Position: The Complexity of Perfect AI Alignment -- Formalizing the RLHF Trilemma
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914169802981376 |
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| author | Sahoo, Subramanyam Chadha, Aman Jain, Vinija Chaudhary, Divya |
| author_facet | Sahoo, Subramanyam Chadha, Aman Jain, Vinija Chaudhary, Divya |
| contents | Reinforcement Learning from Human Feedback (RLHF) is widely used for aligning large language models, yet practitioners face a persistent puzzle: improving safety often reduces fairness, scaling to diverse populations becomes computationally intractable, and making systems robust often amplifies majority biases. We formalize this tension as the Alignment Trilemma: no RLHF system can simultaneously achieve (i) epsilon-representativeness across diverse human values, (ii) polynomial tractability in sample and compute complexity, and (iii) delta-robustness against adversarial perturbations and distribution shift. Through a complexity-theoretic analysis integrating statistical learning theory and robust optimization, we prove that achieving both representativeness (epsilon <= 0.01) and robustness (delta <= 0.001) for global-scale populations requires Omega(2^{d_context}) operations, which is super-polynomial in the context dimensionality. We show that current RLHF implementations resolve this trilemma by sacrificing representativeness: they collect only 10^3--10^4 samples from homogeneous annotator pools while 10^7--10^8 samples are needed for true global representation. Our framework provides a unified explanation for documented RLHF pathologies including preference collapse, sycophancy, and systematic bias amplification. We conclude with concrete directions for navigating these fundamental trade-offs through strategic relaxations of alignment requirements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Position: The Complexity of Perfect AI Alignment -- Formalizing the RLHF Trilemma Sahoo, Subramanyam Chadha, Aman Jain, Vinija Chaudhary, Divya Machine Learning Reinforcement Learning from Human Feedback (RLHF) is widely used for aligning large language models, yet practitioners face a persistent puzzle: improving safety often reduces fairness, scaling to diverse populations becomes computationally intractable, and making systems robust often amplifies majority biases. We formalize this tension as the Alignment Trilemma: no RLHF system can simultaneously achieve (i) epsilon-representativeness across diverse human values, (ii) polynomial tractability in sample and compute complexity, and (iii) delta-robustness against adversarial perturbations and distribution shift. Through a complexity-theoretic analysis integrating statistical learning theory and robust optimization, we prove that achieving both representativeness (epsilon <= 0.01) and robustness (delta <= 0.001) for global-scale populations requires Omega(2^{d_context}) operations, which is super-polynomial in the context dimensionality. We show that current RLHF implementations resolve this trilemma by sacrificing representativeness: they collect only 10^3--10^4 samples from homogeneous annotator pools while 10^7--10^8 samples are needed for true global representation. Our framework provides a unified explanation for documented RLHF pathologies including preference collapse, sycophancy, and systematic bias amplification. We conclude with concrete directions for navigating these fundamental trade-offs through strategic relaxations of alignment requirements. |
| title | Position: The Complexity of Perfect AI Alignment -- Formalizing the RLHF Trilemma |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2511.19504 |