Yeheng Ge

Yuanhang Luo, Yeheng Ge, Ruijian Han et al.

In this work, we study the learning theory of reward modeling with pairwise comparison data using deep neural networks. We establish a novel non-asymptotic regret bound for deep reward estimators in a non-parametric setting, which depends explicitly on the network architecture. Furthermore, to underscore the critical importance of clear human beliefs, we introduce a margin-type condition that assumes the conditional winning probability of the optimal action in pairwise comparisons is significantly distanced from 1/2. This condition enables a sharper regret bound, which substantiates the empirical efficiency of Reinforcement Learning from Human Feedback and highlights clear human beliefs in its success. Notably, this improvement stems from high-quality pairwise comparison data implied by the margin-type condition, is independent of the specific estimators used, and thus applies to various learning algorithms and models.

Xin He, Yeheng Ge, Xingdong Feng

In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some specific settings under certain model assumptions, this paper proposes a general and novel framework for recovering true structures of target functions by using unstructured M-regression in a reproducing kernel Hilbert space (RKHS). The proposed framework is inspired by the fact that gradient functions can be employed as a valid tool to learn underlying structures, including sparse learning, interaction selection and model identification, and it is easy to implement by taking advantage of the nice properties of the RKHS. More importantly, it admits a wide range of loss functions, and thus includes many commonly used methods, such as mean regression, quantile regression, likelihood-based classification, and margin-based classification, which is also computationally efficient by solving convex optimization tasks. The asymptotic results of the proposed framework are established within a rich family of loss functions without any explicit model specifications. The superior performance of the proposed framework is also demonstrated by a variety of simulated examples and a real case study.