arXiv subjects

Qian Lin

Publications and source records attributed to Qian Lin.

At least 55 records · Page 3Linked to original sources

arXiv2024

The phase diagram of kernel interpolation in large dimensions

The generalization ability of kernel interpolation in large dimensions (i.e., $n \asymp d^γ$ for some $γ>0$) might be one of the most interesting problems in the recent renaissance of kernel regression, since it may help us understand the 'benign overfitting phenomenon' reported in the neural networks literature. Focusing on the inner product kernel on the sphere, we fully characterized the exact order of both the variance and bias of large-dimensional kernel interpolation under various source conditions $s\geq 0$. Consequently, we obtained the $(s,γ)$-phase diagram of large-dimensional kernel interpolation, i.e., we determined the regions in $(s,γ)$-plane where the kernel interpolation is minimax optimal, sub-optimal and inconsistent.

cs.LG↗

arXiv2024

Off-Policy Primal-Dual Safe Reinforcement Learning

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since this estimation serves as the key bond connecting the primal and dual update processes. We show that this problem causes significant underestimation of cost when using off-policy methods, leading to the failure to satisfy the safety constraint. To address this issue, we propose conservative policy optimization, which learns a policy in a constraint-satisfying area by considering the uncertainty in cost estimation. This improves constraint satisfaction but also potentially hinders reward maximization. We then introduce local policy convexification to help eliminate such suboptimality by gradually reducing the estimation uncertainty. We provide theoretical interpretations of the joint coupling effect of these two ingredients and further verify them by extensive experiments. Results on benchmark tasks show that our method not only achieves an asymptotic performance comparable to state-of-the-art on-policy methods while using much fewer samples, but also significantly reduces constraint violation during training. Our code is available at https://github.com/ZifanWu/CAL.

cs.LG↗

arXiv2024

Safe Offline Reinforcement Learning with Real-Time Budget Constraints

Aiming at promoting the safe real-world deployment of Reinforcement Learning (RL), research on safe RL has made significant progress in recent years. However, most existing works in the literature still focus on the online setting where risky violations of the safety budget are likely to be incurred during training. Besides, in many real-world applications, the learned policy is required to respond to dynamically determined safety budgets (i.e., constraint threshold) in real time. In this paper, we target at the above real-time budget constraint problem under the offline setting, and propose Trajectory-based REal-time Budget Inference (TREBI) as a novel solution that models this problem from the perspective of trajectory distribution and solves it through diffusion model planning. Theoretically, we prove an error bound of the estimation on the episodic reward and cost under the offline setting and thus provide a performance guarantee for TREBI. Empirical results on a wide range of simulation tasks and a real-world large-scale advertising application demonstrate the capability of TREBI in solving real-time budget constraint problems under offline settings.

cs.LG↗

arXiv2024

The Optimality of Kernel Classifiers in Sobolev Space

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability $η(x)=\mathbb{P}(Y=1\mid X=x)$, we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of $2η(x)-1$ and apply the method to real datasets.

math.ST↗

arXiv2024

Policy-regularized Offline Multi-objective Reinforcement Learning

In this paper, we aim to utilize only offline trajectory data to train a policy for multi-objective RL. We extend the offline policy-regularized method, a widely-adopted approach for single-objective offline RL problems, into the multi-objective setting in order to achieve the above goal. However, such methods face a new challenge in offline MORL settings, namely the preference-inconsistent demonstration problem. We propose two solutions to this problem: 1) filtering out preference-inconsistent demonstrations via approximating behavior preferences, and 2) adopting regularization techniques with high policy expressiveness. Moreover, we integrate the preference-conditioned scalarized update method into policy-regularized offline RL, in order to simultaneously learn a set of policies using a single policy network, thus reducing the computational cost induced by the training of a large number of individual policies for various preferences. Finally, we introduce Regularization Weight Adaptation to dynamically determine appropriate regularization weights for arbitrary target preferences during deployment. Empirical results on various multi-objective datasets demonstrate the capability of our approach in solving offline MORL problems.

