Related papers: Frank-Wolfe Methods in Probability Space
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…
Motivated by the computation of the non-parametric maximum likelihood estimator (NPMLE) and the Bayesian posterior in statistics, this paper explores the problem of convex optimization over the space of all probability distributions. We…
This paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is a continuous (i.e. off-the-grid or…
Federated learning (FL) has gained a lot of attention in recent years for building privacy-preserving collaborative learning systems. However, FL algorithms for constrained machine learning problems are still limited, particularly when the…
We present a new algorithm for probabilistic planning with no observability. Our algorithm, called Probabilistic-FF, extends the heuristic forward-search machinery of Conformant-FF to problems with probabilistic uncertainty about both the…
Many existing Neural Network pruning approaches rely on either retraining or inducing a strong bias in order to converge to a sparse solution throughout training. A third paradigm, 'compression-aware' training, aims to obtain…
We investigate a more generalized form of submodular maximization, referred to as $k$-submodular maximization, with applications across social networks and machine learning domains. In this work, we propose the multilinear extension of…
We study stochastic projection-free methods for constrained optimization of smooth functions on Riemannian manifolds, i.e., with additional constraints beyond the parameter domain being a manifold. Specifically, we introduce stochastic…
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…
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…
Generalized self-concordance is a key property present in the objective function of many important learning problems. We establish the convergence rate of a simple Frank-Wolfe variant that uses the open-loop step size strategy $\gamma_t =…
In Bayesian inference, the posterior distributions are difficult to obtain analytically for complex models such as neural networks. Variational inference usually uses a parametric distribution for approximation, from which we can easily…
Metarounding is an approach to convert an approximation algorithm for linear optimization over some combinatorial classes to an online linear optimization algorithm for the same class. We propose a new metarounding algorithm under a natural…
This article establishes a method to answer a finite set of linear queries on a given dataset while ensuring differential privacy. To achieve this, we formulate the corresponding task as a saddle-point problem, i.e. an optimization problem…
Optimization-based problems have become of great interest for signal approximation purposes, as they achieved good accuracy results while being extremely flexible and versatile. In this work, we put our focus on the context of periodic…
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…
In this paper, we show that the Away-step Stochastic Frank-Wolfe Algorithm (ASFW) and Pairwise Stochastic Frank-Wolfe algorithm (PSFW) converge linearly in expectation. We also show that if an algorithm convergences linearly in expectation…
It has been well established that first order optimization methods can converge to the maximal objective value of concave functions and provide constant factor approximation guarantees for (non-convex/non-concave) continuous submodular…
Conditional gradient algorithms (also often called Frank-Wolfe algorithms) are popular due to their simplicity of only requiring a linear optimization oracle and more recently they also gained significant traction for online learning. While…