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Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper addresses the problem of learning to sparsify stochastic linear bandits, where a decision-maker sequentially selects actions from a high-dimensional space subject to a sparsity constraint on the number of nonzero elements in the…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
The analysis in Part I revealed interesting properties for subgradient learning algorithms in the context of stochastic optimization when gradient noise is present. These algorithms are used when the risk functions are non-smooth and…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
This paper provides examples of various synchronous and asynchronous signal processing systems for performing optimization, utilizing the framework and elements developed in a preceding paper. The general strategy in that paper was to…
Joint sparsity regularization in multi-task learning has attracted much attention in recent years. The traditional convex formulation employs the group Lasso relaxation to achieve joint sparsity across tasks. Although this approach leads to…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…
This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…
This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our…
The parameters of a neural network are naturally organized in groups, some of which might not contribute to its overall performance. To prune out unimportant groups of parameters, we can include some non-differentiable penalty to the…
Despite widespread adoption in practice, guarantees for the LASSO and Group LASSO are strikingly lacking in settings beyond statistical problems, and these algorithms are usually considered to be a heuristic in the context of sparse convex…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
Multitask learning can be effective when features useful in one task are also useful for other tasks, and the group lasso is a standard method for selecting a common subset of features. In this paper, we are interested in a less restrictive…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…