The Self-Improvement Problem

arXiv:2610.21646v1 Announce Type: new Abstract: With the rise of large language models, agentic systems are becoming increasingly autonomous, as they write code, call tools, revise prompts, and propose modifications to their own components. This autonomy raises a fundamental question for safe self-improvement: can an automated gate like a reward model or an automated reviewer reliably decide whether a proposed update should be accepted? The difficulty is structural. The gate must be a terminating, computable procedure, while the property we ultimately care about, namely whether an update is a

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