Near-Future Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) plays a pivotal role in improving the reasoning ability of large language models. However, widely used PPO surrogate objectives are fundamentally local, as they rely on a local approximation of the exact policy gradient objective. While this approximation improves stability by reducing the variance induced by importance sampling, it also introduces structural bias into the surrogate objective, which must be controlled through trust region mechanisms. In this work, we introduce the $N$-step forward trace, which augments the PPO surrogate objective using the cumulative likelihood ratio of the next $N-1$ tokens. Building on this idea, we propose $N$-Step Forward-Trace Policy Optimization (NFPO), a practical RLVR algorithm that integrates the $N$-step forward trace into the masked policy gradient framework. NFPO provides a continuous bridge between the PPO surrogate objective and the exact policy gradient objective, offering a principled mechanism for controlling the bias-variance trade-off. Our theoretical analysis shows that, with an appropriate choice of $N$, the proposed objective yields a tighter policy-improvement bound than the standard PPO surrogate. Experiments on comprehensive reasoning benchmarks demonstrate that NFPO consistently improves performance, supporting our theoretical findings.

Reinforcement learning with verifiable rewards is typically performed on-policy, keeping training data close to the current policy but limiting learning to trajectories that the policy can discover itself. Off-policy methods such as supervised fine-tuning, on the other hand, can leverage external knowledge beyond the base model's capabilities, but may suffer from large distribution shift. The key challenge is thus to expand exploration without sacrificing learnability. In this work, we introduce Minimal Intervention Reinforcement Learning (MInTRL), which expands the exploration frontier through sparse, local interventions in otherwise on-policy rollouts. During generation, a judge-intervention policy periodically reviews the current policy's output, replaces erroneous suffixes with short corrections, and immediately returns control to the policy. During training, MInTRL adopts a sequence-level advantage-regression objective that eliminates the need for importance sampling. We show that sparse, local interventions can substantially improve coverage beyond finite-budget on-policy sampling while preserving the overall on-policy nature of the resulting trajectories. Across math and code benchmarks, MInTRL consistently outperforms standard on-policy and off-policy baselines. Ablations show that MInTRL remains effective with self-intervention and across different judge policies, while performance peaks at moderate intervention intensity, highlighting the importance of intervening minimally. These results establish minimal intervention as an effective paradigm for enhancing on-policy RL.

Reinforcement learning has become a central post-training paradigm for improving LLM and agent capabilities. Yet existing RL post-training methods share a common blind spot: they construct local learning signals from sampled trajectories, rewards, or feedback-conditioned targets, then update the policy without explicitly verifying whether the resulting policy outperforms its predecessor. Optimizing these local signals does not necessarily produce a better policy, while finite sampling, generation stochasticity and feedback noise can further widen this gap. We argue that the missing ingredient is policy improvement feedback: the ability to measure progress across policy iterations. We introduce Policy Improvement Reinforcement Learning (PIRL), which formulates inter-iteration performance gain as an explicit objective structurally aligned with final task performance. Building on PIRL, we propose Policy Improvement Policy Optimization (PIPO), a plug-in closed-loop framework that verifies the previous update against a sliding-window historical performance anchor. PIPO uses this improvement feedback to modulate the local learning signal of the base policy optimization algorithm, reinforcing updates associated with measured progress and suppressing those associated with performance drops. We provide theoretical evidence that PIPO locally aligns policy updates with the PIRL improvement objective. Experiments on mathematical reasoning, code, tool-use, and self-distillation settings show that PIPO yields consistent gains across PPO, group-relative, and self-distillation policy optimization families.