Direct alignment algorithms (DAAs), such as direct preference optimization (DPO), have become popular alternatives to Reinforcement Learning from Human Feedback (RLHF) due to their simplicity, efficiency, and stability. However, the preferences used by DAAs are usually collected before alignment training begins and remain unchanged (off-policy). This design leads to two problems where the policy model (1) picks up on spurious correlations in the dataset (as opposed to only learning alignment to human preferences), and (2) overfits to feedback on off-policy trajectories that have less likelihood of being generated by the updated policy model. To address these issues, we introduce Self-Reviewing and Alignment (SeRA), a cost-efficient and effective method that can be readily combined with existing DAAs. SeRA comprises of two components: (1) sample selection using implicit reward margin to alleviate over-optimization on such undesired features, and (2) preference bootstrapping using implicit rewards to augment preference data with updated policy models in a cost-efficient manner. Extensive experiments, including on instruction-following tasks, demonstrate the effectiveness and generality of SeRA in training LLMs with diverse offline preference datasets and and DAAs.