Budgeted Prompt-Set Expansion and Refinement for Language Models via Simulation Optimization

Prompt optimizers automate the search for prompts that improve language-model performance, but existing methods rely on a predefined optimization procedure: the algorithm determines which candidates to explore and how the search progresses, while the language model generates or refines prompt proposals. We introduce RLMOpt, a prompt optimizer that makes the search policy itself language-model-driven through a recursive language model (RLM). The RLM agent operates over a tool-based environment, inspecting task information, analyzing failures, generating candidates, allocating evaluation budget, and deciding when to stop. A deterministic harness complements the agent by enforcing objective scoring, Pareto-based selection, and regression constraints. We evaluate RLMOpt across four benchmarks spanning structured clinical information extraction (Chia), multi-hop question answering (HotpotQA), verifiable instruction following (IFBench-2025), and multi-turn tool-calling agents (BFCL). In a matched comparison at a single seed, RLMOpt obtains the best held-out score on all four benchmarks and leads the four-task mean (0.610 against 0.589 for GEPA). Repeating each benchmark across seeds yields 11 matched benchmark-seed comparisons, in which RLMOpt outperforms GEPA in 9 cases. Across all 11 runs, it never produced a prompt that underperformed its seed, whereas GEPA fell below its starting point twice. It is also more efficient, achieving these results with fewer search rollouts while producing prompts that are 27-79% the size of those produced by GEPA. Our results further show that optimization gains are determined primarily by the headroom available in the seed prompt, rather than by the search budget. Efficient optimization therefore depends on reaching the available headroom reliably and with minimal search

Automatic prompt optimization (APO) has been widely employed to adapt large language models without updating their weights, yielding promising results. However, existing methods such as GEPA and OPRO assume hundreds to thousands of subject-model calls, far more than is practical behind paid, rate-limited APIs. Under tight budgets they fail in two ways: multi-stage pipelines can exhaust the budget and return the seed prompt unchanged, while single-stage methods compare candidates on fixed-size minibatches, regardless of each task's noise. As a remedy, we introduce BudgetAPO, a single-stage optimizer for the tight-budget regime. BudgetAPO incorporates (1) a noise-adaptive rule that sizes the evaluation slice to each task's noise, measured by a short probe; (2) a fixed slice that turns every accept/reject decision into a paired comparison; and (3) a reflective operator that rewrites reasoning strategy and output format jointly. Extensive results across seven benchmarks and five subject models demonstrate that BudgetAPO ranks first on every subject and beats every baseline under Holm-corrected paired tests, while returning the seed in 13% of runs at 250 calls against 86% for GEPA. On GPT-OSS-20B, GEPA needs 5 times as many calls to match \method's 100-call score.

Prompt optimization improves language models without updating their weights by searching for a better system prompt, but its effectiveness varies widely across tasks. We study what makes a task amenable to prompt optimization. We show that the reward variance across different system prompts can be decomposed into two components: variance among responses, which captures generation stochasticity, and variance among system prompts, which captures differences in system prompt quality. Prompt optimization succeeds when variance among system prompts is sufficiently large, but fails when variance among responses dominates the variance of the system prompts. Surprisingly, we further show that scaling to more user prompts can hurt optimization by reducing variance among system prompts, especially on heterogeneous datasets where different user prompts favor different system prompts. Motivated by this insight, we propose $p1$, a simple user prompt filtering method that selects a small subset of user prompts with high variance across candidate system prompts. This subset of user prompts allows one to distinguish a good system prompt from a bad one, making system optimization easier. Experiments on reasoning benchmarks show that $p1$ substantially improves prompt optimization over training on the full dataset and outperforms strong baselines such as GEPA. Notably, training on only two prompts from AIME 24 yields a system prompt that generalizes well to other reasoning benchmarks.