SAGE: A Statistical Acceptance Gate for Self-Evolving Agents
Yihao Wang (Peking University), with collaborators at Tencent, Imperial College London and Michigan, show that the usual acceptance rule in skill self-evolution, keep any edit that raises the average validation score, admits regressions and noise, and replace it with a paired statistical gate called SAGE.
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Two failure modes of the standard gate. An edit can raise the average while breaking items the skill already solved, and the best observed score on a small noisy validation set is biased upward (the Optimizer's Curse).
Method. SAGE compares the current and edited skill on the same validation items, penalizes newly broken items asymmetrically, and commits an edit only when a one-sided paired test says its wins reliably exceed its losses. Otherwise it abstains. At a boundary setting it reduces exactly to the standard gate.
Regressions. Across five benchmarks and four backbone LLMs under an equal-budget protocol, SAGE lowers the regression rate in 19 of 20 settings and ties in the last, for example from 36.5% to 0% on LiveMath and from 42.8% to 0% on OfficeQA with DeepSeek-V4.
Final score. SAGE reaches the highest final score in all 20 settings, raising LiveMath from 34.15 to 48.78, while committing fewer edits than the baseline.
Abstract
Large Language Model (LLM)-based agents increasingly self-evolve by editing a persistent skill document that encodes their workflow, tool-use rules, and decision logic. This loop has two steps, an optimizer that proposes a candidate edit and a gate that accepts or rejects it. Prior work has concentrated on the optimizer, while the gate still follows a naive rule that keeps any edit which improves an aggregate validation score. We show that this rule fails in two ways. First, it admits permanent regressions, since an edit can raise the average while breaking items the skill already solves. Second, it is vulnerable to the Optimizer's Curse, since the best observed score on a finite and noisy validation set is upward biased. To solve the above two limitations, we propose a statistical acceptance gate for self-evolving agents (SAGE). Compared with previous work, SAGE has two contributions. First, SAGE proposes a per-item paired comparison that evaluates the current skill and the edited skill on identical validation items, which exposes regressions that an aggregate score hides and penalizes them asymmetrically. Second, SAGE also employs a one-sided paired test that commits an edit only when its wins are statistically reliable against its losses, and it abstains otherwise. SAGE is a conservative refinement of the standard gate that recovers the baseline exactly at a boundary setting. It commits only a subset of the baseline's edits, filtering out those whose gains are unreliable or purchased by breaking already-solved items. Across five benchmarks and four backbone LLMs under an equal-budget protocol, SAGE lowers the regression rate in 19 of 20 settings and matches the baseline in the remaining one, for example from 36.5% to 0% on LiveMath and from 42.8% to 0% on OfficeQA with DeepSeek-V4. SAGE also attains the highest final score in all 20 settings, raising LiveMath from 34.15 to 48.78.