cs.LG↗

arXiv2024

Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions

Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the sample size $n \asymp d^γ$ for some $γ> 0$. Given an RKHS $\mathcal{H}$ associated with an inner product kernel defined on the sphere $\mathbb{S}^{d}$, we suppose that the true function $f_ρ^{*} \in [\mathcal{H}]^{s}$, the interpolation space of $\mathcal{H}$ with source condition $s>0$. We first determined the exact order (both upper and lower bound) of the generalization error of kernel ridge regression for the optimally chosen regularization parameter $λ$. We then further showed that when $0 1$, KRR is not minimax optimal (a.k.a. he saturation effect). Our results illustrate that the curves of rate varying along $γ$ exhibit the periodic plateau behavior and the multiple descent behavior and show how the curves evolve with $s>0$. Interestingly, our work provides a unified viewpoint of several recent works on kernel regression in the large-dimensional setting, which correspond to $s=0$ and $s=1$ respectively.

cs.LG↗

arXiv2023

On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay

The widely observed 'benign overfitting phenomenon' in the neural network literature raises the challenge to the 'bias-variance trade-off' doctrine in the statistical learning theory. Since the generalization ability of the 'lazy trained' over-parametrized neural network can be well approximated by that of the neural tangent kernel regression, the curve of the excess risk (namely, the learning curve) of kernel ridge regression attracts increasing attention recently. However, most recent arguments on the learning curve are heuristic and are based on the 'Gaussian design' assumption. In this paper, under mild and more realistic assumptions, we rigorously provide a full characterization of the learning curve: elaborating the effect and the interplay of the choice of the regularization parameter, the source condition and the noise. In particular, our results suggest that the 'benign overfitting phenomenon' exists in very wide neural networks only when the noise level is small.

cs.LG↗

arXiv2023

Kernel interpolation generalizes poorly

One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in the literature on deep networks. In this paper, under mild conditions, we show that for any $\varepsilon>0$, the generalization error of kernel interpolation is lower bounded by $Ω(n^{-\varepsilon})$. In other words, the kernel interpolation generalizes poorly for a large class of kernels. As a direct corollary, we can show that overfitted wide neural networks defined on the sphere generalize poorly.

cs.LG↗

arXiv2023

Generalization Ability of Wide Residual Networks

In this paper, we study the generalization ability of the wide residual network on $\mathbb{S}^{d-1}$ with the ReLU activation function. We first show that as the width $m\rightarrow\infty$, the residual network kernel (RNK) uniformly converges to the residual neural tangent kernel (RNTK). This uniform convergence further guarantees that the generalization error of the residual network converges to that of the kernel regression with respect to the RNTK. As direct corollaries, we then show $i)$ the wide residual network with the early stopping strategy can achieve the minimax rate provided that the target regression function falls in the reproducing kernel Hilbert space (RKHS) associated with the RNTK; $ii)$ the wide residual network can not generalize well if it is trained till overfitting the data. We finally illustrate some experiments to reconcile the contradiction between our theoretical result and the widely observed ``benign overfitting phenomenon''

stat.ML↗

arXiv2023

On the Optimality of Misspecified Kernel Ridge Regression

In the misspecified kernel ridge regression problem, researchers usually assume the underground true function $f_ρ^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for some $s\in (0,1)$. The existing minimax optimal results require $\|f_ρ^{*}\|_{L^{\infty}}<\infty$ which implicitly requires $s > α_{0}$ where $α_{0}\in (0,1)$ is the embedding index, a constant depending on $\mathcal{H}$. Whether the KRR is optimal for all $s\in (0,1)$ is an outstanding problem lasting for years. In this paper, we show that KRR is minimax optimal for any $s\in (0,1)$ when the $\mathcal{H}$ is a Sobolev RKHS.

