# Learn What's Left, Not What's Mastered: Saturation Aware Advantage Reweighting for Multi-Reward Policy Optimization

arXiv: https://arxiv.org/abs/2608.16072 · HTML: https://mlsanity.com/paper/2608.16072/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL training of language and agent models, one of 15 directions in Deep reinforcement learning methods.
- Builds on 29 of its 32 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Placed in

- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 29 of 29)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [ShieldAgent: Shielding Agents via Verifiable Safety Policy Reasoning](https://mlsanity.com/paper/2503.22738/) (2025)
- [Beyond One-Preference-Fits-All Alignment: Multi-Objective Direct Preference Optimization](https://mlsanity.com/paper/2310.03708/) (2023)
- [Thinkless: LLM Learns When to Think](https://mlsanity.com/paper/2505.13379/) (2025)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [R2R: Efficiently Navigating Divergent Reasoning Paths with Small-Large Model Token Routing](https://mlsanity.com/paper/2505.21600/) (2025)
- [Gradient-Adaptive Policy Optimization: Towards Multi-Objective Alignment of Large Language Models](https://mlsanity.com/paper/2507.01915/) (2025)
- [Learning to Optimize Multi-Objective Alignment Through Dynamic Reward Weighting](https://mlsanity.com/paper/2509.11452/) (2025)
- [Multi-Objective Alignment of Large Language Models Through Hypervolume Maximization](https://mlsanity.com/paper/2412.05469/) (2024)
- [Multi-Task GRPO: Reliable LLM Reasoning Across Tasks](https://mlsanity.com/paper/2602.05547/) (2026)
- [Towards Safe Reasoning in Large Reasoning Models via Corrective Intervention](https://mlsanity.com/paper/2509.24393/) (2025)
- [AMoPO: Adaptive Multi-objective Preference Optimization without Reward Models and Reference Models](https://mlsanity.com/paper/2506.07165/) (2025)
- [FROST: Filtering Reasoning Outliers with Attention for Efficient Reasoning](https://mlsanity.com/paper/2601.19001/) (2026)
- [Focal Reward: Balanced Reinforcement Learning under Rubric-Based Rewards](https://mlsanity.com/paper/2605.26579/) (2026)
- [DVAO: Dynamic Variance-adaptive Advantage Optimization for Multi-reward Reinforcement Learning](https://mlsanity.com/paper/2605.25604/) (2026)
- [SAW: Stage-Aware Dynamic Weighting for Multi-Objective Reinforcement Learning in Large Language Models](https://mlsanity.com/paper/2606.07705/) (2026)
- [GD2PO: Mitigating Multi-Reward Conflicts via Group-Dynamic reward-Decoupled Policy Optimization](https://mlsanity.com/paper/2606.16771/) (2026)
- [SMOPD: Multi-Reward Reinforcement Learning via Specialize-and-Merge Online Policy Distillation](https://mlsanity.com/paper/2608.03092/) (2026)
- [Don't Mix Rewards, Mix Policies: Policy Decomposition and Optimization for Multi-Reward RL](https://mlsanity.com/paper/2607.29246/) (2026)

## Built on by (most cited first, 2 of 2)

- [MatrixReward: Reward from Rubric Matrix for Open-Ended Generation](https://mlsanity.com/paper/2610.00389/) (2026)
- [Make Sparse Rewards Count: Density-Aware Reward Aggregation for Multi-Reward RL](https://mlsanity.com/paper/2610.00574/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) with group-relative advantages has become the de facto standard for post-training language model reasoners. However, when optimizing multiple reward objectives, existing methods typically scalarize the reward vector with a fixed weighted sum before group-wise standardization. We show that this design leads to two fundamental problems: rollouts with distinct reward profiles can receive identical advantages, and all objectives are optimized with fixed relative weights regardless of their current level of saturation. Consequently, an objective whose rewards are already near their upper bound can retain substantial influence when its rewards still vary within rollout groups. We introduce Saturation Aware Advantage Reweighting for Multi-Reward Policy Optimization (SA-MRPO), which standardizes each reward objective independently and adaptively discounts its contribution according to a batch-level estimate of objective saturation. This changes the relative contribution of each objective according to its observed reward headroom. We further derive an exact condition under which saturation aware reweighting reverses the sign of a rollout's aggregate advantage. Across mathematical reasoning with two- and three-objective reward combinations, SA-MRPO improves the harder correctness objective over GDPO in 12 of 15 benchmark comparisons, with gains of up to 5% on AIME24. On adaptive reasoning it improves accuracy on all five benchmarks, by 3.8% on average and up to 9.2 % on AMC23, and on coding benchmarks it improves pass rate by up to 2.3%, while in all settings maintaining the easier objectives near their already satisfied levels. Additional experiments characterize the accompanying reward tradeoffs and sensitivity to corrupted rewards.