Zhe Zhang

Zaiwei Chen, Sheng Zhang, Zhe Zhang et al.

We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically, in the deterministic setting, we prove a fixed-point theorem for seminorm-contractive operators, showing that iterates converge geometrically to the kernel of the seminorm. In the stochastic setting, we analyze the corresponding stochastic approximation (SA) algorithm under seminorm-contractive operators and Markovian noise, providing a finite-sample analysis for various stepsize choices. A benchmark for equation solving is linear systems of equations, where the convergence behavior of fixed-point iteration is closely tied to the stability of linear dynamical systems. In this special case, our results provide a complete characterization of system stability with respect to a seminorm, linking it to the solution of a Lyapunov equation in terms of positive semi-definite matrices. In the stochastic setting, we establish a finite-sample analysis for linear Markovian SA without requiring the Hurwitzness assumption. Our theoretical results offer a unified framework for deriving finite-sample bounds for various reinforcement learning algorithms in the average reward setting, including TD($λ$) for policy evaluation (which is a special case of solving a Poisson equation) and Q-learning for control.

Jie Zhu, Bo Peng, Wanqing Li et al.

This paper proposes a network, referred to as MVSTR, for Multi-View Stereo (MVS). It is built upon Transformer and is capable of extracting dense features with global context and 3D consistency, which are crucial to achieving reliable matching for MVS. Specifically, to tackle the problem of the limited receptive field of existing CNN-based MVS methods, a global-context Transformer module is first proposed to explore intra-view global context. In addition, to further enable dense features to be 3D-consistent, a 3D-geometry Transformer module is built with a well-designed cross-view attention mechanism to facilitate inter-view information interaction. Experimental results show that the proposed MVSTR achieves the best overall performance on the DTU dataset and strong generalization on the Tanks & Temples benchmark dataset.