We consider the problem of bandit optimization, inspired by stochastic optimization and online learning problems with bandit feedback. In this problem, the objective is to minimize a global loss function of all the actions, not necessarily a cumulative loss. This framework allows us to study a very general class of problems, with applications in statistics, machine learning, and other fields. T...

Abstract We propose a simple variant of the generalized Frank–Wolfe method for solving strongly convex composite optimization problems, by introducing an additional averaging step on dual variables. show that in this variant, one can choose constant step-size and obtain linear convergence rate duality gaps. By leveraging analysis we then analyze local logistic fictitious play algorithm, which i...

Often in the analysis of first-order methods for both smooth and nonsmooth optimization, assuming existence a growth/error bound or KL condition facilitates much stronger convergence analysis. Hence, separate is typically needed general case growth bounded cases. We give meta-theorems deriving rates from those lower bound. Applying this simple but conceptually powerful tool to proximal point, s...

In 1956, Frank and Wolfe extended the fundamental existence theorem of linear programming by proving that an arbitrary quadratic function f attains its minimum over a nonempty convex polyhedral set X provided f is bounded from below over X . We show that a similar statement holds if f is a convex polynomial and X is the solution set of a system of convex polynomial inequalities. In fact, this r...

The k-support-norm regularized minimization has recently been applied with success to sparse prediction problems. The proximal gradient method is conventionally used to minimize this composite model. However it tends to suffer from expensive iteration cost thus the model solving could be time consuming. In our work, we reformulate the k-support-norm regularized formulation into a constrained fo...

Given A := {a1, . . . , am} ⊂ Rn and > 0, we propose and analyze two algorithms for the problem of computing a (1 + )-approximation to the radius of the minimum enclosing ball of A. The first algorithm is closely related to the Frank-Wolfe algorithm with a proper initialization applied to the dual formulation of the minimum enclosing ball problem. We establish that this algorithm converges in O...

Domain knowledge is useful to improve the generalization performance of learning machines. Sign constraints are a handy representation combine domain with machine. In this paper, we consider constraining signs weight coefficients in linear support vector machine, and develop an optimization algorithm for minimizing empirical risk under sign constraints. The based on Frank-Wolfe method that also...

Abstract Projection-free optimization via different variants of the Frank–Wolfe method has become one cornerstones large scale for machine learning and computational statistics. Numerous applications within these fields involve minimization functions with self-concordance like properties. Such generalized self-concordant do not necessarily feature a Lipschitz continuous gradient, nor are they s...

We review and analyze nonlinear programming approaches to modeling and solving certain flow problems in telecommunications, transportation and supply chain management. We emphasize the common aspects of telecommunications and road networks, and indicate the importance of game theoretic and equilibrium approaches. Algorithms based on the Frank-Wolfe method are developed in depth and their implem...