Related papers: Improved Approximate Regret for Decentralized Onli…
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 investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
In online convex optimization, some efficient algorithms have been designed for each of the individual classes of objective functions, e.g., convex, strongly convex, and exp-concave. However, existing regret analyses, including those of…
Universal online learning aims to achieve optimal regret guarantees without requiring prior knowledge of the curvature of online functions. Existing methods have established minimax-optimal regret bounds for universal online learning, where…
The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as an optimal control problem. Using regret as a metric for an…
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…
The constrained version of the standard online convex optimization (OCO) framework, called COCO is considered, where on every round, a convex cost function and a convex constraint function are revealed to the learner after it chooses the…
Online optimization has emerged as powerful tool in large scale optimization. In this pa- per, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization…
A new algorithm for regret minimization in online convex optimization is described. The regret of the algorithm after $T$ time periods is $O(\sqrt{T \log T})$ - which is the minimum possible up to a logarithmic term. In addition, the new…
Recently, several universal methods have been proposed for online convex optimization, and attain minimax rates for multiple types of convex functions simultaneously. However, they need to design and optimize one surrogate loss for each…
An online decision-making problem is a learning problem in which a player repeatedly makes decisions in order to minimize the long-term loss. These problems that emerge in applications often have nonlinear combinatorial objective functions,…
We consider the online convex optimization problem. In the setting of arbitrary sequences and finite set of parameters, we establish a new fast-rate quantile regret bound. Then we investigate the optimization into the L1-ball by…
Maximizing a monotone submodular function is a fundamental task in machine learning, economics, and statistics. In this paper, we present two communication-efficient decentralized online algorithms for the monotone continuous DR-submodular…
We investigate distributed online convex optimization with compressed communication, where $n$ learners connected by a network collaboratively minimize a sequence of global loss functions using only local information and compressed data…
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,…
We introduce a novel framework for decentralized projection-free optimization, extending projection-free methods to a broader class of upper-linearizable functions. Our approach leverages decentralized optimization techniques with the…
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…
We consider a basic problem at the interface of two fundamental fields: submodular optimization and online learning. In the online unconstrained submodular maximization (online USM) problem, there is a universe $[n]=\{1,2,...,n\}$ and a…
We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and…
Reflecting the greater significance of recent history over the distant past in non-stationary environments, $\lambda$-discounted regret has been introduced in online convex optimization (OCO) to gracefully forget past data as new…