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A well-studied generalization of the standard online convex optimization (OCO) is constrained online convex optimization (COCO). In COCO, on every round, a convex cost function and a convex constraint function are revealed to the learner…
This paper addresses safe distributed online optimization over an unknown set of linear safety constraints. A network of agents aims at jointly minimizing a global, time-varying function, which is only partially observable to each…
We study Online Convex Optimization (OCO) with adversarial constraints, where an online algorithm must make sequential decisions to minimize both convex loss functions and cumulative constraint violations. We focus on a setting where the…
We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of…
We study the problem of safe online convex optimization, where the action at each time step must satisfy a set of linear safety constraints. The goal is to select a sequence of actions to minimize the regret without violating the safety…
In this paper, we broaden the horizon of online convex optimization (OCO), and consider multi-objective OCO, where there are $K$ distinct loss function sequences, and an algorithm has to choose its action at time $t$, before the $K$ loss…
In this work, we study the online convex optimization problem with curved losses and delayed feedback. When losses are strongly convex, existing approaches obtain regret bounds of order $d_{\max} \ln T$, where $d_{\max}$ is the maximum…
We provide an online convex optimization algorithm with regret that interpolates between the regret of an algorithm using an optimal preconditioning matrix and one using a diagonal preconditioning matrix. Our regret bound is never worse…
In this paper, we develop a novel virtual-queue-based online algorithm for online convex optimization (OCO) problems with long-term and time-varying constraints and conduct a performance analysis with respect to the dynamic regret and…
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,…
Projection operations are a typical computation bottleneck in online learning. In this paper, we enable projection-free online learning within the framework of Online Convex Optimization with Memory (OCO-M) -- OCO-M captures how the history…
We consider the problem of Online Convex Optimization (OCO) with two-point bandit feedback. In this setting, a player attempts to minimize a sequence of adversarially generated convex loss functions, while only observing the value of each…
Motivated by the stringent safety requirements that are often present in real-world applications, we study a safe online convex optimization setting where the player needs to simultaneously achieve sublinear regret and zero constraint…
Learning and computation of equilibria are central problems in game theory, theory of computation, and artificial intelligence. In this work, we introduce proximal regret, a new notion of regret based on proximal operators that lies…
Recently, several universal methods have been proposed for online convex optimization which can handle convex, strongly convex and exponentially concave cost functions simultaneously. However, most of these algorithms have been designed…
Diminishing-returns (DR) submodular optimization is an important field with many real-world applications in machine learning, economics and communication systems. It captures a subclass of non-convex optimization that provides both…
This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number…
We study online inverse linear optimization, also known as contextual recommendation, where a learner sequentially infers an agent's hidden objective vector from observed optimal actions over feasible sets that change over time. The learner…
This paper studies online optimization from a high-level unified theoretical perspective. We not only generalize both Optimistic-DA and Optimistic-MD in normed vector space, but also unify their analysis methods for dynamic regret. Regret…
We study an online mixed discrete and continuous optimization problem where a decision maker interacts with an unknown environment for a number of $T$ rounds. At each round, the decision maker needs to first jointly choose a discrete and a…