arXiv subjects

Qi Lei

Publications and source records attributed to Qi Lei.

At least 55 records · Page 3Linked to original sources

arXiv2022

Reconnecting the Estranged Relationships: Optimizing the Influence Propagation in Evolving Networks

Influence Maximization (IM), which aims to select a set of users from a social network to maximize the expected number of influenced users, has recently received significant attention for mass communication and commercial marketing. Existing research efforts dedicated to the IM problem depend on a strong assumption: the selected seed users are willing to spread the information after receiving benefits from a company or organization. In reality, however, some seed users may be reluctant to spread the information, or need to be paid higher to be motivated. Furthermore, the existing IM works pay little attention to capture user's influence propagation in the future period as well. In this paper, we target a new research problem, named Reconnecting Top-l Relationships (RTlR) query, which aims to find l number of previous existing relationships but being stranged later, such that reconnecting these relationships will maximize the expected benefit of influenced users by the given group in a future period. We prove that the RTlR problem is NP-hard. An efficient greedy algorithm is proposed to answer the RTlR queries with the influence estimation technique and the well-chosen link prediction method to predict the near future network structure. We also design a pruning method to reduce unnecessary probing from candidate edges. Further, a carefully designed order-based algorithm is proposed to accelerate the RTlR queries. Finally, we conduct extensive experiments on real-world datasets to demonstrate the effectiveness and efficiency of our proposed methods.

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arXiv2022

Nearly Minimax Algorithms for Linear Bandits with Shared Representation

We give novel algorithms for multi-task and lifelong linear bandits with shared representation. Specifically, we consider the setting where we play $M$ linear bandits with dimension $d$, each for $T$ rounds, and these $M$ bandit tasks share a common $k(\ll d)$ dimensional linear representation. For both the multi-task setting where we play the tasks concurrently, and the lifelong setting where we play tasks sequentially, we come up with novel algorithms that achieve $\widetilde{O}\left(d\sqrt{kMT} + kM\sqrt{T}\right)$ regret bounds, which matches the known minimax regret lower bound up to logarithmic factors and closes the gap in existing results [Yang et al., 2021]. Our main technique include a more efficient estimator for the low-rank linear feature extractor and an accompanied novel analysis for this estimator.

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arXiv2022

Bi-CLKT: Bi-Graph Contrastive Learning based Knowledge Tracing

The goal of Knowledge Tracing (KT) is to estimate how well students have mastered a concept based on their historical learning of related exercises. The benefit of knowledge tracing is that students' learning plans can be better organised and adjusted, and interventions can be made when necessary. With the recent rise of deep learning, Deep Knowledge Tracing (DKT) has utilised Recurrent Neural Networks (RNNs) to accomplish this task with some success. Other works have attempted to introduce Graph Neural Networks (GNNs) and redefine the task accordingly to achieve significant improvements. However, these efforts suffer from at least one of the following drawbacks: 1) they pay too much attention to details of the nodes rather than to high-level semantic information; 2) they struggle to effectively establish spatial associations and complex structures of the nodes; and 3) they represent either concepts or exercises only, without integrating them. Inspired by recent advances in self-supervised learning, we propose a Bi-Graph Contrastive Learning based Knowledge Tracing (Bi-CLKT) to address these limitations. Specifically, we design a two-layer contrastive learning scheme based on an "exercise-to-exercise" (E2E) relational subgraph. It involves node-level contrastive learning of subgraphs to obtain discriminative representations of exercises, and graph-level contrastive learning to obtain discriminative representations of concepts. Moreover, we designed a joint contrastive loss to obtain better representations and hence better prediction performance. Also, we explored two different variants, using RNN and memory-augmented neural networks as the prediction layer for comparison to obtain better representations of exercises and concepts respectively. Extensive experiments on four real-world datasets show that the proposed Bi-CLKT and its variants outperform other baseline models.

