Although application examples of multilevel optimization have already been discussed since the '90s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem.
We propose a new formulation of Multiple-Instance Learning (MIL), in which a unit of data consists of a set of instances called a bag.
Classifiers based on a single shapelet are not sufficiently strong for certain applications.
However, a fairness level as a constraint induces a nonconvexity of the feasible region, which disables the use of an off-the-shelf convex optimizer.
Even more severe, small insignificant partial correlations due to noise can dramatically change the clustering result when evaluating for example with the Bayesian Information Criteria (BIC).
Moreover, for a large class of loss functions and regularizers, the KL exponent of the corresponding potential function are shown to be 1/2, which implies that the pDCA$_e$ is locally linearly convergent when applied to these problems.
Motivated by online advertising, we study a multiple-play multi-armed bandit problem with position bias that involves several slots and the latter slots yield fewer rewards.
We consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and a finite number of nonnegative proper closed possibly nonsmooth functions (whose proximal mappings are easy to compute), some of which are further composed with linear maps.
We consider binary classification problems using local features of objects.
For learning parameters such as the regularization parameter in our algorithm, we derive a simple formula that guarantees the robustness of the classifier.
However, Bayesian learning is often obstructed by computational difficulty: the rigorous Bayesian learning is intractable in many models, and its variational Bayesian (VB) approximation is prone to suffer from local minima.