arXiv subjects

Jinchi Chen

Publications and source records attributed to Jinchi Chen.

18 recordsLinked to original sources

arXiv2026

Downlink Channel Matrix Estimation from PMI-Only Feedback in FDD Systems: Maximum Likelihood and Sharp Excess Risk Bound

We study downlink channel estimation in a frequency-division duplex (FDD) massive MIMO system from PMI-only feedback under a 5G NR-type limited-feedback architecture. In this architecture, the user selects a preferred codeword from a shared codebook based on the reduced-dimensional channel and only reports its index (known as the precoding matrix indicator, PMI) back to the base station. Therefore, the channel must be estimated from these highly quantized, nonlinear PMI observations. Based on a probabilistic perturbation model, a constrained maximum likelihood estimator (MLE) is proposed for this estimation problem, whose objective can also be interpreted as a relaxation of the hard empirical decision error. The Cram\'er--Rao bound is derived for the complex-valued model, with the global phase ambiguity handled via gauge-fixing. For the real-valued setting, a global excess-risk bound of order $O(1/\sqrt{T})$ is established, which is then refined to a sharp local rate of order $O(1/T)$ under suitable identifiability conditions. Numerical results show that the MLE asymptotically attains the Cram\'er--Rao bound and outperforms several baseline methods on both synthetic data and realistic FDD channels.

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arXiv2024

Riemannian Gradient Descent Method to Joint Blind Super-Resolution and Demixing in ISAC

Integrated Sensing and Communication (ISAC) has emerged as a promising technology for next-generation wireless networks. In this work, we tackle an ill-posed parameter estimation problem within ISAC, formulating it as a joint blind super-resolution and demixing problem. Leveraging the low-rank structures of the vectorized Hankel matrices associated with the unknown parameters, we propose a Riemannian gradient descent (RGD) method. Our theoretical analysis demonstrates that the proposed method achieves linear convergence to the target matrices under standard assumptions. Additionally, extensive numerical experiments validate the effectiveness of the proposed approach.

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arXiv2024

Fast and Provable Simultaneous Blind Super-Resolution and Demixing for Point Source Signals: Scaled Gradient Descent without Regularization

We address the problem of simultaneously recovering a sequence of point source signals from observations limited to the low-frequency end of the spectrum of their summed convolution, where the point spread functions (PSFs) are unknown. By exploiting the low-dimensional structures of the signals and PSFs, we formulate this as a low-rank matrix demixing problem. To solve this, we develop a scaled gradient descent method without balancing regularization. We establish theoretical guarantees under mild conditions, demonstrating that our method, with spectral initialization, converges to the ground truth at a linear rate, independent of the condition number of the underlying data matrices. Numerical experiments indicate that our approach is competitive with existing convex methods in terms of both recovery accuracy and computational efficiency.

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arXiv2024

Simultaneous Blind Demixing and Super-resolution via Vectorized Hankel Lift

In this work, we investigate the problem of simultaneous blind demixing and super-resolution. Leveraging the subspace assumption regarding unknown point spread functions, this problem can be reformulated as a low-rank matrix demixing problem. We propose a convex recovery approach that utilizes the low-rank structure of each vectorized Hankel matrix associated with the target matrix. Our analysis reveals that for achieving exact recovery, the number of samples needs to satisfy the condition $n\gtrsim Ksr \log (sn)$. Empirical evaluations demonstrate the recovery capabilities and the computational efficiency of the convex method.

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arXiv2024

Global Convergence of Natural Policy Gradient with Hessian-aided Momentum Variance Reduction

Natural policy gradient (NPG) and its variants are widely-used policy search methods in reinforcement learning. Inspired by prior work, a new NPG variant coined NPG-HM is developed in this paper, which utilizes the Hessian-aided momentum technique for variance reduction, while the sub-problem is solved via the stochastic gradient descent method. It is shown that NPG-HM can achieve the global last iterate $\epsilon$-optimality with a sample complexity of $\mathcal{O}(\epsilon^{-2})$, which is the best known result for natural policy gradient type methods under the generic Fisher non-degenerate policy parameterizations. The convergence analysis is built upon a relaxed weak gradient dominance property tailored for NPG under the compatible function approximation framework, as well as a neat way to decompose the error when handling the sub-problem. Moreover, numerical experiments on Mujoco-based environments demonstrate the superior performance of NPG-HM over other state-of-the-art policy gradient methods.

