; they allow, for instance, for efficient application of the SGE to statistical estimation problems under heavy tail noises and discontinuous score functions. We also discuss the application of the SGE to problems satisfying quadratic growth conditions, and show how it can be used to recover sparse solutions. Finally, we report on some simulation experiments to illustrate numerical performance of our proposed algorithms in high-dimensional settings.

math.OC↗

arXiv2024

A simple uniformly optimal method without line search for convex optimization

Line search (or backtracking) procedures have been widely employed into first-order methods for solving convex optimization problems, especially those with unknown problem parameters (e.g., Lipschitz constant). In this paper, we show that line search is superfluous in attaining the optimal rate of convergence for solving a convex optimization problem whose parameters are not given a priori. In particular, we present a novel accelerated gradient descent type algorithm called auto-conditioned fast gradient method (AC-FGM) that can achieve an optimal $\mathcal{O}(1/k^2)$ rate of convergence for smooth convex optimization without requiring the estimate of a global Lipschitz constant or the employment of line search procedures. We then extend AC-FGM to solve convex optimization problems with Hölder continuous gradients and show that it automatically achieves the optimal rates of convergence uniformly for all problem classes with the desired accuracy of the solution as the only input. Finally, we report some encouraging numerical results that demonstrate the advantages of AC-FGM over the previously developed parameter-free methods for convex optimization.

math.OC↗

arXiv2024

Action Detection via an Image Diffusion Process

Action detection aims to localize the starting and ending points of action instances in untrimmed videos, and predict the classes of those instances. In this paper, we make the observation that the outputs of the action detection task can be formulated as images. Thus, from a novel perspective, we tackle action detection via a three-image generation process to generate starting point, ending point and action-class predictions as images via our proposed Action Detection Image Diffusion (ADI-Diff) framework. Furthermore, since our images differ from natural images and exhibit special properties, we further explore a Discrete Action-Detection Diffusion Process and a Row-Column Transformer design to better handle their processing. Our ADI-Diff framework achieves state-of-the-art results on two widely-used datasets.

cs.CV↗

arXiv2023

SoccerNet 2023 Challenges Results

The SoccerNet 2023 challenges were the third annual video understanding challenges organized by the SoccerNet team. For this third edition, the challenges were composed of seven vision-based tasks split into three main themes. The first theme, broadcast video understanding, is composed of three high-level tasks related to describing events occurring in the video broadcasts: (1) action spotting, focusing on retrieving all timestamps related to global actions in soccer, (2) ball action spotting, focusing on retrieving all timestamps related to the soccer ball change of state, and (3) dense video captioning, focusing on describing the broadcast with natural language and anchored timestamps. The second theme, field understanding, relates to the single task of (4) camera calibration, focusing on retrieving the intrinsic and extrinsic camera parameters from images. The third and last theme, player understanding, is composed of three low-level tasks related to extracting information about the players: (5) re-identification, focusing on retrieving the same players across multiple views, (6) multiple object tracking, focusing on tracking players and the ball through unedited video streams, and (7) jersey number recognition, focusing on recognizing the jersey number of players from tracklets. Compared to the previous editions of the SoccerNet challenges, tasks (2-3-7) are novel, including new annotations and data, task (4) was enhanced with more data and annotations, and task (6) now focuses on end-to-end approaches. More information on the tasks, challenges, and leaderboards are available on https://www.soccer-net.org. Baselines and development kits can be found on https://github.com/SoccerNet.

cs.CV↗

arXiv2023

Elucidating Interfacial Dynamics of Ti-Al Systems Using Molecular Dynamics Simulation and Markov State Modeling

Due to their remarkable mechanical and chemical properties, Ti-Al based materials are attracting considerable interest in numerous fields of engineering, such as automotive, aerospace, and defense. With their low density, high strength, and resistance to corrosion and oxidation, these intermetallic alloys and compound metal-metallic composites have found diverse applications. The present study delves into the interfacial dynamics of these Ti-Al systems, particularly focusing on the behavior of Ti and Al atoms in the presence of TiAl$_3$ grain boundaries under experimental heat treatment conditions. Using a combination of Molecular Dynamics and Markov State Model analyses, we scrutinize the kinetic processes involved in the formation of TiAl$_3$. The Molecular Dynamics simulation indicates that at the early stage of heat treatment, the predominating process is the diffusion of Al atoms towards the Ti surface through the TiAl$_3$ grain boundaries. The Markov State Modeling identifies three distinct dynamic states of Al atoms within the Ti/Al mixture that forms during the process, each exhibiting a unique spatial distribution. Using transition timescales as a qualitative measure of the rapidness of the dynamics, it is observed that the Al dynamics is significantly less rapid near the Ti surface compared to the Al surface. Put together, the results offer a comprehensive understanding of the interfacial dynamics and reveals a three-stage diffusion mechanism. The process initiates with the premelting of Al, proceeds with the prevalent diffusion of Al atoms towards the Ti surface, and eventually ceases as the Ti concentration within the mixture progressively increases. The insights gained from this study could contribute significantly to the control and optimization of manufacturing processes for these high-performing Ti-Al based materials.

