Large Language Models as Optimization Tools大型语言模型作为优化工具

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Context

This collection addresses a paradigm shift in optimization: using Large Language Models not as tools to be optimized, but as optimizers themselves. Traditional derivative-based methods fail when gradients are unavailable or expensive to compute—a common constraint in hyperparameter tuning, experimental design, and real-world engineering. By framing optimization as a natural language reasoning task, researchers are exploring whether LLMs' pattern recognition and contextual understanding can rival or augment classical methods like Bayesian optimization. This matters now because LLMs have demonstrated surprising competence in mathematical reasoning, and their ability to incorporate domain knowledge through prompting offers a potential escape from local optima traps that plague blind search algorithms.

Key Insights

LLMs as meta-optimizers outperform hand-crafted heuristics in prompt engineering. Yang et al.’s OPRO framework demonstrates that LLMs can iteratively refine solutions by conditioning on historical performance—achieving up to 50% improvement over human-designed prompts on reasoning benchmarks. This suggests LLMs excel when the optimization landscape can be encoded linguistically, exploiting their pre-trained semantic knowledge rather than relying solely on numerical gradients.

Hybrid systems combining LLMs with Bayesian optimization show complementary strengths. LLAMBO integrates LLMs for zero-shot warm-starting and surrogate modeling in early search stages, while BORA uses LLMs to inject domain knowledge from literature into experimental design. These approaches address Bayesian optimization’s sample inefficiency in high dimensions by leveraging LLMs' ability to reason about plausible regions—though they inherit LLMs' hallucination risks when proposing scientifically implausible candidates.

Natural language interfaces democratize expert-level optimization but introduce cognitive tradeoffs. Niwa et al.’s cooperative framework enables designers to steer optimization mid-flight through conversational input, matching performance of automated methods with lower cognitive load. However, the explainability gains (LLMs narrating their reasoning) compete with potential over-reliance on plausible-sounding but suboptimal suggestions—a tension between human agency and algorithmic efficiency.

Open Questions

• When do LLMs' semantic biases help versus harm search? If pre-training data over-represents certain solution types, could LLM-guided optimization systematically miss unconventional optima in scientific discovery tasks?

• Can we quantify the sample efficiency frontier between pure BO and LLM-augmented methods? Under what dimensionality, evaluation cost, and prior knowledge regimes does linguistic contextualization outweigh the risk of premature convergence to plausible-but-local solutions?