Related papers: A Frank-Wolfe Based Branch-and-Bound Algorithm for…
In this paper, we consider approximate Frank-Wolfe (FW) algorithms to solve convex optimization problems over graph-structured support sets where the linear minimization oracle (LMO) cannot be efficiently obtained in general. We first…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
In portfolio analysis, the traditional approach of replacing population moments with sample counterparts may lead to suboptimal portfolio choices. I show that optimal portfolio weights can be estimated using a machine learning (ML)…
We consider Bayesian optimization of objective functions of the form $\rho[ F(x, W) ]$, where $F$ is a black-box expensive-to-evaluate function and $\rho$ denotes either the VaR or CVaR risk measure, computed with respect to the randomness…
The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are…
This paper introduces unified projection-free Frank-Wolfe type algorithms for adversarial continuous DR-submodular optimization, spanning scenarios such as full information and (semi-)bandit feedback, monotone and non-monotone functions,…
We propose a novel generalization of the conditional gradient (CG / Frank-Wolfe) algorithm for minimizing a smooth function $f$ under an intersection of compact convex sets, using a first-order oracle for $\nabla f$ and linear minimization…
We introduce novel techniques to enhance Frank-Wolfe algorithms by leveraging function smoothness beyond traditional short steps. Our study focuses on Frank-Wolfe algorithms with step sizes that incorporate primal-dual guarantees, offering…
This paper introduces a neural network-based nonlinear shrinkage estimator of covariance matrices for the purpose of minimum variance portfolio optimization. It is a hybrid approach that integrates statistical estimation with machine…
The Frank-Wolfe method is a popular method in sparse constrained optimization, due to its fast per-iteration complexity. However, the tradeoff is that its worst case global convergence is comparatively slow, and importantly, is…
Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear…
The boosted Frank-Wolfe algorithm accelerates the classical Frank-Wolfe algorithm by better aligning the update direction with the negative gradient. Its analysis, however, has been limited to deterministic convex problems, with step sizes…
Stochastic compositional optimization minimizes objectives of the form $\min_{\bm{x} \in \mathcal{X}} F(\bm{f}(\bm{x}), \bm{x})$, where $\bm{f}$ is accessible only through noisy stochastic queries. Existing methods for this problem assume…
We consider the oracle complexity of constrained convex optimization given access to a Linear Minimization Oracle (LMO) for the constraint set and a gradient oracle for the $L$-smooth, strongly convex objective. This model includes…
Portfolio diversification is one of the most effective ways to minimize investment risk. Individuals and fund managers aim to create a portfolio of assets that not only have high returns but are also uncorrelated. This goal can be achieved…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
The optimal transport (OT) problem has been used widely for machine learning. It is necessary for computation of an OT problem to solve linear programming with tight mass-conservation constraints. These constraints prevent its application…
We propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily…
In this paper, we study a mean-variance optimization problem in an infinite horizon discrete time discounted Markov decision process (MDP). The objective is to minimize the variance of system rewards with the constraint of mean performance.…
In constrained convex optimization, existing methods based on the ellipsoid or cutting plane method do not scale well with the dimension of the ambient space. Alternative approaches such as Projected Gradient Descent only provide a…