Temporal difference (TD) learning algorithms with neural network function
parameterization have well-established empirical success in many practical
large-scale reinforcement learning tasks. However, theoretical understanding of
these algorithms remains challenging due to the nonlinearity of the
action-value approximation. In this paper, we develop an improved
non-asymptotic analysis of the neural TD method with a general $L$-layer neural
network. New proof techniques are developed and an improved new
$\tilde{\mathcal{O}}(\epsilon^{-1})$ sample complexity is derived. To our best
knowledge, this is the first finite-time analysis of neural TD that achieves an
$\tilde{\mathcal{O}}(\epsilon^{-1})$ complexity under the Markovian sampling,
as opposed to the best known $\tilde{\mathcal{O}}(\epsilon^{-2})$ complexity in
the existing literature.

本文基于非线性的动作价值逼近，对具有神经网络函数参数化的时序差异（TD）学习算法进行改进的有限时间分析，得到了一种改进的新的样本复杂度 Ο̃(ε^(-1))，在马尔可夫采样下取得了 Ο̃(ε^(-1)) 的复杂度，相比现有文献中已知的 Ο̃(ε^(-2)) 复杂度是第一次实现的研究。

改进的有限时间分析：基于深度神经网络的时差学习

An Improved Finite-time Analysis of Temporal Difference Learning with  Deep Neural Networks

This paper addresses a kernel-based learning problem for a network of agents
locally observing a latent multidimensional, nonlinear phenomenon in a noisy
environment. We propose a learning algorithm that requires only mild a priori
knowledge about the phenomenon under investigation and delivers a model with
corresponding non-asymptotic high probability error bounds. Both non-asymptotic
analysis of the method and numerical simulation results are presented and
discussed in the paper.

本文讨论了网络中观察到噪声环境下潜在多维非线性现象的基于核的学习问题，提出了一种学习算法，仅需要关于研究对象的轻微先验知识，并提供了相应的非渐近高概率误差界限的模型。本文还提供了方法的非渐近分析和数值模拟结果。

基于核的学习在多智能体应用中的保证

Kernel-based learning with guarantees for multi-agent applications

We perform a non-asymptotic analysis on the singular vector distribution
under Gaussian noise. In particular, we provide sufficient conditions on a
matrix for its first few singular vectors to have near normal distribution. Our
result can be used to facilitate the error analysis in linear dimension
reduction.

本文对高斯噪声下的奇异向量分布进行了非渐近分析，特别地，我们给出了一个矩阵的充分条件，使其前几个奇异向量具有近似正态分布。我们的结果可用于线性降维中的误差分析。