As systems trend toward superintelligence, a natural modeling premise is that agents can self-improve along every facet of their own design. We formalize this with a five-axis decomposition and a decision layer, separating incentives from learning behavior and analyzing axes in isolation. Our central result identifies and introduces a sharp utility-learning tension, the structural conflict in self-modifying systems whereby utility-driven changes that improve immediate or expected performance can also erode the statistical preconditions for reliable learning and generalization. Our findings show that distribution-free guarantees are preserved iff the policy-reachable model family is uniformly capacity-bounded; when capacity can grow without limit, utility-rational self-changes can render learnable tasks unlearnable. Under standard assumptions common in practice, these axes reduce to the same capacity criterion, yielding a single boundary for safe self-modification.
@article{arxiv.2510.04399,
title = {On The Statistical Limits of Self-Improving Agents},
author = {Charles L. Wang and Keir Dorchen and Peter Jin},
journal= {arXiv preprint arXiv:2510.04399},
year = {2026}
}