Related papers: Online Convex Optimization with Binary Constraints
In this paper, we develop a unified framework for analyzing the tracking error and dynamic regret of inexact online optimization methods under a variety of settings. Specifically, we leverage the quadratic constraint approach from control…
We study various discrete nonlinear combinatorial optimization problems in an online learning framework. In the first part, we address the question of whether there are negative results showing that getting a vanishing (or even vanishing…
Smoothed online combinatorial optimization considers a learner who repeatedly chooses a combinatorial decision to minimize an unknown changing cost function with a penalty on switching decisions in consecutive rounds. We study smoothed…
To address the uncertainty in function types, recent progress in online convex optimization (OCO) has spurred the development of universal algorithms that simultaneously attain minimax rates for multiple types of convex functions. However,…
This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be…
We provide an online learning algorithm that obtains regret $G\|w_\star\|\sqrt{T\log(\|w_\star\|G\sqrt{T})} + \|w_\star\|^2 + G^2$ on $G$-Lipschitz convex losses for any comparison point $w_\star$ without knowing either $G$ or…
This paper mainly addresses the distributed online optimization problem where the local objective functions are assumed to be convex or non-convex. First, the distributed algorithms are proposed for the convex and non-convex situations,…
Regret minimization is treated as the golden rule in the traditional study of online learning. However, regret minimization algorithms tend to converge to the static optimum, thus being suboptimal for changing environments. To address this…
We revisit multi-agent asynchronous online optimization with delays, where only one of the agents becomes active for making the decision at each round, and the corresponding feedback is received by all the agents after unknown delays.…
We consider the problem of controlling an unknown linear dynamical system under adversarially changing convex costs and full feedback of both the state and cost function. We present the first computationally-efficient algorithm that attains…
We consider the framework of non-stationary Online Convex Optimization where a learner seeks to control its dynamic regret against an arbitrary sequence of comparators. When the loss functions are strongly convex or exp-concave, we…
In this book, I introduce the basic concepts of Online Learning through the modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order…
Projection-free online learning has drawn increasing interest due to its efficiency in solving high-dimensional problems with complicated constraints. However, most existing projection-free online methods focus on minimizing the static…
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…
Online optimization has emerged as powerful tool in large scale optimization. In this paper, we introduce efficient online algorithms based on the alternating directions method (ADM). We introduce a new proof technique for ADM in the batch…
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…
This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems, which have potentially non-concave cumulative rewards, hard resource constraints, and a non-separable regularizer. Under…
We consider the problem of online learning with non-convex losses. In terms of feedback, we assume that the learner observes - or otherwise constructs - an inexact model for the loss function encountered at each stage, and we propose a…
In Online Convex Optimization (OCO), when the stochastic gradient has a finite variance, many algorithms provably work and guarantee a sublinear regret. However, limited results are known if the gradient estimate has a heavy tail, i.e., the…
To expand the applicability of decentralized online learning, previous studies have proposed several algorithms for decentralized online continuous submodular maximization (D-OCSM) -- a non-convex/non-concave setting with continuous…