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Support vector machines (SVMs) are popular learning algorithms to deal with binary classification problems. They traditionally assume equal misclassification costs for each class; however, real-world problems may have an uneven class…
Recently, convex nested stochastic composite optimization (NSCO) has received considerable attention for its applications in reinforcement learning and risk-averse optimization. The current NSCO algorithms have worse stochastic oracle…
Motivated by multi-user optimization problems and non-cooperative Nash games in uncertain regimes, we consider stochastic Cartesian variational inequalities (SCVI) where the set is given as the Cartesian product of a collection of component…
In this paper, we consider the general non-oblivious stochastic optimization where the underlying stochasticity may change during the optimization procedure and depends on the point at which the function is evaluated. We develop Stochastic…
Frank-Wolfe algorithm (FW) and its variants have gained a surge of interests in machine learning community due to its projection-free property. Recently people have reduced the gradient evaluation complexity of FW algorithm to…
In this paper, we extend our previous results and formally propose the SCvx-fast algorithm, a new addition to the Successive Convexification algorithmic framework. The said algorithm solves non-convex optimal control problems with specific…
When applying the support vector machine (SVM) to high-dimensional classification problems, we often impose a sparse structure in the SVM to eliminate the influences of the irrelevant predictors. The lasso and other variable selection…
The explosive availability of remote sensing images has challenged supervised classification algorithms such as Support Vector Machines (SVM), as training samples tend to be highly limited due to the expensive and laborious task of ground…
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…
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…
Support vector machines (SVMs) are a standard method in the machine learning toolbox, in particular for tabular data. Non-linear kernel SVMs often deliver highly accurate predictors, however, at the cost of long training times. That problem…
This paper addresses the problem of efficiently classifying high-dimensional data over decentralized networks. Penalized support vector machines (SVMs) are widely used for high-dimensional classification tasks. However, the double…
In many online learning problems the computational bottleneck for gradient-based methods is the projection operation. For this reason, in many problems the most efficient algorithms are based on the Frank-Wolfe method, which replaces…
The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational…
The minimum volume enclosing ellipsoid (MVEE) problem is an optimization problem in the basis of many practical problems. This paper describes some new properties of this model and proposes a first-order oracle algorithm, the Adjusted…
In this paper, we investigate the problem of stochastic multi-level compositional optimization, where the objective function is a composition of multiple smooth but possibly non-convex functions. Existing methods for solving this problem…
This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…
Support Vector Machines (SVMs) are a cornerstone of supervised learning, widely used for data classification. A central component of their success lies in kernel functions, which enable efficient computation of inner products in…
Current multimodal LLMs encode images as static visual prefixes and rely on text-based reasoning, lacking goal-driven and adaptive visual access. Inspired by human visual perception-where attention is selectively and sequentially shifted…
Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a…