Organizations: University of Virginia, Charlottesville, VA 22904, USA · Princeton University, Princeton, NJ 08544, USA · Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
Prompt engineering has become central to eliciting the capabilities of large language models (LLMs). At its core lies prompt selection -- efficiently identifying the most effective prompts. However, most prior investigations overlook a key challenge: the inherently multi-faceted nature of prompt performance, which cannot be captured by a single metric. To fill this gap, we study the multi-objective prompt selection problem under two practical settings: Pareto prompt set recovery and best feasible prompt identification. Casting the problem into the pure-exploration bandits framework, we adapt provably efficient algorithms from multi-objective bandits and further introduce a novel design for best feasible arm identification in structured bandits, with theoretical guarantees on the identification error in the linear case. Extensive experiments across multiple LLMs show that the bandit-based approaches yield significant improvements over baselines, establishing a principled and efficient framework for multi-objective prompt optimization.
Large Language Models are highly sensitive to prompt formulation, necessitating automatic prompt optimization to unlock their full potential. While evolutionary algorithms have emerged as the dominant paradigm, they suffer from a critical bottleneck: data efficiency. Current methods treat the development dataset as a static benchmark, wasting significant compute budget on uninformative data. In this work, we introduce APEX (Automatic Prompt Engineering eXpert), a novel framework that optimizes the data usage alongside the prompt search. APEX dynamically stratifies the dataset into Easy, Hard, and Mixed tiers based on the optimization lineage. By prioritizing the Mixed tier, which identifies the data where the LLM has mixed performance, we identify two high-leverage subsets: the addressable frontier for generating informative mutations and the rank-sensitive frontier for distinguishing candidate quality. We evaluate APEX across three diverse benchmarks: IFBench, SimpleQA Verified, and FACTS Grounding. Under a fixed budget of 5,000 evaluation calls, due to its data efficiency, APEX outperforms the initial prompt by an average of 11.2% on Gemini 2.5 Flash and 6.8% on Gemma 3 27B, demonstrating that a data-centric approach is key to efficient and effective prompt 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
Large language models (LLMs) achieve strong performance across a wide range of tasks but are highly sensitive to prompt design, motivating the need for automatic prompt optimization. Existing methods predominantly focus on performance alone, ignoring competing objectives such as inference cost or latency. At the same time, existing work on multi-objective prompt optimization relies on off-the-shelf NSGA-II, ignoring optimization efficiency. As a remedy, we introduce MO-CAPO, a novel multi-objective prompt optimization algorithm that jointly optimizes performance and inference cost while leveraging budget allocation for cost-efficient optimization. We further propose a deployment-oriented cost objective that captures the full computational profile of LLM inference. We evaluate our approach across four tasks and three LLMs and compare it to an NSGA-II-based multi-objective method and state-of-the-art single-objective prompt optimizers. Results show that MO-CAPO consistently identifies strong, robust, and diverse Pareto front approximations while maintaining cost-efficiency. It outperforms the NSGA-II baseline on 8 out of 12 cases in terms of the noisy R2 metric and achieves competitive performances often already at a considerably lower budget. The discovered solution sets span diverse performance-cost trade-offs that are omitted by single-objective optimizers, yet the top-performance candidates remain competitive with single-objective solutions. Additionally, we conduct the first evaluation of multi-objective machine learning experiments that considers generalization and robustness through noisy R2 and approximation gap, enabling a more realistic assessment of solution quality. MO-CAPO enables practitioners to select from an efficiently discovered set of multiple prompts offering different trade-offs between performance and cost.