Recent years have seen a fast growth in the number of applications of Machine Learning algorithms from Computer Science to Robotics. Nevertheless, while most such attempts were successful in maximizing robot performance after a long learning phase, to our knowledge none of them explicitly takes into account the budget in the algorithm evaluation: e.g. budget limitation on the learning duration or on the maximum number of possible actions by the robot. In this paper, we introduce an algorithm for robot spatial localization based on image classification using a sequential budgeted learning framework. This aims to allow the learning of policies under an explicit budget. In this case our model uses a constraint on the number of actions that can be used by the robot. Our approach enables to reduce the problem to a classification task under budget constraint. We apply this algorithm to a localization problem in a simulated environment. We compare it first to simple neural networks for the classification part and second to different techniques of policy selection. The results show that the model can effectively learn an efficient active sensing policy (i.e. alternating between sensor measurement and movement to get additional information in different positions) in order to optimize its localization performance under each tested fixed budget. We also show that with this algorithm the simulated robot can transfer the learned policy as well as knowledge about which budget gives the best performance/budget ratio in a given environment to other environments with similar properties. We finally test the algorithm with real navigation data acquired in an indoor environment with the PR2 robot. Altogether, these results suggest a promising framework for enabling budgeted localization in robots and avoiding to make robots relearn everything from scratch in each new environment.