Beyond the Capability Boundary: Zeroth-Order Optimization for Self-Evolving LLM Agents

2026-08-10

AI Summary

This work proposes the first zeroth-order optimization framework for self-evolution of large language model (LLM) agents, addressing the limitation that existing methods struggle to generate correct reasoning trajectories on challenging instances due to inherent capability boundaries. The approach perturbs LoRA parameters in parallel, estimates gradient signals via answer perplexity-based loss, and incorporates an adaptive search mechanism to update the model, thereby producing high-quality trajectories for supervised fine-tuning within a closed-loop evolutionary process. Requiring no human annotation, the method substantially increases the number of successful trajectories across multiple deep reasoning benchmarks and consistently outperforms strong baselines—particularly on difficult samples—effectively expanding the capability frontier of LLM agents.

Abstract

Self-evolving methods improve the capabilities of LLM agents by sampling trajectories from the underlying LLMs and learning from these trajectories. However, these methods struggle to learn beyond the inherent capability boundary of the agents, since the agents cannot sample correct trajectories on difficult examples for further improvements. In this paper, we propose a zeroth-order self-evolution framework that enables agents to learn beyond their capability boundary by perturbing LLM parameters to adapt to difficult examples without any trajectory annotations. Specifically, we perturb LoRA parameters of LLMs, run the agent, compute the losses under the perturbed and original parameters, and use the loss difference to estimate gradients and further update the LoRA parameters. We sample trajectories using the updated LLMs for supervised fine-tuning to break through the capability boundary of the agents, forming a closed self-evolution loop. We introduce a parallel perturbation inference mechanism and an adaptive lookup mechanism to reduce time consumption in zeroth-order optimization, with an answer perplexity loss that provides smooth and stable zeroth-order loss values. Experiments on multiple deep research benchmarks show that our method obtains substantially more successful trajectories and consistently outperforms strong baselines, especially on difficult examples. The code and released artifacts are available at https://github.com/hidk1911/ZOForLLMAgents.

Problem

• self-evolving
• capability boundary
• LLM agents
• zeroth-order optimization
• trajectory sampling

Innovation

• zeroth-order optimization
• self-evolving LLM agents
• LoRA parameter perturbation
• capability boundary突破
• trajectory-free learning