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arXiv2023

On the Linear Convergence of Policy Gradient under Hadamard Parameterization

The convergence of deterministic policy gradient under the Hadamard parameterization is studied in the tabular setting and the linear convergence of the algorithm is established. To this end, we first show that the error decreases at an $O(\frac{1}{k})$ rate for all the iterations. Based on this result, we further show that the algorithm has a faster local linear convergence rate after $k_0$ iterations, where $k_0$ is a constant that only depends on the MDP problem and the initialization. To show the local linear convergence of the algorithm, we have indeed established the contraction of the sub-optimal probability $b_s^k$ (i.e., the probability of the output policy $π^k$ on non-optimal actions) when $k\ge k_0$.

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arXiv2023

A Zeroth-Order Variance-Reduced Method for Decentralized Stochastic Non-convex Optimization

In this paper, we consider a distributed stochastic non-convex optimization problem, which is about minimizing a sum of $n$ local cost functions over a network with only zeroth-order information. A novel single-loop Decentralized Zeroth-Order Variance Reduction algorithm, called DZOVR, is proposed, which combines two-point gradient estimation, momentum-based variance reduction technique, and gradient tracking. Under mild assumptions, we show that the algorithm is able to achieve $\mathcal{O}(dn^{-1}ε^{-3})$ sampling complexity at each node to reach an $ε$-accurate stationary point and also exhibits network-independent and linear speedup properties. To the best of our knowledge, this is the first stochastic decentralized zeroth-order algorithm that achieves this sampling complexity. Numerical experiments demonstrate that DZOVR outperforms the other state-of-the-art algorithms and has network-independent and linear speedup properties.

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arXiv2023

Implicit Regularization and Entrywise Convergence of Riemannian Optimization for Low Tucker-Rank Tensor Completion

This paper is concerned with the low Tucker-rank tensor completion problem, which is about reconstructing a tensor $ T \in\mathbb{R}^{n\times n \times n}$ of low multilinear rank from partially observed entries. Riemannian optimization algorithms are a class of efficient methods for this problem, but the theoretical convergence analysis is still lacking. In this manuscript, we establish the entrywise convergence of the vanilla Riemannian gradient method for low Tucker-rank tensor completion under the nearly optimal sampling complexity $O(n^{3/2})$. Meanwhile, the implicit regularization phenomenon of the algorithm has also been revealed. As far as we know, this is the first work that has shown the entrywise convergence and implicit regularization property of a non-convex method for low Tucker-rank tensor completion. The analysis relies on the leave-one-out technique, and some of the technical results developed in the paper might be of broader interest in investigating the properties of other non-convex methods for this problem.

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arXiv2022

Decentralized Natural Policy Gradient with Variance Reduction for Collaborative Multi-Agent Reinforcement Learning

This paper studies a policy optimization problem arising from collaborative multi-agent reinforcement learning in a decentralized setting where agents communicate with their neighbors over an undirected graph to maximize the sum of their cumulative rewards. A novel decentralized natural policy gradient method, dubbed Momentum-based Decentralized Natural Policy Gradient (MDNPG), is proposed, which incorporates natural gradient, momentum-based variance reduction, and gradient tracking into the decentralized stochastic gradient ascent framework. The $\mathcal{O}(n^{-1}ε^{-3})$ sample complexity for MDNPG to converge to an $ε$-stationary point has been established under standard assumptions, where $n$ is the number of agents. It indicates that MDNPG can achieve the optimal convergence rate for decentralized policy gradient methods and possesses a linear speedup in contrast to centralized optimization methods. Moreover, superior empirical performance of MDNPG over other state-of-the-art algorithms has been demonstrated by extensive numerical experiments.

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arXiv2022

Blind Super-resolution of Point Sources via Projected Gradient Descent

Blind super-resolution can be cast as a low rank matrix recovery problem by exploiting the inherent simplicity of the signal and the low dimensional structure of point spread functions. In this paper, we develop a simple yet efficient non-convex projected gradient descent method for this problem based on the low rank structure of the vectorized Hankel matrix associated with the target matrix. Theoretical analysis indicates that the proposed method exactly converges to the target matrix with a linear convergence rate under the similar conditions as convex approaches. Numerical results show that our approach is competitive with existing convex approaches in terms of recovery ability and efficiency.

