Frontier Scaling Laws for Agentic Cost: Measuring Diminishing Returns in AI Agents

The last few years have seen a dramatic acceleration in AI capabilities, most notably in the time horizon metric, which relates the success rate of an AI agent to the number of hours it would take a human to complete the same task. When measured in human-hours, the tasks an AI agent can complete 50% of the time have been doubling approximately every 4 months for the last three years. At the same time the direct inference-time cost of running an AI agent has also experienced rapid growth. Thus, the question remains: which of these two is growing more quickly? That is, for every doubling of time horizon, by what factor does inference-time cost grow? Building on methods from item response theory, we show that at the price-performance frontier there are significant diminishing returns to paying more for AI inference. In particular, we find that cost scales as a superquadratic power law in time horizon.