Spend Less, Fit Better: Budget-Efficient Scaling Law Fitting via Active Experiment Selection

TL;DR

This paper introduces a budget-aware sequential experimental design method for fitting scaling laws efficiently, significantly reducing costs while maintaining high extrapolation accuracy.

Contribution

It proposes an uncertainty-aware approach for selecting experiments that maximizes extrapolation accuracy within a limited budget, outperforming classical methods.

Findings

Method often approaches full-data performance using only 10% of the budget.

Consistently outperforms classical design-based baselines across diverse tasks.

Code available at https://github.com/PlanarG/active-sl.

Abstract

Scaling laws are used to plan multi-million-dollar training runs, but fitting those laws can itself cost millions. In modern large-scale workflows, assembling a sufficiently informative set of pilot experiments is already a major budget-allocation problem rather than a routine preprocessing step. We formulate scaling-law fitting as budget-aware sequential experimental design: given a finite pool of runnable experiments with heterogeneous costs, choose which runs to execute so as to maximize extrapolation accuracy in a high-cost target region. We then propose an uncertainty-aware method for sequentially allocating experimental budget toward the runs most useful for target-region extrapolation. Across a diverse benchmark of scaling-law tasks, our method consistently outperforms classical design-based baselines, and often approaches the performance of fitting on the full experimental set while using only about 10% of the total training budget. Our code is available at https://github.com/PlanarG/active-sl.