Related papers: Between Stochastic and Adversarial Online Convex O…
Hoffman's classical result gives a bound on the distance of a point from a convex and compact polytope in terms of the magnitude of violation of the constraints. Recently, several results showed that Hoffman's bound can be used to derive…
Algorithms for online learning typically require one or more boundedness assumptions: that the domain is bounded, that the losses are Lipschitz, or both. In this paper, we develop a new setting for online learning with unbounded domains and…
Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex…
Recently, there were introduced important classes of relatively smooth, relatively continuous, and relatively strongly convex optimization problems. These concepts have significantly expanded the class of problems for which optimal…
We design learning rate schedules that minimize regret for SGD-based online learning in the presence of a changing data distribution. We fully characterize the optimal learning rate schedule for online linear regression via a novel analysis…
We study Smoothed Online Convex Optimization, a version of online convex optimization where the learner incurs a penalty for changing her actions between rounds. Given a $\Omega(\sqrt{d})$ lower bound on the competitive ratio of any online…
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…
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 work, we develop linear bandit algorithms that automatically adapt to different environments. By plugging a novel loss estimator into the optimization problem that characterizes the instance-optimal strategy, our first algorithm not…
We study fast rates of convergence in the setting of nonparametric online regression, namely where regret is defined with respect to an arbitrary function class which has bounded complexity. Our contributions are two-fold: - In the…
This paper initiates the study of data-dependent regret bounds in constrained MAB settings. These bounds depend on the sequence of losses that characterize the problem instance. Thus, they can be much smaller than classical…
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…
We develop a reduction-based framework for online learning with delayed feedback that recovers and improves upon existing results for both first-order and bandit convex optimization. Our approach introduces a continuous-time model under…
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…
In online learning, the dynamic regret metric chooses the reference (optimal) solution that may change over time, while the typical (static) regret metric assumes the reference solution to be constant over the whole time horizon. The…
This paper studies online convex optimization with stochastic constraints. We propose a variant of the drift-plus-penalty algorithm that guarantees $O(\sqrt{T})$ expected regret and zero constraint violation, after a fixed number of…
We study Constrained Online Convex Optimization with Memory (COCO-M), where both the loss and the constraints depend on a finite window of past decisions made by the learner. This setting extends the previously studied unconstrained online…
We address learning Nash equilibria in convex games under the payoff information setting. We consider the case in which the game pseudo-gradient is monotone but not necessarily strictly monotone. This relaxation of strict monotonicity…
We provide new lower bounds on the regret that must be suffered by adversarial bandit algorithms. The new results show that recent upper bounds that either (a) hold with high-probability or (b) depend on the total lossof the best arm or (c)…
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…