POLCA: Stochastic Generative Optimization with LLM

TL;DR

POLCA is a scalable framework that uses language models to optimize complex systems efficiently by managing stochastic feedback and solution space expansion, outperforming existing methods.

Contribution

We introduce POLCA, a novel stochastic generative optimization framework with theoretical convergence guarantees and practical efficiency improvements for optimizing complex systems with LLMs.

Findings

POLCA outperforms state-of-the-art algorithms on diverse benchmarks.

It demonstrates robust performance under stochastic feedback conditions.

POLCA achieves sample and time efficiency in complex optimization tasks.

Abstract

Optimizing complex systems, ranging from LLM prompts to multi-turn agents, traditionally requires labor-intensive manual iteration. We formalize this challenge as a stochastic generative optimization problem where a generative language model acts as the optimizer, guided by numerical rewards and text feedback to discover the best system. We introduce Prioritized Optimization with Local Contextual Aggregation (POLCA), a scalable framework designed to handle stochasticity in optimization -- such as noisy feedback, sampling minibatches, and stochastic system behaviors -- while effectively managing the unconstrained expansion of solution space. POLCA maintains a priority queue to manage the exploration-exploitation tradeoff, systematically tracking candidate solutions and their evaluation histories. To enhance efficiency, we integrate an $\varepsilon$-Net mechanism to maintain parameter diversity and an LLM Summarizer to perform meta-learning across historical trials. We theoretically prove that POLCA converges to near-optimal candidate solutions under stochasticity. We evaluate our framework on diverse benchmarks, including $\tau$-bench, HotpotQA (agent optimization), VeriBench (code translation) and KernelBench (CUDA kernel generation). Experimental results demonstrate that POLCA achieves robust, sample and time-efficient performance, consistently outperforming state-of-the-art algorithms in both deterministic and stochastic problems. The codebase for this work is publicly available at https://github.com/rlx-lab/POLCA.