Bingyan Wang

Bingyan Wang, Jianqing Fan

This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion problem has attracted much attention in the past decade, there is still lack of theoretical understanding when the observations are contaminated by heavy-tailed noises. Prior theory falls short of explaining the empirical results and is unable to capture the optimal dependence of the estimation error on the noise level. In this paper, we adopt an adaptive Huber loss to accommodate heavy-tailed noise, which is robust against large and possibly asymmetric errors when the parameter in the loss function is carefully designed to balance the Huberization biases and robustness to outliers. Then, we propose an efficient nonconvex algorithm via a balanced low-rank Burer-Monteiro matrix factorization and gradient decent with robust spectral initialization. We prove that under merely bounded second moment condition on the error distributions, rather than the sub-Gaussian assumption, the Euclidean error of the iterates generated by the proposed algorithm decrease geometrically fast until achieving a minimax-optimal statistical estimation error, which has the same order as that in the sub-Gaussian case. The key technique behind this significant advancement is a powerful leave-one-out analysis framework. The theoretical results are corroborated by our simulation studies.

Bingyan Wang, Rongpeng Li, Jianhang Zhu et al.

In recent years, with the rapid development of deep learning and natural language processing technologies, semantic communication has become a topic of great interest in the field of communication. Although existing deep learning-based semantic communication approaches have shown many advantages, they still do not make sufficient use of prior knowledge. Moreover, most existing semantic communication methods focus on the semantic encoding at the transmitter side, while we believe that the semantic decoding capability of the receiver should also be concerned. In this paper, we propose a knowledge enhanced semantic communication framework in which the receiver can more actively utilize the facts in the knowledge base for semantic reasoning and decoding, on the basis of only affecting the parameters rather than the structure of the neural networks at the transmitter side. Specifically, we design a transformer-based knowledge extractor to find relevant factual triples for the received noisy signal. Extensive simulation results on the WebNLG dataset demonstrate that the proposed receiver yields superior performance on top of the knowledge graph enhanced decoding.

Fei Ni, Bingyan Wang, Rongpeng Li et al.

In the swiftly advancing realm of communication technologies, Semantic Communication (SemCom), which emphasizes knowledge understanding and processing, has emerged as a hot topic. By integrating artificial intelligence technologies, SemCom facilitates a profound understanding, analysis and transmission of communication content. In this chapter, we clarify the means of knowledge learning in SemCom with a particular focus on the utilization of Knowledge Graphs (KGs). Specifically, we first review existing efforts that combine SemCom with knowledge learning. Subsequently, we introduce a KG-enhanced SemCom system, wherein the receiver is carefully calibrated to leverage knowledge from its static knowledge base for ameliorating the decoding performance. Contingent upon this framework, we further explore potential approaches that can empower the system to operate in evolving knowledge base more effectively. Furthermore, we investigate the possibility of integration with Large Language Models (LLMs) for data augmentation, offering additional perspective into the potential implementation means of SemCom. Extensive numerical results demonstrate that the proposed framework yields superior performance on top of the KG-enhanced decoding and manifests its versatility under different scenarios.

Bingyan Wang, Yuling Yan, Jianqing Fan

The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space $\mathcal{S}$ and the action space $\mathcal{A}$ are both finite, to obtain a nearly optimal policy with sampling access to a generative model, the minimax optimal sample complexity scales linearly with $|\mathcal{S}|\times|\mathcal{A}|$, which can be prohibitively large when $\mathcal{S}$ or $\mathcal{A}$ is large. This paper considers a Markov decision process (MDP) that admits a set of state-action features, which can linearly express (or approximate) its probability transition kernel. We show that a model-based approach (resp.$~$Q-learning) provably learns an $\varepsilon$-optimal policy (resp.$~$Q-function) with high probability as soon as the sample size exceeds the order of $\frac{K}{(1-γ)^{3}\varepsilon^{2}}$ (resp.$~$$\frac{K}{(1-γ)^{4}\varepsilon^{2}}$), up to some logarithmic factor. Here $K$ is the feature dimension and $γ\in(0,1)$ is the discount factor of the MDP. Both sample complexity bounds are provably tight, and our result for the model-based approach matches the minimax lower bound. Our results show that for arbitrarily large-scale MDP, both the model-based approach and Q-learning are sample-efficient when $K$ is relatively small, and hence the title of this paper.

Yuxin Chen, Jianqing Fan, Bingyan Wang et al.

We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i.e.$~$a sort of random Fourier design and Gaussian design). Despite the wide applicability, the theoretical understanding about these two paradigms remains largely inadequate in the presence of random noise. The current paper makes two contributions by demonstrating that: (1) a two-stage nonconvex algorithm attains minimax-optimal accuracy within a logarithmic number of iterations. (2) convex relaxation also achieves minimax-optimal statistical accuracy vis-à-vis random noise. Both results significantly improve upon the state-of-the-art theoretical guarantees.