Expenditure Horizon

METR's continuous generalization of time horizon: the dollar spend at which an agent's improvement on an optimization problem equals a human's at the same budget, measured by crossing an agent's returns-to-expenditure curve with the local returns to human labor — proof-of-concept on the NanoGPT speedrun, where humans cost ~$2,500 per 1% speedup and six agent runs from record #78 re-validate to horizons of $0-$3,300, of which the maintainer would merge ~70% of the ideas but only 50-60% of the speedup