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In order to model risk aversion in reinforcement learning, an emerging line of research adapts familiar algorithms to optimize coherent risk functionals, a class that includes conditional value-at-risk (CVaR). Because optimizing the…

We study stochastic decentralized optimization for the problem of training machine learning models with large-scale distributed data. We extend the widely used EXTRA and DIGing methods with variance reduction (VR), and propose two methods:…

Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…

We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…

We develop algorithms that find and track the optimal solution trajectory of time-varying convex optimization problems which consist of local and network-related objectives. The algorithms are derived from the prediction-correction…

We consider a new framework where a continuous, though bounded, random variable has unobserved bounds that vary over time. In the context of univariate time series, we look at the bounds as parameters of the distribution of the bounded…

In recent years, by using Bregman distance, the Lipschitz gradient continuity and strong convexity were lifted and replaced by relative smoothness and relative strong convexity. Under the mild assumptions, it was proved that gradient…

Constrained Online Convex Optimization (COCO) can be seen as a generalization of the standard Online Convex Optimization (OCO) framework. At each round, a cost function and constraint function are revealed after a learner chooses an action.…

We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their…

Online convex optimization (OCO) with time-varying constraints is a critical framework for sequential decision-making in dynamic networked systems, where learners must minimize cumulative loss while satisfying regions of feasibility that…

High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…

Distributed optimization increasingly plays a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the complete potential of the technology has not yet been fully exploited in practice due to…

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

Gradient-related first-order methods have become the workhorse of large-scale numerical optimization problems. Many of these problems involve nonconvex objective functions with multiple saddle points, which necessitates an understanding of…

This work examines the convergence of stochastic gradient-based optimization algorithms that use early stopping based on a validation function. The form of early stopping we consider is that optimization terminates when the norm of the…

We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…

In this work, we propose a control scheme for linear systems subject to pointwise in time state and input constraints that aims to minimize time-varying and a priori unknown cost functions. The proposed controller is based on online convex…

Parallelization is a popular strategy for improving the performance of iterative algorithms. Optimization methods are no exception: design of efficient parallel optimization methods and tight analysis of their theoretical properties are…

A semilinear initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For L1-type discretizations of this…

For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method…