Zhong Zheng

Yishun Dou, Zhong Zheng, Qiaoqiao Jin et al.

We propose a novel compact and efficient neural BRDF offering highly versatile material representation, yet with very-light memory and neural computation consumption towards achieving real-time rendering. The results in Figure 1, rendered at full HD resolution on a current desktop machine, show that our system achieves real-time rendering with a wide variety of appearances, which is approached by the following two designs. On the one hand, noting that bidirectional reflectance is distributed in a very sparse high-dimensional subspace, we propose to project the BRDF into two low-dimensional components, i.e., two hemisphere feature-grids for incoming and outgoing directions, respectively. On the other hand, learnable neural reflectance primitives are distributed on our highly-tailored spherical surface grid, which offer informative features for each component and alleviate the conventional heavy feature learning network to a much smaller one, leading to very fast evaluation. These primitives are centrally stored in a codebook and can be shared across multiple grids and even across materials, based on the low-cost indices stored in material-specific spherical surface grids. Our neural BRDF, which is agnostic to the material, provides a unified framework that can represent a variety of materials in consistent manner. Comprehensive experimental results on measured BRDF compression, Monte Carlo simulated BRDF acceleration, and extension to spatially varying effect demonstrate the superior quality and generalizability achieved by the proposed scheme.

Haochen Zhang, Zhong Zheng, Lingzhou Xue

We present the first gap-dependent analysis of regret and communication cost for on-policy federated $Q$-Learning in tabular episodic finite-horizon Markov decision processes (MDPs). Existing FRL methods focus on worst-case scenarios, leading to $\sqrt{T}$-type regret bounds and communication cost bounds with a $\log T$ term scaling with the number of agents $M$, states $S$, and actions $A$, where $T$ is the average total number of steps per agent. In contrast, our novel framework leverages the benign structures of MDPs, such as a strictly positive suboptimality gap, to achieve a $\log T$-type regret bound and a refined communication cost bound that disentangles exploration and exploitation. Our gap-dependent regret bound reveals a distinct multi-agent speedup pattern, and our gap-dependent communication cost bound removes the dependence on $MSA$ from the $\log T$ term. Notably, our gap-dependent communication cost bound also yields a better global switching cost when $M=1$, removing $SA$ from the $\log T$ term.

Haochen Zhang, Zhong Zheng, Lingzhou Xue

We study fine-grained gap-dependent regret bounds for model-free reinforcement learning in episodic tabular Markov Decision Processes. Existing model-free algorithms achieve minimax worst-case regret, but their gap-dependent bounds remain coarse and fail to fully capture the structure of suboptimality gaps. We address this limitation by establishing fine-grained gap-dependent regret bounds for both UCB-based and non-UCB-based algorithms. In the UCB-based setting, we develop a novel analytical framework that explicitly separates the analysis of optimal and suboptimal state-action pairs, yielding the first fine-grained regret upper bound for UCB-Hoeffding (Jin et al., 2018). To highlight the generality of this framework, we introduce ULCB-Hoeffding, a new UCB-based algorithm inspired by AMB (Xu et al.,2021) but with a simplified structure, which enjoys fine-grained regret guarantees and empirically outperforms AMB. In the non-UCB-based setting, we revisit the only known algorithm AMB, and identify two key issues in its algorithm design and analysis: improper truncation in the $Q$-updates and violation of the martingale difference condition in its concentration argument. We propose a refined version of AMB that addresses these issues, establishing the first rigorous fine-grained gap-dependent regret for a non-UCB-based method, with experiments demonstrating improved performance over AMB.