Optimizing f(x): A Preregistered Study of Selecting Agent Configurations for Commit0 Library Generation Under a Token Budget

A company that runs coding agents must decide, task by task, how many agents to use and how to organize them without exceeding a shared token allowance. We call this choice f(x), a function from a task x to an agent configuration. We formalize it as average-budget constrained selection over a finite library of 22 executable policies (solo, independent best-of-N, and Fleet teams, with agent ceilings of 1, 2 and 4) and preregister a protocol that uses the Lagrangian decision layer of Zhai et al. as given. We applied the protocol to Commit0 library generation on Fleet V5 5.0.0-alpha.13, the execution core of the ToolsEnabled Agent Architecture (TEAA); every agent ran Codex gpt-6-luna at high effort. Calibration set the allowance to B = 86,033,000 tokens and gave a noise estimate sigma0 = 0. A fitting matrix of 132 cells (22 policies on 6 repositories, one run each) produced 124 integrity-valid scores. Its unknown and invalid cells left the task-dependent selector unfitted, so the frozen rule ranked constant policies. The top score was shared by 8 constants. The rule froze the cheapest of them, n1-T1-K0-b1-c0 (a Fleet team with an agent ceiling of 2), for every evaluation repository; it cleared the replacement margin over the solo incumbent by 0.000705. On 7 held-out repositories the frozen choice (F), independent best-of-2 (B) and solo (S) produced 17 completed and 4 unknown cells. All 4 known F-B differences are zero. The 7-repository mean difference is bounded only to [-3/7, +3/7] for F-B and [-0.204146, 0.367282] for F-S, so no difference is established and none is claimed. Token totals are known for 17 of 21 evaluation cells, and dollar cost is unknown. The result is null and inconclusive. The contribution is a preregistered protocol, an auditable application with a full accounting of failures and amendments, and a baseline within its tested scope. We claim no optimum.