A Quasi-Newton Approach to Nonsmooth Convex Optimization
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چکیده
We extend the well-known BFGS quasiNewton method and its limited-memory variant (LBFGS) to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: The local quadratic model, the identification of a descent direction, and the Wolfe line search conditions. We apply the resulting sub(L)BFGS algorithm to L2-regularized risk minimization with binary hinge loss, and its directionfinding component to L1-regularized risk minimization with logistic loss. In both settings our generic algorithms perform comparable to or better than their counterparts in specialized state-of-the-art solvers.
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A Quasi-Newton Approach to Nonsmooth Convex Optimization A Quasi-Newton Approach to Nonsmooth Convex Optimization
We extend the well-known BFGS quasi-Newton method and its limited-memory variant (LBFGS) to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: The local quadratic model, the identification of a descent direction, and the Wolfe line search conditions. We apply the resulting subLBFGS algorithm to L2-reg...
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