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

Self-evolving LLMs excel in verifiable domains but struggle in open-ended tasks, where reliance on proxy LLM judges introduces capability bottlenecks and reward hacking. To overcome this, we introduce G-Zero, a verifier-free, co-evolutionary framework for autonomous self-improvement. Our core innovation is Hint-$δ$, an intrinsic reward that quantifies the predictive shift between a Generator model's unassisted response and its response conditioned on a self-generated hint. Using this signal, a Proposer model is trained via GRPO to continuously target the Generator's blind spots by synthesizing challenging queries and informative hints. The Generator is concurrently optimized via DPO to internalize these hint-guided improvements. Theoretically, we prove a best-iterate suboptimality guarantee for an idealized standard-DPO version of G-Zero, provided that the Proposer induces sufficient exploration coverage and the data filteration keeps pseudo-label score noise low. By deriving supervision entirely from internal distributional dynamics, G-Zero bypasses the capability ceilings of external judges, providing a scalable, robust pathway for continuous LLM self-evolution across unverifiable domains.

Modern LLM agents are often improved by modifying prompts, tools, or workflows manually, while the executable scaffold surrounding the model---the \emph{harness}---is typically treated as a fixed artifact after deployment. This work studies an alternative where the harness is \emph{task-specific and continuously evolvable}: each task family maintains its own harness, which is hot-swapped across iterations through a fixed task-injection seam and rewritten using environment feedback. We introduce \textbf{Hierarchical Self-Improvement (HSI)}, a framework in which a single frozen LLM $M$ operates across three hierarchical scopes: a task harness $H$ that executes tasks, an evolver that rewrites $H$, and a meta-evolver that rewrites the evolver's strategy code under a frozen outer anchor. A thinking-on/off design isolates the contribution of harness evolution by disabling reasoning during task execution while enabling it during self-modification. HSI is bounded by two factors: a \emph{feedback-fidelity bound}, since evolution requires informative reward signals to guide selection, and a \emph{backbone capability bound}, since harness redesign cannot overcome limitations of the frozen model. On BALROG with DeepSeek-V4-Flash-Preview as the frozen backbone, HSI achieves consistent gains over the initial harness on moderate-difficulty tasks ($+39.3$ on BabyAI, $+33.0$ on Crafter, $+25.0$ on TextWorld, and $+15.0$ on MiniHack, all in raw % Progress), while obtaining strong held-out generalization on BabaIsAI sub-suites ($0.98$ best-test on BreakStop and $1.00$ on GoTo from a $20\%$ unseen split). On tasks beyond the backbone's capability (NLE), harness evolution provides no improvement. These results demonstrate task-specific harness evolution as a viable axis for improving frozen LLM agents under clear empirical limits. Code is available at https://github.com/TailinZhou/hsi.

Recent advances in LLM agents enable systems that autonomously refine workflows, accumulate reusable skills, self-train their underlying models, and maintain persistent memory. However, we show that such self-evolution is often non-monotonic: adapting to new task distributions can progressively degrade previously acquired capabilities across all major evolution channels. We identify this phenomenon as \emph{capability erosion under self-evolution} and show that it consistently emerges across workflow, skill, model, and memory evolution. To mitigate this issue, we propose \emph{Capability-Preserving Evolution} (CPE), a general stabilization principle that constrains destructive capability drift during continual adaptation. Across all four evolution dimensions, CPE consistently improves retained capability stability while preserving adaptation performance. For example, in workflow evolution, CPE improves retained simple-task performance from 41.8% to 52.8% under GPT-5.1 optimization while simultaneously achieving stronger complex-task adaptation. Our findings suggest that stable long-horizon self-evolving agents require not only acquiring new capabilities, but also explicitly preserving previously learned ones during continual adaptation.