Title: LaSeR: Reinforcement Learning with Last-Token Self-Rewarding
Primary area: foundation or frontier models, including LLMs
Keywords: Reinforcement Learning, LLM Reasoning, Self-Rewarding

Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a core paradigm for enhancing the reasoning capabilities of Large Language Models (LLMs). To address the lack of verification signals at test time after RLVR, prior studies incorporate the training of model's self-verification capabilities into the standard RLVR process, thereby unifying reasoning and verification capabilities within a single LLM. However, previous practice requires the LLM to sequentially generate solutions and self-verifications using two separate prompt templates, which doubles the inference cost per sample and significantly reduces efficiency. In this work, we theoretically reveal that the closed-form solution to the RL objective of self-verification training can be approximately reduced to a remarkably simple form: the true reasoning reward of a solution is equal to its last-token self-rewarding score, which is computed as the difference between the policy model's next-token log-probability assigned to any pre-specified token at the solution's last token and a pre-calculated constant, scaled by the KL coefficient. Based on this insight, we propose LaSeR (Reinforcement Learning with Last-Token Self-Rewarding), an algorithm that simply augments the original RLVR loss with a Mean Squared Error (MSE) loss that aligns the last-token self-rewarding scores with the verifier-based reasoning rewards, and jointly optimizes the reasoning and self-rewarding capabilities of LLMs. 
The optimized self-rewarding scores serve as auxiliary reward signals in both training and testing to enhance model performance. 
Notably, our algorithm derives these scores from the predicted next-token probability distribution of the last solution token immediately after solution generation, thereby incurring only the minimal extra cost of at most one additional token inference. 
Experimental results show that our method not only improves the reasoning performance of the model also equips it with remarkable self-rewarding capability, thereby further boosting its inference-time scaling performance.

TL;DR: We propose LaSeR, an highly efficient and effective algorithm for jointly optimizing the reasoning and self-rewarding capabilities of LLMs.