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Regularized online learning is widely used in machine learning applications. In online learning, performing exact minimization ($i.e.,$ implicit update) is known to be beneficial to the numerical stability and structure of solution. In this…
The development of online algorithms to track time-varying systems has drawn a lot of attention in the last years, in particular in the framework of online convex optimization. Meanwhile, sparse time-varying optimization has emerged as a…
In computational PDE-based inverse problems, a finite amount of data is collected to infer unknown parameters in the PDE. In order to obtain accurate inferences, the collected data must be informative about the unknown parameters. How to…
We consider the problem of distributed online optimization, with a group of learners connected via a dynamic communication graph. The goal of the learners is to track the global minimizer of a sum of time-varying loss functions in a…
Online influence maximization (OIM) is a popular problem in social networks to learn influence propagation model parameters and maximize the influence spread at the same time. Most previous studies focus on the independent cascade (IC)…
In online learning, the dynamic regret metric chooses the reference (optimal) solution that may change over time, while the typical (static) regret metric assumes the reference solution to be constant over the whole time horizon. The…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
Existing approaches to online convex optimization (OCO) make sequential one-slot-ahead decisions, which lead to (possibly adversarial) losses that drive subsequent decision iterates. Their performance is evaluated by the so-called regret…
Stochastically Extended Adversarial (SEA) model is introduced by Sachs et al. [2022] as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition, they demonstrate that the expected…
We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and…
In this paper, we consider an elliptic eigenvalue problem with multiscale, randomly perturbed coefficients. For an efficient and accurate approximation of the solutions for many different realizations of the coefficient, we propose a…
We study monotone submodular maximization under general matroid constraints in the online setting. We prove that online optimization of a large class of submodular functions, namely, weighted threshold potential functions, reduces to online…
This paper studies the online convex optimization problem by using an Online Continuous-Time Nesterov Accelerated Gradient method (OCT-NAG). We show that the continuous-time dynamics generated by the online version of the Bregman Lagrangian…
In this paper, we consider an online optimization problem over $T$ rounds where at each step $t\in[T]$, the algorithm chooses an action $x_t$ from the fixed convex and compact domain set $\mathcal{K}$. A utility function $f_t(\cdot)$ is…
We propose algorithms for online principal component analysis (PCA) and variance minimization for adaptive settings. Previous literature has focused on upper bounding the static adversarial regret, whose comparator is the optimal fixed…
This paper addresses tracking of a moving target in a multi-agent network. The target follows a linear dynamics corrupted by an adversarial noise, i.e., the noise is not generated from a statistical distribution. The location of the target…
We study an algorithmic equivalence technique between non-convex gradient descent and convex mirror descent. We start by looking at a harder problem of regret minimization in online non-convex optimization. We show that under certain…
We consider systems that require timely monitoring of sources over a communication network, where the cost of delayed information is unknown, time-varying and possibly adversarial. For the single source monitoring problem, we design…
Empirical Risk Minimization (ERM) is a foundational framework for supervised learning but primarily optimizes average-case performance, often neglecting fairness and robustness considerations. Tilted Empirical Risk Minimization (TERM)…
This paper studies the problem of online parameter estimation for cyber-physical systems with binary outputs that may be subject to adversarial data tampering. Existing methods are primarily offline and unsuitable for real-time learning. To…