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arXiv2021

Going Beyond Linear RL: Sample Efficient Neural Function Approximation

Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches, little is known about nonlinear RL with neural net approximations of the Q functions. This is the focus of this work, where we study function approximation with two-layer neural networks (considering both ReLU and polynomial activation functions). Our first result is a computationally and statistically efficient algorithm in the generative model setting under completeness for two-layer neural networks. Our second result considers this setting but under only realizability of the neural net function class. Here, assuming deterministic dynamics, the sample complexity scales linearly in the algebraic dimension. In all cases, our results significantly improve upon what can be attained with linear (or eluder dimension) methods.

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arXiv2021

Predicting What You Already Know Helps: Provable Self-Supervised Learning

Self-supervised representation learning solves auxiliary prediction tasks (known as pretext tasks) without requiring labeled data to learn useful semantic representations. These pretext tasks are created solely using the input features, such as predicting a missing image patch, recovering the color channels of an image from context, or predicting missing words in text; yet predicting this \textit{known} information helps in learning representations effective for downstream prediction tasks. We posit a mechanism exploiting the statistical connections between certain {\em reconstruction-based} pretext tasks that guarantee to learn a good representation. Formally, we quantify how the approximate independence between the components of the pretext task (conditional on the label and latent variables) allows us to learn representations that can solve the downstream task by just training a linear layer on top of the learned representation. We prove the linear layer yields small approximation error even for complex ground truth function class and will drastically reduce labeled sample complexity. Next, we show a simple modification of our method leads to nonlinear CCA, analogous to the popular SimSiam algorithm, and show similar guarantees for nonlinear CCA.

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arXiv2021

Provable Hierarchy-Based Meta-Reinforcement Learning

Hierarchical reinforcement learning (HRL) has seen widespread interest as an approach to tractable learning of complex modular behaviors. However, existing work either assume access to expert-constructed hierarchies, or use hierarchy-learning heuristics with no provable guarantees. To address this gap, we analyze HRL in the meta-RL setting, where a learner learns latent hierarchical structure during meta-training for use in a downstream task. We consider a tabular setting where natural hierarchical structure is embedded in the transition dynamics. Analogous to supervised meta-learning theory, we provide "diversity conditions" which, together with a tractable optimism-based algorithm, guarantee sample-efficient recovery of this natural hierarchy. Furthermore, we provide regret bounds on a learner using the recovered hierarchy to solve a meta-test task. Our bounds incorporate common notions in HRL literature such as temporal and state/action abstractions, suggesting that our setting and analysis capture important features of HRL in practice.

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arXiv2021

A Theory of Label Propagation for Subpopulation Shift

One of the central problems in machine learning is domain adaptation. Unlike past theoretical work, we consider a new model for subpopulation shift in the input or representation space. In this work, we propose a provably effective framework for domain adaptation based on label propagation. In our analysis, we use a simple but realistic expansion assumption, proposed in \citet{wei2021theoretical}. Using a teacher classifier trained on the source domain, our algorithm not only propagates to the target domain but also improves upon the teacher. By leveraging existing generalization bounds, we also obtain end-to-end finite-sample guarantees on the entire algorithm. In addition, we extend our theoretical framework to a more general setting of source-to-target transfer based on a third unlabeled dataset, which can be easily applied in various learning scenarios. Inspired by our theory, we adapt consistency-based semi-supervised learning methods to domain adaptation settings and gain significant improvements.

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arXiv2021

Optimal Gradient-based Algorithms for Non-concave Bandit Optimization

Bandit problems with linear or concave reward have been extensively studied, but relatively few works have studied bandits with non-concave reward. This work considers a large family of bandit problems where the unknown underlying reward function is non-concave, including the low-rank generalized linear bandit problems and two-layer neural network with polynomial activation bandit problem. For the low-rank generalized linear bandit problem, we provide a minimax-optimal algorithm in the dimension, refuting both conjectures in [LMT21, JWWN19]. Our algorithms are based on a unified zeroth-order optimization paradigm that applies in great generality and attains optimal rates in several structured polynomial settings (in the dimension). We further demonstrate the applicability of our algorithms in RL in the generative model setting, resulting in improved sample complexity over prior approaches. Finally, we show that the standard optimistic algorithms (e.g., UCB) are sub-optimal by dimension factors. In the neural net setting (with polynomial activation functions) with noiseless reward, we provide a bandit algorithm with sample complexity equal to the intrinsic algebraic dimension. Again, we show that optimistic approaches have worse sample complexity, polynomial in the extrinsic dimension (which could be exponentially worse in the polynomial degree).

