To operate distributed applications with high availability, operators must rapidly diagnose and mitigate any incident. LLM-based agents can help, but unlike experienced human operators they do not improve as they handle more incidents. Each investigation starts from scratch, re-deriving likely causes and re-testing hypotheses even when a similar fault was resolved in the past. We present a self-defining operator (SDO) that improves with time by updating its operational behavior and memory. When SDO resolves an incident, it distills that experience into playbooks, which describe reusable diagnostic instructions for future incidents with similar faults, and detectors, scripts that take application telemetry as input and output relevant playbook(s). SDO continuously runs the detectors and invokes LLMs only when one fires, so its token cost scales with incident count rather than with operational time. Across 11 open-source microservice applications, SDO cuts resolution time by 52% on recurring faults while keeping per-incident cost low. SDO is open source at https://github.com/uw-syfi/sdo.

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