2850842d92
- Applied reviewer-requested changes - Quality gate pass (fix-from-feedback) Pentagon-Agent: Auto-Fix <HEADLESS>
31 lines
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2.9 KiB
Markdown
31 lines
No EOL
2.9 KiB
Markdown
---
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type: claim
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domain: ai-alignment
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created: 2024-09-00
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source: gaikwad-murphys-laws-alignment
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confidence: experimental
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description: |
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Feedback misspecification in RLHF creates an exponential sample complexity barrier (Ω(exp(d))) that calibration oracles can overcome by providing access to the true reward function, enabling polynomial sample complexity.
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---
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# Feedback misspecification creates exponential sample complexity barrier that calibration oracles overcome
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Gaikwad (2024) proves that when the feedback model is misspecified in RLHF, the sample complexity becomes exponential in the dimension d of the policy space (Ω(exp(d))). However, with access to a calibration oracle that provides the true reward for any state-action pair, the sample complexity reduces to polynomial (Õ(d³/ε²)).
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This formal result suggests that [[human-feedback-is-easier-to-specify-than-objective-functions]] may underestimate the difficulty of alignment through feedback alone. The exponential barrier arises because misspecified feedback creates a compounding error that grows with the complexity of the policy space.
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The calibration oracle framework connects to [[collective-intelligence-infrastructure-enables-alignment]] by suggesting that distributed expert judgment could serve as a practical approximation of the theoretical oracle, though this requires coordination mechanisms.
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## Enrichments
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### Challenges [[human-feedback-is-easier-to-specify-than-objective-functions]]
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The exponential sample complexity barrier under feedback misspecification suggests that human feedback may be harder to use effectively than previously thought. While feedback may be easier to provide than complete objective functions, the formal result shows that even small misspecifications in the feedback model create exponential learning costs. This doesn't invalidate the ease-of-specification claim, but it reveals a critical gap between "easy to specify" and "sufficient for alignment."
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### Extends [[collective-intelligence-infrastructure-enables-alignment]]
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The calibration oracle framework provides a formal foundation for why collective intelligence infrastructure matters. If calibration oracles can overcome exponential barriers, and if distributed expert networks can approximate oracle access, then collective intelligence becomes not just helpful but potentially necessary for scalable alignment. The polynomial vs exponential distinction makes the infrastructure question quantitatively urgent rather than merely qualitative.
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### Confirms [[alignment-requires-interpretable-representations]]
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The need for calibration oracles to access "true rewards" for state-action pairs implicitly requires interpretable representations of both states and actions. Without interpretability, experts cannot provide meaningful calibration signals. This formal requirement strengthens the case that interpretability is not optional but structurally necessary for alignment approaches that rely on human judgment. |