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arXiv2021

A Short Note on the Relationship of Information Gain and Eluder Dimension

Eluder dimension and information gain are two widely used methods of complexity measures in bandit and reinforcement learning. Eluder dimension was originally proposed as a general complexity measure of function classes, but the common examples of where it is known to be small are function spaces (vector spaces). In these cases, the primary tool to upper bound the eluder dimension is the elliptic potential lemma. Interestingly, the elliptic potential lemma also features prominently in the analysis of linear bandits/reinforcement learning and their nonparametric generalization, the information gain. We show that this is not a coincidence -- eluder dimension and information gain are equivalent in a precise sense for reproducing kernel Hilbert spaces.

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arXiv2021

Solving Inverse Problems with a Flow-based Noise Model

We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with arbitrary dependencies as well as non-linear forward operators. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns. We also present initial theoretical recovery guarantees for solving inverse problems with a flow prior.

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arXiv2021

Near-Optimal Linear Regression under Distribution Shift

Transfer learning is essential when sufficient data comes from the source domain, with scarce labeled data from the target domain. We develop estimators that achieve minimax linear risk for linear regression problems under distribution shift. Our algorithms cover different transfer learning settings including covariate shift and model shift. We also consider when data are generated from either linear or general nonlinear models. We show that linear minimax estimators are within an absolute constant of the minimax risk even among nonlinear estimators for various source/target distributions.

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arXiv2021

Steepest Descent Neural Architecture Optimization: Escaping Local Optimum with Signed Neural Splitting

Developing efficient and principled neural architecture optimization methods is a critical challenge of modern deep learning. Recently, Liu et al.[19] proposed a splitting steepest descent (S2D) method that jointly optimizes the neural parameters and architectures based on progressively growing network structures by splitting neurons into multiple copies in a steepest descent fashion. However, S2D suffers from a local optimality issue when all the neurons become "splitting stable", a concept akin to local stability in parametric optimization. In this work, we develop a significant and surprising extension of the splitting descent framework that addresses the local optimality issue. The idea is to observe that the original S2D is unnecessarily restricted to splitting neurons into positive weighted copies. By simply allowing both positive and negative weights during splitting, we can eliminate the appearance of splitting stability in S2D and hence escape the local optima to obtain better performance. By incorporating signed splittings, we significantly extend the optimization power of splitting steepest descent both theoretically and empirically. We verify our method on various challenging benchmarks such as CIFAR-100, ImageNet and ModelNet40, on which we outperform S2D and other advanced methods on learning accurate and energy-efficient neural networks.

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arXiv2021

How Fine-Tuning Allows for Effective Meta-Learning

Representation learning has been widely studied in the context of meta-learning, enabling rapid learning of new tasks through shared representations. Recent works such as MAML have explored using fine-tuning-based metrics, which measure the ease by which fine-tuning can achieve good performance, as proxies for obtaining representations. We present a theoretical framework for analyzing representations derived from a MAML-like algorithm, assuming the available tasks use approximately the same underlying representation. We then provide risk bounds on the best predictor found by fine-tuning via gradient descent, demonstrating that the algorithm can provably leverage the shared structure. The upper bound applies to general function classes, which we demonstrate by instantiating the guarantees of our framework in the logistic regression and neural network settings. In contrast, we establish the existence of settings where any algorithm, using a representation trained with no consideration for task-specific fine-tuning, performs as well as a learner with no access to source tasks in the worst case. This separation result underscores the benefit of fine-tuning-based methods, such as MAML, over methods with "frozen representation" objectives in few-shot learning.

