# Beyond Importance Sampling: Rejection-Gated Policy Optimization

arXiv: https://arxiv.org/abs/2604.14895 · HTML: https://mlsanity.com/paper/2604.14895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and multimodal model alignment, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 16 of its 20 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Diffusion and multimodal model alignment](https://mlsanity.com/alignment/diffusion-and-multimodal-model-alignment/)

## Builds on (most cited first, 16 of 16)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [AWAC: Accelerating Online Reinforcement Learning with Offline Datasets](https://mlsanity.com/paper/2006.09359/) (2020)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [Sample Efficient Actor-Critic with Experience Replay](https://mlsanity.com/paper/1611.01224/) (2016)

## Abstract (arXiv)

We propose a new perspective on policy optimization: rather than reweighting all samples by their importance ratios, an optimizer should select which samples are trustworthy enough to drive a policy update. Building on this view, we introduce Rejection-Gated Policy Optimization (RGPO), which replaces the importance sampling ratio r_theta = pi_theta / pi_old with a smooth, differentiable acceptance gate alpha_theta(s, a) = g(r_theta(s, a)) in the range [0, 1]. Unlike prior work that applies rejection sampling as a data-level heuristic before training, RGPO elevates rejection to an optimization principle: the gate participates directly in gradient computation and is implicitly updated alongside the policy. RGPO provides a unified framework: the policy gradients of TRPO, PPO, and REINFORCE all correspond to specific choices of the effective gradient weight w(r) = g'(r) * r. We prove that RGPO guarantees finite, bounded gradient variance even when importance sampling ratios are heavy-tailed (where IS variance diverges). We further show that RGPO incurs only a bounded, controllable bias and provides an approximate monotonic policy improvement guarantee analogous to TRPO. RGPO matches PPO in computational cost, requires no second-order optimization, and extends naturally to RLHF-style preference alignment. In online preference fine-tuning of Qwen2.5-1.5B-Instruct on Anthropic HH-RLHF (n = 3 seeds), RGPO uses a dual-ratio gate that anchors learning to both the previous policy and the reference model, achieving a Pareto-dominant outcome: the highest reward among online RL methods (+14.8% vs. PPO-RLHF) and the lowest KL divergence to the reference model (-16.0% vs. PPO-RLHF, -53.1% vs. GRPO).