From RLVR to RLSVR: Task Transformation Induces Self-Verifiable Rewards for Open-Ended LLM Self-Improvement

Reinforcement Learning from Verifiable Rewards (RLVR) has improved language models in domains such as mathematics and code, where correctness can be checked automatically. However, many important tasks are only partially verifiable: prompts contain multiple requirements, responses may satisfy some but not all of them, or no single reference answer might exist. We introduce Soft-RLVR, a framework for reinforcement learning from decomposed, learned verification signals. Soft-RLVR converts each prompt into a checklist of atomic requirements, scores candidate responses item by item with an LLM verifier, and trains on the resulting soft reward. Checklist-based rewards turn sparse pass/fail supervision into a denser partial-credit signal, but they also introduce a tradeoff: averaging item-level judgments can reduce verifier noise, while partial credit can reward incomplete responses. We formalize this tradeoff and identify conditions under which checklist-based verification gives a more reliable RL training signal than holistic verification. We further introduce Soft-SVeRL, a self-verifying variant of Soft-RLVR in which the policy also acts as the verifier. We show that self-verification is prone to reward inflation from overly permissive self-judgments, and that explicit stabilization is needed to prevent this collapse. In a controlled instruction-following setting with rule-based ground-truth evaluation, checklist-based Soft-RLVR improves IFEval by up to 11.1 points using only learned verifier rewards. Our experiments further show that verifier quality and checklist quality both affect downstream RL outcomes, and that explicit stabilization is essential for effective self-verification.

RL with verifiable rewards (RLVR) has emerged as a powerful paradigm for training LMs on tasks with well-defined success metrics, such as code generation and mathematical reasoning. However, current RLVR methods optimize only what can be objectively scored, often neglecting subjective, non-verifiable aspects of human-like outputs, such as style and structure. This limitation leads to well-documented failure modes such as diversity collapse, unnatural-sounding responses, and reward hacking. We propose an adversarial generator-discriminator framework that augments verifiable rewards with a learned signal from human demonstrations. A generator model is trained using RL to maximize both task accuracy and an adversarial reward derived from a discriminator. The discriminator, trained alongside the generator policy, learns to distinguish human-written outputs from model-generated ones. The discriminator serves as a learned proxy for the human output distribution, providing feedback on aspects of generation that are difficult to formalize as scalar rewards. Across diverse domains, including bug fixing and open-ended generation, our approach consistently improves non-verifiable properties while preserving the accuracy gains of RLVR. In bug fixing, our method produces solutions with significantly lower edit distance compared to RLVR baselines while matching end performance. In story generation, our method significantly improves win rate while producing stories that are diverse and more human-like. And in a simple reward hacking benchmark, our method nearly eliminates model misbehavior while maintaining high benchmark scores. Together, these results show that our approach bridges RL and SFT, offering a scalable path toward jointly optimizing the verifiable and non-verifiable properties of a task.

Reinforcement learning from verifiable rewards (RLVR) has improved the reasoning abilities of large language models (LLMs), but most existing approaches rely on sparse outcome-level feedback. This sparsity creates a credit assignment challenge in long-horizon agentic reasoning: a trajectory may fail despite containing many correct intermediate decisions, or succeed despite containing flawed ones. In this work, we study a class of densely-verifiable agentic reasoning problems, where intermediate actions can be objectively checked by symbolic or algorithmic oracles. We propose Verifiable Process Rewards (VPR), a framework that converts such oracles into dense turn-level supervision for reinforcement learning, and instantiate it in three representative settings: search-based verification for dynamic deduction, constraint-based verification for logical reasoning, and posterior-based verification for probabilistic inference. We further provide a theoretical analysis showing that dense verifier-grounded rewards can improve long-horizon credit assignment by providing more localized learning signals, with the benefit depending on the reliability of the verifier. Empirically, VPR outperforms outcome-level reward and rollout-based process reward baselines across controlled environments, and more importantly, transfers to both general and agentic reasoning benchmarks, suggesting that verifiable process supervision can foster general reasoning skills applicable beyond the training environments. Our results indicate that VPR is a promising approach for enhancing LLM agents whenever reliable intermediate verification is available, while also highlighting its dependence on oracle quality and the open challenge of extending VPR to less structured, open-ended environments.