Related papers: Convex Optimization with Nested Evolving Feasible …
In online learning an algorithm plays against an environment with losses possibly picked by an adversary at each round. The generality of this framework includes problems that are not adversarial, for example offline optimization, or saddle…
This paper considers the distributed online bandit optimization problem with nonconvex loss functions over a time-varying digraph. This problem can be viewed as a repeated game between a group of online players and an adversary. At each…
In repeated interaction problems with adaptive agents, our objective often requires anticipating and optimizing over the space of possible agent responses. We show that many problems of this form can be cast as instances of online…
We consider online convex optimization with time-varying constraints and conduct performance analysis using two stringent metrics: dynamic regret with respect to the online solution benchmark, and hard constraint violation that does not…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation…
Centered around solving the Online Saddle Point problem, this paper introduces the Online Convex-Concave Optimization (OCCO) framework, which involves a sequence of two-player time-varying convex-concave games. We propose the generalized…
We consider online algorithms under both the competitive ratio criteria and the regret minimization one. Our main goal is to build a unified methodology that would be able to guarantee both criteria simultaneously. For a general class of…
We study an online linear optimization (OLO) problem in which the learner is provided access to $K$ "hint" vectors in each round prior to making a decision. In this setting, we devise an algorithm that obtains logarithmic regret whenever…
In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…
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 study three families of online convex optimization algorithms: follow-the-proximally-regularized-leader (FTRL-Proximal), regularized dual averaging (RDA), and composite-objective mirror descent. We first prove equivalence theorems that…
We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds. We prove a new lower bound on the…
This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous…
This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while…
The trade-off between regret and computational cost is a fundamental problem for online kernel regression, and previous algorithms worked on the trade-off can not keep optimal regret bounds at a sublinear computational complexity. In this…
We recently highlighted a fundamental problem recognized to confound algorithmic optimization, namely, \textit{conflating} the objective with the objective function. Even when the former is well defined, the latter may not be obvious, e.g.,…
Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…
Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…
This paper investigates the problem of regret minimization in linear time-varying (LTV) dynamical systems. Due to the simultaneous presence of uncertainty and non-stationarity, designing online control algorithms for unknown LTV systems…