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arXiv2022

Blind super-resolution of point sources via fast iterative hard thresholding

In this work, we develop a provable fast algorithm for blind super-resolution based on the low rank structure of vectorized Hankel matrix associated with the target matrix. Theoretical results show that the proposed method converges to the ground truth with linear convergence rate. Numerical experiments are also conducted to illustrate the linear convergence and effectiveness of the proposed approach.

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arXiv2021

Blind Super-resolution via Projected Gradient Descent

Blind super-resolution can be cast as low rank matrix recovery problem by exploiting the inherent simplicity of the signal. In this paper, we develop a simple yet efficient nonconvex method for this problem based on the low rank structure of the vectorized Hankel matrix associated with the target matrix. Theoretical guarantees have been established under the similar conditions as convex approaches. Numerical experiments are also conducted to demonstrate its performance.

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arXiv2021

Vectorized Hankel Lift: A Convex Approach for Blind Super-Resolution of Point Sources

We consider the problem of resolving $ r$ point sources from $n$ samples at the low end of the spectrum when point spread functions (PSFs) are not known. Assuming that the spectrum samples of the PSFs lie in low dimensional subspace (let $s$ denote the dimension), this problem can be reformulated as a matrix recovery problem, followed by location estimation. By exploiting the low rank structure of the vectorized Hankel matrix associated with the target matrix, a convex approach called Vectorized Hankel Lift is proposed for the matrix recovery. It is shown that $n\gtrsim rs\log^4 n$ samples are sufficient for Vectorized Hankel Lift to achieve the exact recovery. For the location retrieval from the matrix, applying the single snapshot MUSIC method within the vectorized Hankel lift framework corresponds to the spatial smoothing technique proposed to improve the performance of the MMV MUSIC for the direction-of-arrival (DOA) estimation.

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arXiv2019

Exact matrix completion based on low rank Hankel structure in the Fourier domain

Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix simplicity is low rank. In this paper we study matrix completion based on another low dimensional structure, namely the low rank Hankel structure in the Fourier domain. It is shown that matrices with this structure can be exactly recovered by solving a convex optimization program provided the sampling complexity is nearly optimal. Empirical results are also presented to justify the effectiveness of the convex method.

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arXiv2019

Towards More Usable Dataset Search: From Query Characterization to Snippet Generation

Reusing published datasets on the Web is of great interest to researchers and developers. Their data needs may be met by submitting queries to a dataset search engine to retrieve relevant datasets. In this ongoing work towards developing a more usable dataset search engine, we characterize real data needs by annotating the semantics of 1,947 queries using a novel fine-grained scheme, to provide implications for enhancing dataset search. Based on the findings, we present a query-centered framework for dataset search, and explore the implementation of snippet generation and evaluate it with a preliminary user study.

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arXiv2019

A Framework for Evaluating Snippet Generation for Dataset Search

Reusing existing datasets is of considerable significance to researchers and developers. Dataset search engines help a user find relevant datasets for reuse. They can present a snippet for each retrieved dataset to explain its relevance to the user's data needs. This emerging problem of snippet generation for dataset search has not received much research attention. To provide a basis for future research, we introduce a framework for quantitatively evaluating the quality of a dataset snippet. The proposed metrics assess the extent to which a snippet matches the query intent and covers the main content of the dataset. To establish a baseline, we adapt four state-of-the-art methods from related fields to our problem, and perform an empirical evaluation based on real-world datasets and queries. We also conduct a user study to verify our findings. The results demonstrate the effectiveness of our evaluation framework, and suggest directions for future research.

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arXiv2017

Stable Recovery of Structured Signals From Corrupted Sub-Gaussian Measurements

This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledge are available. In each case, we provide conditions (in terms of the number of measurements) for stable signal recovery from structured corruption with added unstructured noise. Our results theoretically demonstrate how to choose the regularization parameters in both partially and fully penalized recovery procedures and shed some light on the relationships among the three procedures. The key ingredient in our analysis is an extended matrix deviation inequality for isotropic sub-Gaussian matrices, which implies a tight lower bound for the restricted singular value of the extended sensing matrix. Numerical experiments are presented to verify our theoretical results.

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arXiv2017

Corrupted Sensing with Sub-Gaussian Measurements

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