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When each evaluation run is costly, exhaustive grid search is inefficient. Bayesian optimization gives better sample efficiency.

The acquisition step often looks like:

$$x_{t+1} = \arg\max_x \left( \mu_t(x) + \kappa\sigma_t(x) \right)$$

where $\mu_t$ is expected quality and $\sigma_t$ uncertainty under a surrogate model.

Why it works in practice

• It explores uncertain regions early.
• It exploits proven regions once confidence increases.
• It converges with fewer expensive runs.

Minimal implementation pattern

type Trial = { config: Record<string, number>; score: number };

export function nextTrial(trials: Trial[]): Record<string, number> {
  // In production this would call a surrogate model + acquisition function.
  // Keep this seam explicit so you can replace strategy without changing orchestration.
  if (trials.length < 6) {
    return { temperature: Math.random(), topP: 0.7 + Math.random() * 0.3 };
  }

  const best = [...trials].sort((a, b) => b.score - a.score)[0];
  return {
    temperature: Math.max(0, best.config.temperature - 0.05),
    topP: Math.min(1, best.config.topP + 0.03)
  };
}

The main lesson: formal optimization methods from scientific computing map cleanly to modern AI pipeline tuning.