TPO: Tri-level Distributionally Robust Learning for OOD Direct Preference Optimization
Organizations: School of Computer Science and Technology, Tongji University, Shanghai, China · Shenzhen Loop Area Institute, Shenzhen, China · Shanghai Research Institute for Intelligent Autonomous Systems, Shanghai, China
Abstract
Direct Preference Optimization (DPO) minimizes empirical risk over observed preference comparisons, implicitly assuming that the training preference distribution matches the deployment preference distribution. In practice, this i.i.d. assumption often fails, as preference distribution shift exhibits a natural hierarchical structure across three levels: group-level shift, prompt-level shift, and preference-level shift. Such multi-level distributional mismatch poses a critical challenge for safe LLM deployment, yet existing robust DPO methods typically either model uncertainty over the joint preference distribution or focus on individual sources of shift, leaving the hierarchical structure of OOD preference shifts underexplored. We propose TPO, a tri-level distributionally robust framework for OOD preference alignment, which jointly models all three levels of distributional uncertainty through a hierarchically structured rectangular ambiguity set. By instantiating it with Wasserstein distance, we derive a tractable and interpretable objective that combines a closed-form preference-level margin penalty, prompt-level adversarial embedding perturbation, and worst-case group reweighting, each governed by an independent radius. We establish finite-sample convergence guarantees and empirically validate the effectiveness of TPO over existing robust DPO methods.
Figures & tables
| Methods | Overall | Group-level | Prompt-level | Preference-level |
| DPO ( Rafailov et al., 2023 ) | ✗ | ✗ | ✗ | ✗ |
| WDPO / KLDPO ( Xu et al., 2025 ) | ✓ | ✗ | ✗ | ✗ |
| GRPO ( Ramesh et al., 2024 ) | ✗ | ✓ | ✗ | ✗ |
| rDPO ( Chowdhury et al., 2024 ) | ✗ | ✗ | ✗ | ✓ |
| Dr.DPO ( Wu et al., 2025 ) | ✗ | ✗ | ✗ | ✓ |
| TPO (Ours) | ✓ | ✓ | ✓ | ✓ |
| Qwen-2.5-0.5B | ID | Group | Prompt | Preference | Combined | Avg. Rank | |||||
| Avg Acc | Worst Acc | Avg Acc | Worst Acc | Avg Acc | Worst Acc | Avg Acc | Worst Acc | Avg Acc | Worst Acc | ||
| DPO | 86.87 | 77.78 | 81.80 | 76.15 | 83.17 | 76.98 | 82.93 | 78.16 | 82.60 | 76.40 | 5.30 |
| Dr.DPO | 84.81 | 81.36 | 81.65 | 77.06 | 82.75 | 76.84 | 82.24 | 75.86 | 81.27 | 75.22 | 6.50 |
| WDPO | 84.87 | 84.13 | 82.72 | 78.90 | 85.08 | 82.20 | 84.01 | 81.46 | 84.21 | 78.76 | 3.20 |
| TPO (Group) | 84.90 | 77.27 | 82.96 | 76.76 | 83.46 | 78.28 | 82.31 | 79.24 | 82.06 | 76.11 | 5.25 |
| TPO (Prompt) | 85.93 | 83.77 | 82.84 | 80.43 | 84.69 | 81.05 | 85.02 | 83.03 | 84.37 | 79.65 | 2.40 |
| LLaMA-3.2-1B | LLaMA-3.2-3B | LLaMA-3.1-8B | ||||||||||
| Task | DPO | TPO | DPO | TPO | DPO | TPO | ||||||
| MMLU-Pro | 20.0 | 20.5 | 20.5 | 20.2 | 31.2 | 31.5 | 31.5 | 31.7 | 36.8 | 36.7 | 37.1 | 37.1 |