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arXiv2021

Few-Shot Learning via Learning the Representation, Provably

This paper studies few-shot learning via representation learning, where one uses $T$ source tasks with $n_1$ data per task to learn a representation in order to reduce the sample complexity of a target task for which there is only $n_2 (\ll n_1)$ data. Specifically, we focus on the setting where there exists a good \emph{common representation} between source and target, and our goal is to understand how much of a sample size reduction is possible. First, we study the setting where this common representation is low-dimensional and provide a fast rate of $O\left(\frac{\mathcal{C}\left(Φ\right)}{n_1T} + \frac{k}{n_2}\right)$; here, $Φ$ is the representation function class, $\mathcal{C}\left(Φ\right)$ is its complexity measure, and $k$ is the dimension of the representation. When specialized to linear representation functions, this rate becomes $O\left(\frac{dk}{n_1T} + \frac{k}{n_2}\right)$ where $d (\gg k)$ is the ambient input dimension, which is a substantial improvement over the rate without using representation learning, i.e. over the rate of $O\left(\frac{d}{n_2}\right)$. This result bypasses the $Ω(\frac{1}{T})$ barrier under the i.i.d. task assumption, and can capture the desired property that all $n_1T$ samples from source tasks can be \emph{pooled} together for representation learning. Next, we consider the setting where the common representation may be high-dimensional but is capacity-constrained (say in norm); here, we again demonstrate the advantage of representation learning in both high-dimensional linear regression and neural network learning. Our results demonstrate representation learning can fully utilize all $n_1T$ samples from source tasks.

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arXiv2020

Fast Convergence of Langevin Dynamics on Manifold: Geodesics meet Log-Sobolev

Sampling is a fundamental and arguably very important task with numerous applications in Machine Learning. One approach to sample from a high dimensional distribution $e^{-f}$ for some function $f$ is the Langevin Algorithm (LA). Recently, there has been a lot of progress in showing fast convergence of LA even in cases where $f$ is non-convex, notably [53], [39] in which the former paper focuses on functions $f$ defined in $\mathbb{R}^n$ and the latter paper focuses on functions with symmetries (like matrix completion type objectives) with manifold structure. Our work generalizes the results of [53] where $f$ is defined on a manifold $M$ rather than $\mathbb{R}^n$. From technical point of view, we show that KL decreases in a geometric rate whenever the distribution $e^{-f}$ satisfies a log-Sobolev inequality on $M$.

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arXiv2020

SGD Learns One-Layer Networks in WGANs

Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax optimization problem to global optimality, but are in practice successfully trained using stochastic gradient descent-ascent. In this paper, we show that, when the generator is a one-layer network, stochastic gradient descent-ascent converges to a global solution with polynomial time and sample complexity.

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arXiv2020

CAT: Customized Adversarial Training for Improved Robustness

Adversarial training has become one of the most effective methods for improving robustness of neural networks. However, it often suffers from poor generalization on both clean and perturbed data. In this paper, we propose a new algorithm, named Customized Adversarial Training (CAT), which adaptively customizes the perturbation level and the corresponding label for each training sample in adversarial training. We show that the proposed algorithm achieves better clean and robust accuracy than previous adversarial training methods through extensive experiments.

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arXiv2019

Communication-Efficient Asynchronous Stochastic Frank-Wolfe over Nuclear-norm Balls

Large-scale machine learning training suffers from two prior challenges, specifically for nuclear-norm constrained problems with distributed systems: the synchronization slowdown due to the straggling workers, and high communication costs. In this work, we propose an asynchronous Stochastic Frank Wolfe (SFW-asyn) method, which, for the first time, solves the two problems simultaneously, while successfully maintaining the same convergence rate as the vanilla SFW. We implement our algorithm in python (with MPI) to run on Amazon EC2, and demonstrate that SFW-asyn yields speed-ups almost linear to the number of machines compared to the vanilla SFW.

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