# ODRPO: Ordinal Decompositions of Discrete Rewards for Robust Policy Optimization

arXiv: https://arxiv.org/abs/2605.12667 · HTML: https://mlsanity.com/paper/2605.12667/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Process reward models for reasoning, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 19 of its 31 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 19 of 19)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey](https://mlsanity.com/paper/2003.04960/) (2020)
- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [Judging the Judges: A Systematic Study of Position Bias in LLM-as-a-Judge](https://mlsanity.com/paper/2406.07791/) (2024)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [Reinforcement Learning with Rubric Anchors](https://mlsanity.com/paper/2508.12790/) (2025)
- [Enigmata: Scaling Logical Reasoning in Large Language Models with Synthetic Verifiable Puzzles](https://mlsanity.com/paper/2505.19914/) (2025)
- [Evaluating Scoring Bias in LLM-as-a-Judge](https://mlsanity.com/paper/2506.22316/) (2025)
- [ViCrit: A Verifiable Reinforcement Learning Proxy Task for Visual Perception in VLMs](https://mlsanity.com/paper/2506.10128/) (2025)
- [What is the objective of reasoning with reinforcement learning?](https://mlsanity.com/paper/2510.13651/) (2025)
- [The FACTS Leaderboard: A Comprehensive Benchmark for Large Language Model Factuality](https://mlsanity.com/paper/2512.10791/) (2025)
- [Examining Reasoning LLMs-as-Judges in Non-Verifiable LLM Post-Training](https://mlsanity.com/paper/2603.12246/) (2026)
- [Evaluating GRPO and DPO for Faithful Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2512.22631/) (2025)

## Built on by (most cited first, 1 of 1)

- [Tail-Likelihood Reinforcement Learning](https://mlsanity.com/paper/2609.02987/) (2026)

## Abstract (arXiv)

The alignment of Large Language Models (LLMs) utilizes Reinforcement Learning from AI Feedback (RLAIF) for non-verifiable domains such as long-form question answering and open-ended instruction following. These domains often rely on LLM based auto-raters to provide granular, multi-tier discrete rewards (e.g., 1-10 rubrics) that are inherently stochastic due to prompt sensitivity and sampling randomness. We empirically verify the stochasticity of auto-raters that can propagate and corrupt standard advantage estimators like GRPO and MaxRL, as a noisy reward samples can skew normalization statistics and degrade the global learning signal. Empirically, sampling more rewards and taking majority voting may reduce the noise and improve performance, but this approach is computationally expensive. To address this bottleneck, we introduce Ordinal Decomposition for Robust Policy Optimization (ODRPO), a framework that structurally isolates evaluation noise by decomposing discrete rewards into a sequence of ordinal binary indicators. By independently computing and accumulating advantages across these progressively challenging success thresholds, ODRPO prevents outlier evaluations from corrupting the global update while establishing an implicit, variance-aware learning curriculum. Empirically, ODRPO achieves robust performance on Qwen2.5-7B and Qwen3-4B models, outperforming baselines with relative improvements of upto 14.8% on FACTS-grounding-v2 and 7.5% on Alpaca-Evals. Critically, these gains are achieved with negligible training-time overhead, as ODRPO requires no additional compute per step compared to standard estimators. Supported by theoretical analysis confirming its optimization stability, ODRPO provides a scalable and robust framework for aligning models within the noisy, discrete evaluation landscape of modern RLAIF.