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Skill routing is an important component in large-scale conversational systems. In contrast to traditional rule-based skill routing, state-of-the-art systems use a model-based approach to enable natural conversations. To provide supervision signal required to train such models, ideas such as human annotation, replication of a rule-based system, relabeling based on user paraphrases, and bandit-based learning were suggested. However, these approaches: (a) do not scale in terms of the number of skills and skill on-boarding, (b) require a very costly expert annotation/rule-design, (c) introduce risks in the user experience with each model update. In this paper, we present a scalable self-learning approach to explore routing alternatives without causing abrupt policy changes that break the user experience, learn from the user interaction, and incrementally improve the routing via frequent model refreshes. To enable such robust frequent model updates, we suggest a simple and effective approach that ensures controlled policy updates for individual domains, followed by an off-policy evaluation for making deployment decisions without any need for lengthy A/B experimentation. We conduct various offline and online A/B experiments on a commercial large-scale conversational system to demonstrate the effectiveness of the proposed method in real-world production settings.