Learning Guarantee of Reward Modeling Using Deep Neural Networks

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.

Transfer Learning through Enhanced Sufficient Representation: Enriching Source Domain Knowledge with Target Data

Transfer learning is an important approach for addressing the challenges posed by limited data availability in various applications. It accomplishes this by transferring knowledge from well-established source domains to a less familiar target domain. However, traditional transfer learning methods often face difficulties due to rigid model assumptions and the need for a high degree of similarity between source and target domain models. In this paper, we introduce a novel method for transfer learning called Transfer learning through Enhanced Sufficient Representation (TESR). Our approach begins by estimating a sufficient and invariant representation from the source domains. This representation is then enhanced with an independent component derived from the target data, ensuring that it is sufficient for the target domain and adaptable to its specific characteristics. A notable advantage of TESR is that it does not rely on assuming similar model structures across different tasks. For example, the source domain models can be regression models, while the target domain task can be classification. This flexibility makes TESR applicable to a wide range of supervised learning problems. We explore the theoretical properties of TESR and validate its performance through simulation studies and real-world data applications, demonstrating its effectiveness in finite sample settings.