With the growing demand to perform increasingly complex computations such as image, audio or video processing or machine learning on mobile devices, energy consumption becomes a crucial factor for the lifetime and usability of these devices. A common way to reduce the amount of consumed energy is to offload the computation to a cloud server with a stable power supply. However, the decision of whether to offload a computation or to perform it locally is not always unambiguous. Using cellular or wireless network to send data to, and receive data from an offloading site can require a non-negligible amount of energy surpassing the energy required for local computation. In this thesis linear contextual bandits are employed to make informed offloading decisions based on contextual information of the task to be executed. To reduce the load on the central server federated, individually acting contextual bandits, able to share collected and aggregated data via synchronization, are considered as well. An increasing privacy consciousness among users further motivates the use of a differentially private mechanism to protect the shared data. While more work on privacy mechanisms that do not compromise prediction performance is needed, result on three real-world datasets show that the linear contextual bandit can improve energy saving when compared supervised solutions.