Reinforcement Learning with Human Feedback (RLHF) is the most prominent method for Language Model (LM) alignment. However, RLHF is an unstable and data-hungry process that continually requires new high-quality LM-generated data for finetuning. We introduce Advantage-Leftover Lunch RL (A-LoL), a new class of offline policy gradient algorithms that enable RL training on any pre-existing data. By assuming the entire LM output sequence as a single action, A-LoL allows incorporating sequence-level classifiers or human-designed scoring functions asrewards. Subsequently, by using LM’s value estimate, A-LoL only trains on positive advantage (leftover) data points, making it resilient to noise. Overall, A-LoL is an easy-to-implement, sample-efficient, and stable LM training recipe.We demonstrate the effectiveness of A-LoL and its variants with a set of four different language generation tasks. We compare against both online RL (PPO) and recent preference-based (DPO, PRO) and reward-based (GOLD) offline RL baselines. On the commonly-used RLHF benchmark, Helpful and Harmless Assistant (HHA), LMs trained with A-LoL methods achieve the highest diversity while also being rated more safe and helpful than the baselines according to humans. Additionally, in the remaining three tasks, A-LoL could optimize multiple distinct reward functions even when using noisy or suboptimal training data.