Mitigating Reward Hacking in RLHF via Advantage Sign Robustness
Organizations: The University of Tokyo · RIKEN AIP
Abstract
Reward models (RMs) used in reinforcement learning from human feedback (RLHF) are vulnerable to reward hacking: as the policy maximizes a learned proxy reward, true quality plateaus or degrades. We make the assumption that reward hacking is often caused by flipped advantage signs: instead of reducing the likelihood of a bad response, a flipped sign causes the update to increase it. By considering an adversarial perturbation in the RM parameter space, we can derive a certified sign-preservation radius, which is the smallest perturbation that can flip the advantage sign during policy optimization. Based on this formulation, we propose Sign-Certified Policy Optimization (SignCert-PO), down-weighting non-robust completions in the policy gradient update. Unlike prior approaches that require multiple RMs or access to the RM training data, SignCert-PO is lightweight and operates purely at the policy optimization stage using only the RM parameters and on-policy completions. On TL;DR summarization and AlpacaFarm benchmarks, SignCert-PO consistently achieves a better win rate than baselines and reduces reward hacking.
Figures & tables
| Dataset | TL;DR Summarization | AlpacaFarm | ||||
|---|---|---|---|---|---|---|
| Model | P 1B | Q 1.5B | P 2.8B | Q 3B | Q 1.5B | Q 3B |
| SFT | 25.2 | 35.6 | 37.8 | 47.9 | ||
| Dr.GRPO | 68.0 | 90.2 | 32.6 | 46.9 | ||
| UWO | 38.1 | 81.8 | 38.3 | 46.9 | ||
| BSPO | 50.0 | 63.1 | 31.3 | 43.8 | ||
| AdvPO | 69.1 | 90.0 | 37.5 | 50.0 | ||
| Method | Pythia 1B | Qwen2.5 1.5B |
|---|---|---|
| Dr.GRPO | 7.54 | 10.67 |
| UWO | 7.48 | 10.76 |
| BSPO | 9.92 | 13.37 |
| AdvPO | 10.93 | 16.32 |
| SignCert-PO | 7.47 | 10.78 |
Appendix figures & tables15 assets
Supplementary material from the paper’s appendix.
Appendix
| Model | Uncertainty set | Certified radius | Interpretation |
|---|---|---|---|
| Head param. | Feature geometry | ||
| Feature | Advantage magnitude | ||
| Full param. | Gradient sharpness |
| Hyperparameter | Pythia 1B | Pythia 2.8B | Qwen2.5 1.5B | Qwen2.5 3B |
|---|---|---|---|---|
| SFT | ||||
| Epochs | 1 | 1 | 1 | 1 |
| Learning rate | ||||
| LR scheduler | cosine | cosine | cosine | cosine |
| Per-device batch size | 16 | 16 | 16 | 16 |
| bf16 | ✓ | ✓ | ✓ | ✓ |
| Hyperparameter | Pythia 1B | Qwen2.5 1.5B |
|---|---|---|
| Preference data epochs | ||
| Max length | 512 | 512 |
| Learning rate | ||
| LR scheduler | cosine | cosine |
| Warmup ratio | 0.03 | 0.03 |
| Weight decay | 0.1 | 0.1 |
| Hyperparameter | Pythia 1B | Pythia 2.8B | Qwen2.5 1.5B | Qwen2.5 3B |
|---|---|---|---|---|
| Training steps | 2,000 | 2,000 | 500 | 500 |
| Generations per prompt | 8 | 8 | 8 | 8 |
| Max new tokens | 53 | 53 | 63 | 63 |
| Temperature | 1.0 | 1.0 | 1.0 | 1.0 |
| Per-device batch size | 2 | 2 | 2 | 2 |
| Gradient accumulation steps | 16 | 16 | 16 | 16 |
| Method | RM size | Win rate |
|---|---|---|
| UWO ( ) | 410M | |
| UWO ( ) | 1B | 5.9 |
| SignCert-PO | 1B |
| RM Epochs | GRPO | SignCert-PO | |||||
|---|---|---|---|---|---|---|---|
| 1 | 52.89 0.22% | 60.62 0.54% | 60.25 0.41% | 62.04 0.20% | 62.09 0.92% | 62.80 0.54% | 64.63 0.15% |
| 5 | 58.26% | 56.97% | 59.23% | 60.82% | 61.66% | 64.77% | 65.15% |
| 10 | 57.32% | 58.14% | 60.47% | 62.20% | 61.08% | 64.93% | 65.32% |
| 20 | 59.82% | 61.28% | 63.76% | 62.53% | 62.61% | 69.18% | 67.21% |
| RM Epochs | GRPO | SignCert-PO | |||||
|---|---|---|---|---|---|---|---|
| 1 | 65.82 0.88% | 67.09 0.78% | 68.78 0.80% | 69.19 0.56% | 69.32 0.33% | 71.04 0.22% | 71.72 0.70% |
| 5 | 66.94% | 67.05% | 68.84% | 68.55% | 68.25% | 70.54% | 73.28% |
| 10 | 68.22% | 68.48% | 69.99% | 69.83% | 71.86% | 71.11% | 75.94% |
| 20 | 69.51% | 67.95% | 69.30% | 71.22% | 71.32% | 71.96% | 74.31% |
| RM Epochs | GRPO | SignCert-PO | |||||
|---|---|---|---|---|---|---|---|
| 1 | 20.96 4.38% | 20.31 6.40% | 30.08 7.16% | 42.77 1.81% | 49.81 8.98% | 60.03 1.61% | 53.39 3.86% |
| 5 | 63.28% | 50.98% | 52.54% | 67.58% | 67.97% | 66.41% | 49.61% |
| 10 | 55.27% | 66.80% | 73.44% | 70.12% | 71.29% | 77.93% | 67.38% |
| 20 | 64.06% | 53.32% | 56.06% | 48.24% | 47.27% | 42.97% | 49.22% |
| RM Epochs | GRPO | SignCert-PO | |||||
|---|---|---|---|---|---|---|---|
| 1 | 66.86 3.13% | 66.01 1.92% | 65.11 1.27% | 64.06 0.70% | 63.74 1.07% | 60.09 1.27% | 53.58 1.30% |
| 5 | 94.53% | 94.92% | 95.90% | 95.51% | 92.58% | 94.34% | 90.43% |
