Deploying Large Language Models to data-scarce programming domains poses significant challenges, particularly for kernel synthesis on emerging Domain-Specific Architectures where a "Data Wall" limits available training data. While models excel on data-rich platforms like CUDA, they suffer catastrophic performance drops on data-scarce ecosystems such as NPU programming. To overcome this cold-start barrier without expensive fine-tuning, we introduce EvoKernel, a self-evolving agentic framework that automates the lifecycle of kernel synthesis from initial drafting to continual refining. EvoKernel addresses this by formulating the synthesis process as a memory-based reinforcement learning task. Through a novel value-driven retrieval mechanism, it learns stage-specific Q-values that prioritize experiences based on their contribution to the current objective, whether bootstrapping a feasible draft or iteratively refining latency. Furthermore, by enabling cross-task memory sharing, the agent generalizes insights from simple to complex operators. By building an NPU variant of KernelBench and evaluating on it, EvoKernel improves frontier models' correctness from 11.0% to 83.0% and achieves a median speedup of 3.60x over initial drafts through iterative refinement. This demonstrates that value-guided experience accumulation allows general-purpose models to master the kernel synthesis task on niche hardware ecosystems. Our official page is available at https://evokernel.zhuo.li.

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