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A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
Modern policy optimization methods roughly follow the policy mirror descent (PMD) algorithmic template, for which there are by now numerous theoretical convergence results. However, most of these either target tabular environments, or can…
In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Holder continuous operators in both deterministic and stochastic settings. The proposed methods automatically adapt not only to the…
This study presents a novel Equiangular Direction Method (EDM) to solve a multi-objective optimization problem. We consider optimization problems, where multiple differentiable losses have to be minimized. The presented method computes…
We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
Recent years have seen the rapid development of fairness-aware machine learning in mitigating unfairness or discrimination in decision-making in a wide range of applications. However, much less attention has been paid to the fairness-aware…
Many real-life optimization problems frequently contain one or more constraints or objectives for which there are no explicit formulas. If data is however available, these data can be used to learn the constraints. The benefits of this…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural…
MM (majorization--minimization) algorithms are an increasingly popular tool for solving optimization problems in machine learning and statistical estimation. This article introduces the MM algorithm framework in general and via three…
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…
An approach to the classification problem of machine learning, based on building local classification rules, is developed. The local rules are considered as projections of the global classification rules to the event we want to classify. A…
Consider the following variant of the set cover problem. We are given a universe $U=\{1,...,n\}$ and a collection of subsets $\mathcal{C} = \{S_1,...,S_m\}$ where $S_i \subseteq U$. For every element $u \in U$ we need to find a set $\phi(u)…
Multi-Task Learning is a learning paradigm that uses correlated tasks to improve performance generalization. A common way to learn multiple tasks is through the hard parameter sharing approach, in which a single architecture is used to…
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
Recommender systems are one of the most applied methods in machine learning and find applications in many areas, ranging from economics to the Internet of things. This article provides a general overview of modern approaches to recommender…