Efficiently Estimating Optimal Hyperparameter Scaling Laws through Power-Law Entropy Search

[Submitted on 1 Sep 2026 (v1), last revised 3 Sep 2026 (this version, v2)]

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Abstract:Optimal hyperparameter scaling laws describe how the best hyperparameters for large language model (LLM) training change with model and data scale, enabling practitioners to predict optimal configurations at production scales without expensive large-scale tuning. However, estimating these scaling laws conventionally requires exhaustive grid searches over thousands of training runs, consuming enormous computational resources. We introduce Power-Law Entropy Search (PLES), a computational cost-aware acquisition function built on multi-fidelity Bayesian optimization that efficiently estimates optimal hyperparameter scaling laws through adaptive experimentation. A key innovation in PLES is that it searches for candidates that reduce the overall uncertainty of a scaling law estimate, instead of optimizing a single objective function. At each iteration, PLES selects the candidate configuration that maximally reduces the uncertainty of the scaling law estimates per unit computational cost, naturally favoring informative small-scale experiments. We evaluate PLES on synthetic benchmarks, surrogate models fitted to real LLM training data, and actual LLM pre-training runs. Across all settings, PLES converges to accurate optimal hyperparameter scaling laws using less than one-tenth of the computational budget required by conventional grid search and other baselines.

Submission history

From: Zhiliang Chen [view email]
[v1] Tue, 1 Sep 2026 15:41:59 UTC (10,686 KB)
[v2] Thu, 3 Sep 2026 15:16:24 UTC (10,686 KB)