cs.LG↗

arXiv2023

Generalization Ability of Wide Neural Networks on $\mathbb{R}$

We perform a study on the generalization ability of the wide two-layer ReLU neural network on $\mathbb{R}$. We first establish some spectral properties of the neural tangent kernel (NTK): $a)$ $K_{d}$, the NTK defined on $\mathbb{R}^{d}$, is positive definite; $b)$ $λ_{i}(K_{1})$, the $i$-th largest eigenvalue of $K_{1}$, is proportional to $i^{-2}$. We then show that: $i)$ when the width $m\rightarrow\infty$, the neural network kernel (NNK) uniformly converges to the NTK; $ii)$ the minimax rate of regression over the RKHS associated to $K_{1}$ is $n^{-2/3}$; $iii)$ if one adopts the early stopping strategy in training a wide neural network, the resulting neural network achieves the minimax rate; $iv)$ if one trains the neural network till it overfits the data, the resulting neural network can not generalize well. Finally, we provide an explanation to reconcile our theory and the widely observed ``benign overfitting phenomenon''.

stat.ML↗

arXiv2023

SMORES-EP, a Modular Robot with Parallel Self-assembly

Self-assembly of modular robotic systems enables the construction of complex robotic configurations to adapt to different tasks. This paper presents a framework for SMORES types of modular robots to efficiently self-assemble into tree topologies. These modular robots form kinematic chains that have been shown to be capable of a large variety of manipulation and locomotion tasks, yet they can reconfigure using a mobile reconfiguration. A desired kinematic topology can be mapped onto a planar pattern with optimal module assignment based on the modules' locations, then the mobile reconfiguration assembly process can be executed in parallel. A docking controller is developed to guarantee the success of docking processes. A hybrid control architecture is designed to handle a large number of modules and complex behaviors of each individual, and achieve efficient and robust self-assembly actions. The framework is demonstrated in both hardware and simulation on the SMORES-EP platform.

cs.RO↗

arXiv2022

A Semi-supervised Learning Approach with Two Teachers to Improve Breakdown Identification in Dialogues

Identifying breakdowns in ongoing dialogues helps to improve communication effectiveness. Most prior work on this topic relies on human annotated data and data augmentation to learn a classification model. While quality labeled dialogue data requires human annotation and is usually expensive to obtain, unlabeled data is easier to collect from various sources. In this paper, we propose a novel semi-supervised teacher-student learning framework to tackle this task. We introduce two teachers which are trained on labeled data and perturbed labeled data respectively. We leverage unlabeled data to improve classification in student training where we employ two teachers to refine the labeling of unlabeled data through teacher-student learning in a bootstrapping manner. Through our proposed training approach, the student can achieve improvements over single-teacher performance. Experimental results on the Dialogue Breakdown Detection Challenge dataset DBDC5 and Learning to Identify Follow-Up Questions dataset LIF show that our approach outperforms all previous published approaches as well as other supervised and semi-supervised baseline methods.

cs.CL↗

arXiv2021

MLCask: Efficient Management of Component Evolution in Collaborative Data Analytics Pipelines

With the ever-increasing adoption of machine learning for data analytics, maintaining a machine learning pipeline is becoming more complex as both the datasets and trained models evolve with time. In a collaborative environment, the changes and updates due to pipeline evolution often cause cumbersome coordination and maintenance work, raising the costs and making it hard to use. Existing solutions, unfortunately, do not address the version evolution problem, especially in a collaborative environment where non-linear version control semantics are necessary to isolate operations made by different user roles. The lack of version control semantics also incurs unnecessary storage consumption and lowers efficiency due to data duplication and repeated data pre-processing, which are avoidable. In this paper, we identify two main challenges that arise during the deployment of machine learning pipelines, and address them with the design of versioning for an end-to-end analytics system MLCask. The system supports multiple user roles with the ability to perform Git-like branching and merging operations in the context of the machine learning pipelines. We define and accelerate the metric-driven merge operation by pruning the pipeline search tree using reusable history records and pipeline compatibility information. Further, we design and implement the prioritized pipeline search, which gives preference to the pipelines that probably yield better performance. The effectiveness of MLCask is evaluated through an extensive study over several real-world deployment cases. The performance evaluation shows that the proposed merge operation is up to 7.8x faster and saves up to 11.9x storage space than the baseline method that does not utilize history records.

