Related papers: Exp-Concavity of Proper Composite Losses
We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints , which are constraints that need to be satisfied when accumulated over a finite number of rounds T , but can…
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…
In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts. At each step of the online game several experts predict a function, and the learner has to efficiently aggregate these functional…
We consider Constrained Online Convex Optimization (COCO) with adversarially chosen constraints. At each round, the learner chooses an action before observing the loss and constraint function for that round. The goal is to achieve small…
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…
In this paper, we investigate the online non-convex optimization problem which generalizes the classic {online convex optimization problem by relaxing the convexity assumption on the cost function. For this type of problem, the classic…
Non-stationary online learning has drawn much attention in recent years. Despite considerable progress, dynamic regret minimization has primarily focused on convex functions, leaving the functions with stronger curvature (e.g., squared or…
Online Convex Optimization plays a key role in large scale machine learning. Early approaches to this problem were conservative, in which the main focus was protection against the worst case scenario. But recently several algorithms have…
We study a variant of online convex optimization where the player is permitted to switch decisions at most $S$ times in expectation throughout $T$ rounds. Similar problems have been addressed in prior work for the discrete decision set…
This paper investigates online composite optimization in dynamic environments, where each objective or loss function contains a time-varying nondifferentiable regularizer. To resolve it, an online proximal gradient algorithm is studied for…
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…
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…
In this paper, we study adaptive online convex optimization, and aim to design a universal algorithm that achieves optimal regret bounds for multiple common types of loss functions. Existing universal methods are limited in the sense that…
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,…
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…
Mixability of a loss is known to characterise when constant regret bounds are achievable in games of prediction with expert advice through the use of Vovk's aggregating algorithm. We provide a new interpretation of mixability via convex…
Constrained Online Convex Optimization (COCO) can be seen as a generalization of the standard Online Convex Optimization (OCO) framework. At each round, a cost function and constraint function are revealed after a learner chooses an action.…
We consider prediction with expert advice for strongly convex and bounded losses, and investigate trade-offs between regret and "variance" (i.e., squared difference of learner's predictions and best expert predictions). With $K$ experts,…
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…
This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to…