Verification and Self-Improvement in Agentic AI: Foundations and Limits
A self-improving agent can find accepted solutions more often without expanding the tasks its verification interface can accept.
Arxiv 2 versions
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9 new sentences, beginning: “A self-improving agent can find accepted solutions more often without expanding the tasks its verification interface can accept.”
Verification and Self-Improvement in Agentic AI: Foundations and Limits
A self-improving agent can find accepted solutions more often without expanding the tasks its verification interface can accept. We extend task-relative verification with explicit support and transcript interfaces to distinguish search gains from changes in accepted-task coverage. A stage's native reach contains tasks accepted with default support; its closure frontier contains tasks accepted with any support the declared interface permits. A semantic containment criterion identifies the authority or exposure condition that every verified escape must violate, while guard-transfer invariance prevents a change of representation from being counted as a capability expansion. An executable Boolean-program repair agent makes the distinction concrete: over 36,864 paired runs, counterexample feedback reduces verifier calls without changing coverage, whereas an enforced permission change admits a new target with a proof excluding every old-interface program. Exact and uniformly gapped randomized verification share this account; independent majority amplification improves reliability while preserving the accepted language. Separate adaptive-selection contracts state what is additionally required to interpret a proposed successor's score as evidence of deployment improvement. Classical hierarchy results and finite audits provide supporting boundaries. The framework specifies the evidence needed to establish improved search, wider accepted capability, and reliable successor selection.
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Verification and Self-Improvement in Agentic AI: Foundations and Limits
Agentic AI systems can improve by searching longer, receiving additional support, or modifying how they propose and verify outputs. A performance score does not distinguish these mechanisms. We compare these changes through bounded verification with hidden terminal randomness. A stage specifies admissible transcripts, polynomial bounds, an alternating verification protocol, and a terminal checker. Its native reach uses default support; its closure frontier permits all support already admitted by the interface. Under a uniform pointwise probability gap and task-relative soundness, these are well-defined languages. We prove that independent majority amplification preserves both languages, whereas existential acceptance over random tapes can admit incorrect outputs. Exact verification is the zero-randomness case, with placement and completeness results. The randomized-verifier classes satisfy $\Sigma_k^{\mathrm{P}}\subseteq\Sigma_k^{\mathrm{RV}}\subseteq\Sigma_{k+1}^{\mathrm{P}}$; strict enlargement and depth separation require explicit complexity assumptions, while $\mathrm{BPP}=\mathrm{P}$ yields exact companions with the same frontiers. Representation analysis separates invariant acceptance from core-versus-support labels that can change under refactoring. For recursive self-improvement, uniformly bounded self-modification under a common sound interpreter and fixed verification protocol remains within the same verification class. A separate conditional-error budget controls false selection across adaptively chosen candidates. A quota-enforced XOR-synthesis family separates unbounded ratios of search success from changes in the accepted languages; exact and probabilistic audits check the resulting evidence requirements. The framework ties self-improvement claims to obligations on correctness, admissible evidence, verification resources, and selection error.
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A self-improving agent can find accepted solutions more often without expanding the tasks its verification interface can accept. We extend task-relative verification with explicit support and transcript interfaces to distinguish search gains from changes in accepted-task coverage. A stage's native reach contains tasks accepted with default support; its closure frontier contains tasks accepted with any support the declared interface permits. A semantic containment criterion identifies the authority or exposure condition that every verified escape must violate, while guard-transfer invariance prevents a change of representation from being counted as a capability expansion.
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