cs.SE↗

arXiv2021

Blockchains vs. Distributed Databases: Dichotomy and Fusion

Blockchain has come a long way: a system that was initially proposed specifically for cryptocurrencies is now being adapted and adopted as a general-purpose transactional system. As blockchain evolves into another data management system, the natural question is how it compares against distributed database systems. Existing works on this comparison focus on high-level properties, such as security and throughput. They stop short of showing how the underlying design choices contribute to the overall differences. Our work fills this important gap and provides a principled framework for analyzing the emerging trend of blockchain-database fusion. We perform a twin study of blockchains and distributed database systems as two types of transactional systems. We propose a taxonomy that illustrates the dichotomy across four dimensions, namely replication, concurrency, storage, and sharding. Within each dimension, we discuss how the design choices are driven by two goals: security for blockchains, and performance for distributed databases. To expose the impact of different design choices on the overall performance, we conduct an in-depth performance analysis of two blockchains, namely Quorum and Hyperledger Fabric, and two distributed databases, namely TiDB, and etcd. Lastly, we propose a framework for back-of-the-envelope performance forecast of blockchain-database hybrids.

cs.DB↗

arXiv2020

Boosting High-Level Vision with Joint Compression Artifacts Reduction and Super-Resolution

Due to the limits of bandwidth and storage space, digital images are usually down-scaled and compressed when transmitted over networks, resulting in loss of details and jarring artifacts that can lower the performance of high-level visual tasks. In this paper, we aim to generate an artifact-free high-resolution image from a low-resolution one compressed with an arbitrary quality factor by exploring joint compression artifacts reduction (CAR) and super-resolution (SR) tasks. First, we propose a context-aware joint CAR and SR neural network (CAJNN) that integrates both local and non-local features to solve CAR and SR in one-stage. Finally, a deep reconstruction network is adopted to predict high quality and high-resolution images. Evaluation on CAR and SR benchmark datasets shows that our CAJNN model outperforms previous methods and also takes 26.2% shorter runtime. Based on this model, we explore addressing two critical challenges in high-level computer vision: optical character recognition of low-resolution texts, and extremely tiny face detection. We demonstrate that CAJNN can serve as an effective image preprocessing method and improve the accuracy for real-scene text recognition (from 85.30% to 85.75%) and the average precision for tiny face detection (from 0.317 to 0.611).

cs.CV↗

arXiv2020

Communication-efficient Decentralized Machine Learning over Heterogeneous Networks

In the last few years, distributed machine learning has been usually executed over heterogeneous networks such as a local area network within a multi-tenant cluster or a wide area network connecting data centers and edge clusters. In these heterogeneous networks, the link speeds among worker nodes vary significantly, making it challenging for state-of-the-art machine learning approaches to perform efficient training. Both centralized and decentralized training approaches suffer from low-speed links. In this paper, we propose a decentralized approach, namely NetMax, that enables worker nodes to communicate via high-speed links and, thus, significantly speed up the training process. NetMax possesses the following novel features. First, it consists of a novel consensus algorithm that allows worker nodes to train model copies on their local dataset asynchronously and exchange information via peer-to-peer communication to synchronize their local copies, instead of a central master node (i.e., parameter server). Second, each worker node selects one peer randomly with a fine-tuned probability to exchange information per iteration. In particular, peers with high-speed links are selected with high probability. Third, the probabilities of selecting peers are designed to minimize the total convergence time. Moreover, we mathematically prove the convergence of NetMax. We evaluate NetMax on heterogeneous cluster networks and show that it achieves speedups of 3.7X, 3.4X, and 1.9X in comparison with the state-of-the-art decentralized training approaches Prague, Allreduce-SGD, and AD-PSGD, respectively.

cs.DC↗

arXiv2020

Optimal control of coupled forward-backward stochastic system with jumps and related Hamilton-Jacobi-Bellman equations

In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian motion and Poisson random measure. For this end, we first study the regularity of solutions for this kind of forward-backward stochastic differential equations. We obtain that the value function is a deterministic function and satisfies the dynamic programming principle for this kind of optimal control problem. Moreover, we prove that the value functions is a viscosity solutions of the associated Hamilton-Jacobi-Bellman equations with integral-differential operators.

math.PR↗