Related papers: A Unified Analysis Method for Online Optimization …
This paper introduces a new problem-dependent regret measure for online convex optimization with smooth losses. The notion, which we call the $G^\star$ regret, depends on the cumulative squared gradient norm evaluated at the decision in…
We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us…
We propose the algorithms for online convex optimization which lead to cumulative squared constraint violations of the form $\sum\limits_{t=1}^T\big([g(x_t)]_+\big)^2=O(T^{1-\beta})$, where $\beta\in(0,1)$. Previous literature has focused…
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…
This paper considers distributed online nonconvex optimization with time-varying inequality constraints over a network of agents, where the nonconvex local loss and convex local constraint functions can vary arbitrarily across iterations.…
We investigate online convex optimization in changing environments, and choose the adaptive regret as the performance measure. The goal is to achieve a small regret over every interval so that the comparator is allowed to change over time.…
We investigate constrained online convex optimization, in which decisions must belong to a fixed and typically complicated domain, and are required to approximately satisfy additional time-varying constraints over the long term. In this…
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…
We address online linear optimization problems when the possible actions of the decision maker are represented by binary vectors. The regret of the decision maker is the difference between her realized loss and the best loss she would have…
The framework of online learning with memory naturally captures learning problems with temporal constraints, and was previously studied for the experts setting. In this work we extend the notion of learning with memory to the general Online…
This paper considers the problem of distributed bandit online convex optimization with time-varying coupled inequality constraints. This problem can be defined as a repeated game between a group of learners and an adversary. The learners…
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,…
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…
In this paper, we consider Riemannian online convex optimization with dynamic regret. First, we propose two novel algorithms, namely the Riemannian Online Optimistic Gradient Descent (R-OOGD) and the Riemannian Adaptive Online Optimistic…
Although online convex optimization (OCO) under arbitrary delays has received increasing attention recently, previous studies focus on stationary environments with the goal of minimizing static regret. In this paper, we investigate the…
We propose an online convex optimization algorithm (RescaledExp) that achieves optimal regret in the unconstrained setting without prior knowledge of any bounds on the loss functions. We prove a lower bound showing an exponential separation…
We propose an algorithm based on online convex optimization for controlling discrete-time linear dynamical systems. The algorithm is data-driven, i.e., does not require a model of the system, and is able to handle a priori unknown 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…
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 consider online learning in episodic loop-free Markov decision processes (MDPs), where the loss function can change arbitrarily between episodes, and the transition function is not known to the learner. We show…