POLCA: Stochastic Generative Optimization with LLM

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 ε-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 τ -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-theart algorithms in both deterministic and stochastic problems. The codebase for this work is publicly available at https://github.com/rlx-lab/POLCA . * Corresponding authors. 1 The term parameter is used here to distinguish the changeable part of a program, as defined by the programmer. In the most general case, the entire program can be treated as a parameter.