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We propose a learning approach to tracking explicitly minimizing the computational complexity of the tracking process subject to user-defined probability of failure (loss-of-lock) and precision. The tracker is formed by a Number of Sequences of Learned Linear Predictors (NoSLLiP). Robustness of NoSLLiP is achieved by modeling the object as a collection of local motion predictors - object motion is estimated by the outlier-tolerant RANSAC algorithm from local predictions. Efficiency of the NoSLLiP tracker stems from (i) the simplicity of the local predictors and (ii) from the fact that all design decisions - the number of local predictors used by the tracker, their computational complexity (i.e. the number of observations the prediction is based on), locations as well as the number of RANSAC iterations are all subject to the optimization (learning) process. All time-consuming operations are performed during the learning stage - tracking is reduced to only a few hundreds integer multiplications in each step. On PC with 1timesK8 3200+, a predictor evaluation requires about 30 mus. The proposed approach is verified on publicly-available sequences with approximately 12000 frames with ground-truth. Experiments demonstrates, superiority in frame rates and robustness with respect to the SIFT detector, Lucas-Kanade tracker and other trackers.