Peng Yang

Yang Peng

Object detection and tracking are vital and fundamental tasks for autonomous driving, aiming at identifying and locating objects from those predefined categories in a scene. 3D point cloud learning has been attracting more and more attention among all other forms of self-driving data. Currently, there are many deep learning methods for 3D object detection. However, the tasks of object detection and tracking for point clouds still need intensive study due to the unique characteristics of point cloud data. To help get a good grasp of the present situation of this research, this paper shows recent advances in deep learning methods for 3D object detection and tracking.

Yang Peng, Kaicheng Jin, Liangyu Zhang et al.

In this paper, we study the finite-sample statistical rates of distributional temporal difference (TD) learning with linear function approximation. The aim of distributional TD learning is to estimate the return distribution of a discounted Markov decision process for a given policy π. Previous works on statistical analysis of distributional TD learning mainly focus on the tabular case. In contrast, we first consider the linear function approximation setting and derive sharp finite-sample rates. Our theoretical results demonstrate that the sample complexity of linear distributional TD learning matches that of classic linear TD learning. This implies that, with linear function approximation, learning the full distribution of the return from streaming data is no more difficult than learning its expectation (value function). To derive tight sample complexity bounds, we conduct a fine-grained analysis of the linear-categorical Bellman equation and employ the exponential stability arguments for products of random matrices. Our results provide new insights into the statistical efficiency of distributional reinforcement learning algorithms.

Yang Peng, Liangyu Zhang, Zhihua Zhang

Distributional reinforcement learning (DRL) has achieved empirical success in various domains. One core task in DRL is distributional policy evaluation, which involves estimating the return distribution $η^π$ for a given policy $π$. Distributional temporal difference learning has been accordingly proposed, which extends the classic temporal difference learning (TD) in RL. In this paper, we focus on the non-asymptotic statistical rates of distributional TD. To facilitate theoretical analysis, we propose non-parametric distributional TD (NTD). For a $γ$-discounted infinite-horizon tabular Markov decision process, we show that for NTD with a generative model, we need $\tilde{O}(\varepsilon^{-2}μ_{\min}^{-1}(1-γ)^{-3})$ interactions with the environment to achieve an $\varepsilon$-optimal estimator with high probability, when the estimation error is measured by the $1$-Wasserstein. This sample complexity bound is minimax optimal up to logarithmic factors. In addition, we revisit categorical distributional TD (CTD), showing that the same non-asymptotic convergence bounds hold for CTD in the case of the $1$-Wasserstein distance. We also extend our analysis to the more general setting where the data generating process is Markovian. In the Markovian setting, we propose variance-reduced variants of NTD and CTD, and show that both can achieve a $\tilde{O}(\varepsilon^{-2} μ_{π,\min}^{-1}(1-γ)^{-3}+t_{mix}μ_{π,\min}^{-1}(1-γ)^{-1})$ sample complexity bounds in the case of the $1$-Wasserstein distance, which matches the state-of-the-art statistical results for classic policy evaluation. To achieve the sharp statistical rates, we establish a novel Freedman's inequality in Hilbert spaces. This new Freedman's inequality would be of independent interest for statistical analysis of various infinite-dimensional online learning problems.

Kaicheng Jin, Yang Peng, Jiansheng Yang et al.

In this paper, we study the finite-sample statistical rates of distributional temporal difference (TD) learning with linear function approximation. The purpose of distributional TD learning is to estimate the return distribution of a discounted Markov decision process for a given policy. Previous works on statistical analysis of distributional TD learning focus mainly on the tabular case. We first consider the linear function approximation setting and conduct a fine-grained analysis of the linear-categorical Bellman equation. Building on this analysis, we further incorporate variance reduction techniques in our new algorithms to establish tight sample complexity bounds independent of the support size $K$ when $K$ is large. Our theoretical results imply that, when employing distributional TD learning with linear function approximation, learning the full distribution of the return function from streaming data is no more difficult than learning its expectation. This work provide new insights into the statistical efficiency of distributional reinforcement learning algorithms.