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Machine learning techniques have been actively studied and achieved significant performance improvements in various kinds of tasks. While we benefit from such techniques in many ways, they can be a serious security threat to the Internet if malicious attackers become able to utilize them to discover unknown software vulnerabilities. This paper introduces a new concept of self-evolving botnets, where computing resources of infected hosts are exploited to discover unknown vulnerabilities in non-infected hosts and the botnets evolve autonomously. We provide a stochastic epidemic model for the self-evolving botnets, and show its behaviors through numerical and simulation experiments.