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The unprecedented growth of the global Internet traffic, coupled with the large spatio-temporal fluctuations that create, to some extent, predictable tidal traffic conditions, are motivating the evolution from reactive to proactive and eventually towards adaptive optical networks. In these networks, traffic-driven service provisioning can address the problem of network over-provisioning and better adapt to traffic variations, while keeping the quality-of-service at the required levels. Such an approach will reduce network resource over-provisioning and thus reduce the total network cost. This survey provides a comprehensive review of the state of the art on machine learning (ML)-based techniques at the optical layer for traffic-driven service provisioning. The evolution of service provisioning in optical networks is initially presented, followed by an overview of the ML techniques utilized for traffic-driven service provisioning. ML-aided service provisioning approaches are presented in detail, including predictive and prescriptive service provisioning frameworks in proactive and adaptive networks. For all techniques outlined, a discussion on their limitations, research challenges, and potential opportunities is also presented.