### Introduction * *Curriculum Learning*  When training machine learning models, start with easier subtasks and gradually increase the difficulty level of the tasks. * Motivation comes from the observation that humans and animals seem to learn better when trained with a curriculum like a strategy. * [Link](http://ronan.collobert.com/pub/matos/2009_curriculum_icml.pdf) to the paper. ### Contributions of the paper * Explore cases that show that curriculum learning benefits machine learning. * Offer hypothesis around when and why does it happen. * Explore relation of curriculum learning with other machine learning approaches. ### Experiments with convex criteria * Training perceptron where some input data is irrelevant(not predictive of the target class). * Difficulty can be defined in terms of the number of irrelevant samples or margin from the separating hyperplane. * Curriculum learning model outperforms nocurriculum based approach. * Surprisingly, in the case of difficulty defined in terms of the number of irrelevant examples, the anticurriculum strategy also outperforms nocurriculum strategy. ### Experiments on shape recognition with datasets having different variability in shapes * Standard(target) dataset  Images of rectangles, ellipses, and triangles. * Easy dataset  Images of squares, circles, and equilateral triangles. * Start performing gradient descent on easy dataset and switch to target data set at a particular epoch (called *switch epoch*). * For nocurriculum learning, the first epoch is the *switch epoch*. * As *switch epoch* increases, the classification error comes down with the best performance when *switch epoch* is half the total number of epochs. * Paper does not report results for higher values of *switch epoch*. ### Experiments on language modeling * Standard data set is the set of all possible windows of the text of size 5 from Wikipedia where all words in the window appear in 20000 most frequent words. * Easy dataset considers only those windows where all words appear in 5000 most frequent words in vocabulary. * Each word from the vocabulary is embedded into a *d* dimensional feature space using a matrix **W** (to be learnt). * The model predicts the score of next word, given a window of words. * Expected value of ranking loss function is minimized to learn **W**. * Curriculum Learningbased model overtakes the other model soon after switching to the target vocabulary, indicating that curriculumbased model quickly learns new words. ### Curriculum as a continuation method * Continuation methods start with a smoothed objective function and gradually move to less smoothed function. * Useful in the case where the objective function in nonconvex. * Consider a family of cost functions $C_\lambda (\theta)$ such that $C_0(\theta)$ can be easily optimized and $C_1(\theta)$ is the actual objective function. * Start with $C_0 (\theta)$ and increase $\lambda$, keeping $\theta$ at a local minimum of $C_\lambda (\theta)$. * Idea is to move $\theta$ towards a dominant (if not global) minima of $C_1(\theta)$. * Curriculum learning can be seen as a sequence of training criteria starting with an easytooptimise objective and moving all the way to the actual objective. * The paper provides a mathematical formulation of curriculum learning in terms of a target training distribution and a weight function (to model the probability of selecting anyone training example at any step). ### Advantages of Curriculum Learning * Faster training in the online setting as learner does not try to learn difficult examples when it is not ready. * Guiding training towards better local minima in parameter space, specifically useful for nonconvex methods. ### Relation to other machine learning approaches * **Unsupervised preprocessing**  Both have a regularizing effect and lower the generalization error for the same training error. * **Active learning**  The learner would benefit most from the examples that are close to the learner's frontier of knowledge and are neither too hard nor too easy. * **Boosting Algorithms**  Difficult examples are gradually emphasised though the curriculum starts with a focus on easier examples and the training criteria do not change. * **Transfer learning** and **Lifelong learning**  Initial tasks are used to guide the optimisation problem. ### Criticism * Curriculum Learning is not well understood, making it difficult to define the curriculum. * In one of the examples, anticurriculum performs better than nocurriculum. Given that curriculum learning is modeled on the idea that learning benefits when examples are presented in order of increasing difficulty, one would expect anticurriculum to perform worse.
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