| 10 | 94.34% | 95.70% | 94.92% | 95.51% | 94.53% | 90.43% | 91.21% |
| 20 | 95.31% | 96.09% | 94.53% | 96.09% | 94.34% | 96.88% | 94.92% |
| Content | GR |
|---|---|
| SUBREDDIT: r/relationships TITLE: Me [17 M] with a girl [16 F] who I don’t know how to let down. POST: There is a backstory behind this so let me give it to everyone straight. I’m 17 M never dated anyone before. I have made posts prior to this one based around my issues with being able to date. My biggest issue is that once a girl peeks my interest I pursue her until she develops the same feelings. Once I understand she is interested too I sort of back off. A friend of mine called me a “chaser” which is what I feel I am. Now I have this girl that I know, really sweet, really smart, talented, the whole thing. I found recently she has feelings for me and we talked a bit about it after I mentioned I was aware of them. When we talked I gave her the impression that I wanted to date her and that we should talk in person and hang out a big more to be dating. The only issue is my gut AGAIN like always is telling me I’m not interested even though I really want to be, I’m just not. | – |
| Reference : I don’t know how to let this girl down after already giving her the impression I wanted to date her. I feel absolutely terrible about it. | |
| Dr.GRPO : talks/ possible dates/ feelings for girl/ situation changed but am I worried about telling/ situation affecting date/ how to let down girlfriend/ options available/ outcome. Advice please but worried about telling/ situation affecting date/ outcome. | |
| AdvPO : communication/dating situation, possibility of dating but am not sure if to let down friend/ possible date/ talk in person/ hang out/ possible outcome. Do I tell friend or risk hurting friendship? worried about outcome. worried about outcome | |
| UWO : Don’t know how to let her down. Help. Help. Help help help. help help. help help. help. not sure how to best approach help help help. not sure how to best approach help. not sure how to tell. not sure how to | |
| BSPO : I’m 17 M never dated before, have feelings for girl, want to date her, but not sure if I’m interested or not. not sure how to let her down. any advice or suggestions would be appreciated. any thoughts or comments would be appreciated. any |
| Content | GR |
|---|---|
| Generate a list of the seven most iconic locations in Colorado. | – |
| Reference : 1. Garden of the Gods – Colorado Springs 2. Maroon Bells – Aspen 3. Mesa Verde National Park – Montezuma 4. Royal Gorge Bridge – Cañon City 5. Red Rocks Amphitheater – Denver 6. Pikes Peak – Colorado Springs 7. Rocky Mountain National Park – Estes Park | |
| Dr.GRPO : The seven most iconic locations in Colorado are: Rocky Mountain National Park, Denver, Colorado, Pikes Peak, Colorado, Colorado Springs, Colorado, and the Great Sand Dunes National Park. Explanation: These locations are iconic because they are known for their natural beauty, adventure, and history. They are also popular tourist destinations and have a lot of cultural and historical significance. They are also easily accessible and offer a variety of activities and experiences. Finally, they are all located in Colorado and are a great way to experience the state. | |
| AdvPO : The seven most iconic locations in Colorado are: Rocky Mountain National Park, Denver, Colorado Springs, Pikes Peak, Colorado Springs, Colorado Springs. These locations are all known for their natural beauty and are popular tourist destinations. They are also home to many famous landmarks and attractions. | |
| UWO : The seven most iconic locations in Colorado are: 1. Rocky Mountains 2. Grand Canyon 3. Mesa Verde 4. Garden of the Gods 5. Pikes Peak 6. Rocky Mountain National Park 7. Denver. These locations are iconic because they are beautiful, unique and have a rich history. They are also popular tourist destinations and have a significant impact on the state’s economy. Therefore, they are considered to be the most iconic locations in Colorado. | |
| BSPO : The seven most iconic locations in Colorado are: Rocky Mountain National Park, Denver, Colorado, Denver International Airport, Denver, Colorado, Denver, Colorado, Denver, Colorado. |
Reward Hacking
Reward hacking studies how AI systems exploit imperfect objectives and how to detect, measure, and prevent behavior that scores well but misses intent.
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