cond-mat.mes-hall↗

arXiv2023

Simple and optimal methods for stochastic variational inequalities, I: operator extrapolation

In this paper we first present a novel operator extrapolation (OE) method for solving deterministic variational inequality (VI) problems. Similar to the gradient (operator) projection method, OE updates one single search sequence by solving a single projection subproblem in each iteration. We show that OE can achieve the optimal rate of convergence for solving a variety of VI problems in a much simpler way than existing approaches. We then introduce the stochastic operator extrapolation (SOE) method and establish its optimal convergence behavior for solving different stochastic VI problems. In particular, SOE achieves the optimal complexity for solving a fundamental problem, i.e., stochastic smooth and strongly monotone VI, for the first time in the literature. We also present a stochastic block operator extrapolations (SBOE) method to further reduce the iteration cost for the OE method applied to large-scale deterministic VIs with a certain block structure. Numerical experiments have been conducted to demonstrate the potential advantages of the proposed algorithms. In fact, all these algorithms are applied to solve generalized monotone variational inequality (GMVI) problems whose operator is not necessarily monotone. We will also discuss optimal OE-based policy evaluation methods for reinforcement learning in a companion paper.

math.OC↗

arXiv2023

Token Boosting for Robust Self-Supervised Visual Transformer Pre-training

Learning with large-scale unlabeled data has become a powerful tool for pre-training Visual Transformers (VTs). However, prior works tend to overlook that, in real-world scenarios, the input data may be corrupted and unreliable. Pre-training VTs on such corrupted data can be challenging, especially when we pre-train via the masked autoencoding approach, where both the inputs and masked ``ground truth" targets can potentially be unreliable in this case. To address this limitation, we introduce the Token Boosting Module (TBM) as a plug-and-play component for VTs that effectively allows the VT to learn to extract clean and robust features during masked autoencoding pre-training. We provide theoretical analysis to show how TBM improves model pre-training with more robust and generalizable representations, thus benefiting downstream tasks. We conduct extensive experiments to analyze TBM's effectiveness, and results on four corrupted datasets demonstrate that TBM consistently improves performance on downstream tasks.

cs.CV↗

arXiv2022

Dynamic Spatio-Temporal Specialization Learning for Fine-Grained Action Recognition

The goal of fine-grained action recognition is to successfully discriminate between action categories with subtle differences. To tackle this, we derive inspiration from the human visual system which contains specialized regions in the brain that are dedicated towards handling specific tasks. We design a novel Dynamic Spatio-Temporal Specialization (DSTS) module, which consists of specialized neurons that are only activated for a subset of samples that are highly similar. During training, the loss forces the specialized neurons to learn discriminative fine-grained differences to distinguish between these similar samples, improving fine-grained recognition. Moreover, a spatio-temporal specialization method further optimizes the architectures of the specialized neurons to capture either more spatial or temporal fine-grained information, to better tackle the large range of spatio-temporal variations in the videos. Lastly, we design an Upstream-Downstream Learning algorithm to optimize our model's dynamic decisions during training, improving the performance of our DSTS module. We obtain state-of-the-art performance on two widely-used fine-grained action recognition datasets.

cs.CV↗

arXiv2022

Accelerated and instance-optimal policy evaluation with linear function approximation

We study the problem of policy evaluation with linear function approximation and present efficient and practical algorithms that come with strong optimality guarantees. We begin by proving lower bounds that establish baselines on both the deterministic error and stochastic error in this problem. In particular, we prove an oracle complexity lower bound on the deterministic error in an instance-dependent norm associated with the stationary distribution of the transition kernel, and use the local asymptotic minimax machinery to prove an instance-dependent lower bound on the stochastic error in the i.i.d. observation model. Existing algorithms fail to match at least one of these lower bounds: To illustrate, we analyze a variance-reduced variant of temporal difference learning, showing in particular that it fails to achieve the oracle complexity lower bound. To remedy this issue, we develop an accelerated, variance-reduced fast temporal difference algorithm (VRFTD) that simultaneously matches both lower bounds and attains a strong notion of instance-optimality. Finally, we extend the VRFTD algorithm to the setting with Markovian observations, and provide instance-dependent convergence results. Our theoretical guarantees of optimality are corroborated by numerical experiments.

stat.ML↗

arXiv2022

ERA: Expert Retrieval and Assembly for Early Action Prediction

Early action prediction aims to successfully predict the class label of an action before it is completely performed. This is a challenging task because the beginning stages of different actions can be very similar, with only minor subtle differences for discrimination. In this paper, we propose a novel Expert Retrieval and Assembly (ERA) module that retrieves and assembles a set of experts most specialized at using discriminative subtle differences, to distinguish an input sample from other highly similar samples. To encourage our model to effectively use subtle differences for early action prediction, we push experts to discriminate exclusively between samples that are highly similar, forcing these experts to learn to use subtle differences that exist between those samples. Additionally, we design an effective Expert Learning Rate Optimization method that balances the experts' optimization and leads to better performance. We evaluate our ERA module on four public action datasets and achieve state-of-the-art performance.

