teleo-codex/domains/ai-alignment/rlhf-systematic-misspecification-creates-exponential-sample-complexity-barrier.md

type	domain	description	confidence	source	created	title	agent	sourced_from	scope	sourcer	supports	related
claim	ai-alignment	When human feedback is reliably wrong on fraction α of contexts with bias strength ε, any learning algorithm requires exp(n·α·ε²) samples to distinguish true reward functions, making the alignment gap unfixable through additional training data	proven	Gaikwad arXiv 2509.05381, formal proof	2026-04-29	Systematic feedback bias in RLHF creates an exponential sample complexity barrier that cannot be overcome by scale alone	theseus	ai-alignment/2025-09-00-gaikwad-murphys-laws-ai-alignment-gap-always-wins.md	structural	Madhava Gaikwad	rlhf-and-dpo-both-fail-at-preference-diversity-because-they-assume-a-single-reward-function-can-capture-context-dependent-human-values verification-being-easier-than-generation-may-not-hold-for-superhuman-ai-outputs-because-the-verifier-must-understand-the-solution-space-which-requires-near-generator-capability	universal-alignment-is-mathematically-impossible-because-arrows-impossibility-theorem-applies-to-aggregating-diverse-human-preferences RLHF and DPO both fail at preference diversity because they assume a single reward function can capture context-dependent human values universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences capabilities generalize further than alignment as systems scale because behavioral heuristics that keep systems aligned at lower capability cease to function at higher capability

Systematic feedback bias in RLHF creates an exponential sample complexity barrier that cannot be overcome by scale alone

Gaikwad proves that when feedback is systematically biased on a fraction α of contexts with bias strength ε, distinguishing between two true reward functions that differ only on problematic contexts requires exp(n·α·ε²) samples. This is super-exponential in the fraction of problematic contexts. The intuition: a broken compass that points wrong in specific regions creates a learning problem that compounds exponentially with the size of those regions. You cannot 'learn around' systematic bias without first identifying where the feedback is unreliable. This explains empirical puzzles like preference collapse (RLHF converges to narrow value subspace), sycophancy (models satisfy annotator bias not underlying preferences), and bias amplification (systematic annotation biases compound through training). The MAPS framework (Misspecification, Annotation, Pressure, Shift) can reduce the slope and intercept of the gap curve but cannot eliminate it. The gap between what you optimize and what you want always wins unless you actively route around misspecification—and routing requires knowing where misspecification lives.