Value-Free Policy Optimization via Reward Partitioning

Single-trajectory reinforcement learning (RL) methods aim to optimize policies from datasets consisting of (prompt, response, reward) triplets, where scalar rewards are directly available. This supervision format is highly practical, as it mirrors real-world human feedback, such as thumbs-up/down signals, and avoids the need for structured preference annotations. In contrast, pairwise preference-based methods like Direct Preference Optimization (DPO) rely on datasets with both preferred and dispreferred responses, which are harder to construct and less natural to collect. Among single-trajectory approaches, Direct Reward Optimization (DRO) has shown strong empirical performance due to its simplicity and stability. However, DRO requires approximating a value function, which introduces several limitations: high off-policy variance, coupling between policy and value learning, and a lack of absolute supervision on the policy itself. We introduce Reward Partitioning Optimization (RPO), a new method that resolves these limitations by removing the need to model the value function. Instead, RPO normalizes observed rewards using a partitioning approach estimated directly from data. This leads to a straightforward supervised learning objective on the policy, with no auxiliary models and no joint optimization. RPO provides direct and stable supervision on the policy, making it robust and easy to implement in practice. We validate RPO on scalar-feedback language modeling tasks using Flan-T5 encoder-decoder models. Our results demonstrate that RPO outperforms existing single-trajectory baselines such as DRO and Kahneman-Tversky Optimization (KTO). These findings confirm that RPO is a simple, effective, and theoretically grounded method for single-trajectory policy optimization.