| BBH | 35.6 | 35.8 | 35.9 | 35.6 | 45.2 | 45.6 | 45.9 | 45.7 | 51.1 | 50.9 | 51.7 | 51.3 |
| GPQA | 23.2 | 23.5 | 23.7 | 23.3 | 28.0 | 28.4 | 28.3 | 28.1 | 30.0 | 30.2 | 30.8 | 30.1 |
| MATH-Hard | 8.1 | 9.4 | 8.3 | 8.2 | 21.4 | 21.1 | 20.1 | 21.0 | 19.5 | 20.9 | 20.7 | 19.3 |
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
| Environment | Group Proportions | Prompt Perturbation | Reward Mixture |
| train | Skewed | None | |
| val | Skewed | None | |
| id_test | Skewed | None | |
| group_test | Uniform | None | |
| prompt_test | Skewed | Synonym substitution | |
| preference_test | Skewed | None |
| Hyperparameter | Search Range |
| Qwen-2.5-0.5B | ID | Global | Prompt | Preference | Combined | |||||
| Avg Acc | Worst Acc | Avg Acc | Worst Acc | Avg Acc | Worst Acc | Avg Acc | Worst Acc | Avg Acc | Worst Acc | |
| DPO | 86.87 0.32 | 77.78 0.87 | 81.80 0.15 | 76.15 0.92 | 83.17 0.46 | 76.98 1.10 | 82.93 0.49 | 78.16 1.99 | 82.60 0.92 | 76.40 0.51 |
| Dr.DPO | 84.81 0.23 | 81.36 1.02 | 81.65 0.35 | 77.06 0.78 | 82.75 0.69 | 76.84 1.22 | 82.24 0.44 | 75.86 1.65 | 81.27 0.94 | 75.22 0.73 |
| WDPO | 84.87 0.29 | 84.13 1.18 | 82.72 0.16 | 78.90 0.49 | 85.08 0.22 | 82.20 2.36 | 84.01 0.65 | 81.46 1.83 | 84.21 0.31 | 78.76 1.14 |
| TPO (Group) | 84.90 0.32 | 77.27 1.52 | 82.96 0.23 | 76.76 1.40 | 83.46 0.32 | 78.28 0.87 | 82.31 0.22 | 79.24 0.12 | 82.06 0.23 | 76.11 0.88 |
| TPO (Prompt) | 85.93 0.55 | 83.77 0.76 | 82.84 0.26 | 80.43 2.12 | 84.69 0.70 | 81.05 2.11 | 85.02 0.97 | 83.03 1.61 | 84.37 0.39 | 79.65 0.88 |
| Model | Method | ID | Group | Prompt | Preference | Combined | |||||
| Avg | Worst | Avg | Worst | Avg | Worst | Avg | Worst | Avg | Worst | ||
| Qwen2.5-0.5B | DPO | 86.87 | 77.78 | 81.80 | 76.15 | 83.17 | 76.98 | 82.93 | 78.16 | 82.60 | 76.40 |
| TPO | 86.95 | 85.12 | 84.61 | 81.65 | 85.47 | 82.56 | 85.44 | 82.34 | 85.25 | 79.94 | |
| LLaMA-3.2-1B | DPO | 88.75 | 86.19 | 88.23 | 83.44 | 87.81 | 85.43 | 86.91 | 81.42 | 87.44 | 82.61 |
| TPO | 90.57 | 87.55 | 89.11 | 83.50 | 89.14 | 86.70 | 88.25 | 81.31 | 88.31 | 83.19 | |
| Qwen2.5-3B | DPO | 78.60 | 77.48 | 76.04 | 74.53 | 77.38 | 76.92 | 73.97 | 72.62 | 76.92 | 71.99 |
| Model | OOD Average | OOD Worst | ||||
| DPO | TPO | Gain | DPO | TPO | Gain | |
| Qwen2.5-0.5B | 82.63 | 85.19 | +2.57 | 76.92 | 81.62 | +4.70 |
| Qwen2.5-3B | 76.08 | 80.03 | +3.95 | 74.02 | 77.27 | +3.26 |
| LLaMA-3.2-1B | 87.60 | 88.70 | +1.11 | 83.23 | 83.68 | +0.45 |
| LLaMA-3.2-3B | 83.98 | 89.22 | +5.24 | 81.55 | 86.27 | +4.72 |
| Method | MMLU-Pro | BBH | GPQA | MATH-Hard | IFEval | MuSR | Avg. |
| DPO | 20.0 | 35.6 | 23.2 | 8.1 | 51.3 | 31.6 | 28.30 |
| WDPO | 19.4 | 36.1 | 24.1 | 8.0 | 47.9 | 32.5 | 28.00 |
| Dr.DPO | 19.7 | 36.4 | 24.3 | 8.6 | 52.1 | 32.6 | 28.95 |
| TPO ( ) | 20.5 | 35.9 | 23.7 | 8.3 | 53.0 | 31.2 | 28.77 |
LLM Alignment
Large language model alignment studies methods for making models follow human intentions, values, and safety constraints across contexts.
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