Mini-batch cutting plane method for regularized risk minimization
Accepted： 2019-12-10
Available online：2019-12-10
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Abstract
Although concern has been recently expressed with regard to the solution to the non-convex problem, convex optimization is still important in , especially when the situation requires an interpretable model. Solution to the convex problem is a global minimum, and the final model can be explained mathematically. Typically, the convex problem is re-casted as a regularized risk minimization problem to prevent overfitting. The (CPM) is one of the best solvers for the convex problem, irrespective of whether the objective function is differentiable or not. However, CPM and its variants fail to adequately address large-scale data-intensive cases because these algorithms access the entire dataset in each iteration, which substantially increases the computational burden and memory cost. To alleviate this problem, we propose a novel algorithm named the mini-batch (MBCPM), which iterates with estimated cutting planes calculated on a small batch of sampled data and is capable of handling large-scale problems. Furthermore, the proposed MBCPM adopts a “sink” operation that detects and adjusts noisy estimations to guarantee convergence. Numerical experiments on extensive real-world datasets demonstrate the effectiveness of MBCPM, which is superior to the bundle methods for regularized risk minimization as well as popular stochastic gradient descent methods in terms of convergence speed.
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