This article addresses a particular Transfer Reinforcement Learning (RL) problem: when dynamics do not change from one task to another, and only the reward function does. Our method relies on two ideas, the first one is that transition samples obtained from a task can be reused to learn on any other task: an immediate reward estimator is learnt in a supervised fashion and for each sample, the reward entry is changed by its reward estimate. The second idea consists in adopting the optimism in the face of uncertainty principle and to use upper bound reward estimates. Our method is tested on a navigation task, under four Transfer RL experimental settings: with a known reward function, with strong and weak expert knowledge on the reward function, and with a completely unknown reward function. It is also evaluated in a Multi-Task RL experiment and compared with the state-of-the-art algorithms. Results reveal that this method constitutes a major improvement for transfer/multi-task problems that share dynamics.