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Wearable devices that integrate multiple sensors, processors, and communication technologies have the potential to transform mobile health for remote monitoring of health parameters. However, the small form factor of the wearable devices limits the battery size and operating lifetime. As a result, the devices require frequent recharging, which has limited their widespread adoption. Energy harvesting has emerged as an effective method towards sustainable operation of wearable devices. Unfortunately, energy harvesting alone is not sufficient to fulfill the energy requirements of wearable devices. This paper studies the novel problem of adaptive energy management towards the goal of self-sustainable wearables by using harvested energy to supplement the battery energy and to reduce manual recharging by users. To solve this problem, we propose a principled algorithm referred as AdaEM. There are two key ideas behind AdaEM. First, it uses machine learning (ML) methods to learn predictive models of user activity and energy usage patterns. These models allow us to estimate the potential of energy harvesting in a day as a function of the user activities. Second, it reasons about the uncertainty in predictions and estimations from the ML models to optimize the energy management decisions using a dynamic robust optimization (DyRO) formulation. We propose a light-weight solution for DyRO to meet the practical needs of deployment. We validate the AdaEM approach on a wearable device prototype consisting of solar and motion energy harvesting using real-world data of user activities. Experiments show that AdaEM achieves solutions that are within 5% of the optimal with less than 0.005% execution time and energy overhead.