cs.CV↗

arXiv2021

Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process

The problem of constrained Markov decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its utilities/costs. A new primal-dual approach is proposed with a novel integration of three ingredients: entropy regularized policy optimizer, dual variable regularizer, and Nesterov's accelerated gradient descent dual optimizer, all of which are critical to achieve a faster convergence. The finite-time error bound of the proposed approach is characterized. Despite the challenge of the nonconcave objective subject to nonconcave constraints, the proposed approach is shown to converge to the global optimum with a complexity of $\tilde{\mathcal O}(1/ε)$ in terms of the optimality gap and the constraint violation, which improves the complexity of the existing primal-dual approach by a factor of $\mathcal O(1/ε)$ \citep{ding2020natural,paternain2019constrained}. This is the first demonstration that nonconcave CMDP problems can attain the complexity lower bound of $\mathcal O(1/ε)$ for convex optimization subject to convex constraints. Our primal-dual approach and non-asymptotic analysis are agnostic to the RL optimizer used, and thus are more flexible for practical applications. More generally, our approach also serves as the first algorithm that provably accelerates constrained nonconvex optimization with zero duality gap by exploiting the geometries such as the gradient dominance condition, for which the existing acceleration methods for constrained convex optimization are not applicable.

math.OC↗

arXiv2021

The Multi-Modal Video Reasoning and Analyzing Competition

In this paper, we introduce the Multi-Modal Video Reasoning and Analyzing Competition (MMVRAC) workshop in conjunction with ICCV 2021. This competition is composed of four different tracks, namely, video question answering, skeleton-based action recognition, fisheye video-based action recognition, and person re-identification, which are based on two datasets: SUTD-TrafficQA and UAV-Human. We summarize the top-performing methods submitted by the participants in this competition and show their results achieved in the competition.

cs.CV↗

arXiv2021

UAV-Human: A Large Benchmark for Human Behavior Understanding with Unmanned Aerial Vehicles

Human behavior understanding with unmanned aerial vehicles (UAVs) is of great significance for a wide range of applications, which simultaneously brings an urgent demand of large, challenging, and comprehensive benchmarks for the development and evaluation of UAV-based models. However, existing benchmarks have limitations in terms of the amount of captured data, types of data modalities, categories of provided tasks, and diversities of subjects and environments. Here we propose a new benchmark - UAVHuman - for human behavior understanding with UAVs, which contains 67,428 multi-modal video sequences and 119 subjects for action recognition, 22,476 frames for pose estimation, 41,290 frames and 1,144 identities for person re-identification, and 22,263 frames for attribute recognition. Our dataset was collected by a flying UAV in multiple urban and rural districts in both daytime and nighttime over three months, hence covering extensive diversities w.r.t subjects, backgrounds, illuminations, weathers, occlusions, camera motions, and UAV flying attitudes. Such a comprehensive and challenging benchmark shall be able to promote the research of UAV-based human behavior understanding, including action recognition, pose estimation, re-identification, and attribute recognition. Furthermore, we propose a fisheye-based action recognition method that mitigates the distortions in fisheye videos via learning unbounded transformations guided by flat RGB videos. Experiments show the efficacy of our method on the UAV-Human dataset. The project page: https://github.com/SUTDCV/UAV-Human

cs.CV↗

arXiv2021

Simple and optimal methods for stochastic variational inequalities, II: Markovian noise and policy evaluation in reinforcement learning

The focus of this paper is on stochastic variational inequalities (VI) under Markovian noise. A prominent application of our algorithmic developments is the stochastic policy evaluation problem in reinforcement learning. Prior investigations in the literature focused on temporal difference (TD) learning by employing nonsmooth finite time analysis motivated by stochastic subgradient descent leading to certain limitations. These encompass the requirement of analyzing a modified TD algorithm that involves projection to an a-priori defined Euclidean ball, achieving a non-optimal convergence rate and no clear way of deriving the beneficial effects of parallel implementation. Our approach remedies these shortcomings in the broader context of stochastic VIs and in particular when it comes to stochastic policy evaluation. We developed a variety of simple TD learning type algorithms motivated by its original version that maintain its simplicity, while offering distinct advantages from a non-asymptotic analysis point of view. We first provide an improved analysis of the standard TD algorithm that can benefit from parallel implementation. Then we present versions of a conditional TD algorithm (CTD), that involves periodic updates of the stochastic iterates, which reduce the bias and therefore exhibit improved iteration complexity. This brings us to the fast TD (FTD) algorithm which combines elements of CTD and the stochastic operator extrapolation method of the companion paper. For a novel index resetting policy FTD exhibits the best known convergence rate. We also devised a robust version of the algorithm that is particularly suitable for discounting factors close to 1.

math.OC↗