155 research outputs found

    A Screening Strategy for Structured Optimization Involving Nonconvex â„“q,p\ell_{q,p} Regularization

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    In this paper, we develop a simple yet effective screening rule strategy to improve the computational efficiency in solving structured optimization involving nonconvex â„“q,p\ell_{q,p} regularization. Based on an iteratively reweighted â„“1\ell_1 (IRL1) framework, the proposed screening rule works like a preprocessing module that potentially removes the inactive groups before starting the subproblem solver, thereby reducing the computational time in total. This is mainly achieved by heuristically exploiting the dual subproblem information during each iteration.Moreover, we prove that our screening rule can remove all inactive variables in a finite number of iterations of the IRL1 method. Numerical experiments illustrate the efficiency of our screening rule strategy compared with several state-of-the-art algorithms

    Screening for Sparse Online Learning

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    Sparsity promoting regularizers are widely used to impose low-complexity structure (e.g. l1-norm for sparsity) to the regression coefficients of supervised learning. In the realm of deterministic optimization, the sequence generated by iterative algorithms (such as proximal gradient descent) exhibit "finite activity identification", namely, they can identify the low-complexity structure in a finite number of iterations. However, most online algorithms (such as proximal stochastic gradient descent) do not have the property owing to the vanishing step-size and non-vanishing variance. In this paper, by combining with a screening rule, we show how to eliminate useless features of the iterates generated by online algorithms, and thereby enforce finite activity identification. One consequence is that when combined with any convergent online algorithm, sparsity properties imposed by the regularizer can be exploited for computational gains. Numerically, significant acceleration can be obtained

    Nonsmoothness in Machine Learning: specific structure, proximal identification, and applications

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    Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine learning and illustrate how to leverage this structure in practice, for compression, acceleration, or dimension reduction. We pay a special attention to the presentation to make it concise and easily accessible, with both simple examples and general results
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