SkillCover: Fixed-Pool Skill Library Selection as Noisy Submodular Coverage

When an agent can retain only \(k\) skills, ranking them by individual performance can waste slots on redundant capabilities. SkillCover greedily selects skills from a fixed pool to maximize baseline-relative task coverage on a calibration matrix. This classical submodular objective measures the best performance available in the retained library. We analyze selection under task sampling and rollout noise, and evaluate coverage and agent success separately. On real SkillsBench packages, greedy improves held-out matrix coverage over singleton ranking on GLM-5 (\(+0.083\) at \(k=4\)); results on three other models are mixed. A deliberately redundant MCPAgentBench pool and synthetic controls show when singleton ranking wastes the budget on overlap. Deployment on 14 new tasks does not establish a success advantage. A fresh-calibration diagnostic gives positive mean differences on two models at four repetitions, but intervals include zero and one comparison reverses at two repetitions. Whether coverage gains improve deployment remains unresolved.