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Predicting the output of a dynamical system from streaming data is fundamental to real-time feedback control and decision-making. We first derive an autoregressive representation that relates future local outputs to asynchronous past…
We analyze and evaluate an online gradient descent algorithm with adaptive per-coordinate adjustment of learning rates. Our algorithm can be thought of as an online version of batch gradient descent with a diagonal preconditioner. This…
In the setting of online learning, Implicit algorithms turn out to be highly successful from a practical standpoint. However, the tightest regret analyses only show marginal improvements over Online Mirror Descent. In this work, we shed…
Non-stationary online learning has drawn much attention in recent years. In particular, dynamic regret and adaptive regret are proposed as two principled performance measures for online convex optimization in non-stationary environments. To…
In many quantum tasks, there is an unknown quantum object that one wishes to learn. An online strategy for this task involves adaptively refining a hypothesis to reproduce such an object or its measurement statistics. A common evaluation…
We consider prediction with expert advice when the loss vectors are assumed to lie in a set described by the sum of atomic norm balls. We derive a regret bound for a general version of the online mirror descent (OMD) algorithm that uses a…
This paper studies bandit convex optimization in non-stationary environments with two-point feedback, using dynamic regret as the performance measure. We propose an algorithm based on bandit mirror descent that extends naturally to…
We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…
We study online linear optimization with matrix variables constrained by the operator norm, a setting where the geometry renders designing data-dependent and efficient adaptive algorithms challenging. The best-known adaptive regret bounds…
We study an online linear regression setting in which the observed feature vectors are corrupted by noise and the learner can pay to reduce the noise level. In practice, this may happen for several reasons: for example, because features can…
Partial monitoring is a general model for sequential learning with limited feedback formalized as a game between two players. In this game, the learner chooses an action and at the same time the opponent chooses an outcome, then the learner…
We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…
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…
We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
Self-normalized martingale inequalities lie at the heart of confidence ellipsoids for online least squares and, more broadly, many bandit and reinforcement-learning results. Yet existing vector and scalar results typically rely on bounded…
We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of…
Prediction with experts' advice is one of the most fundamental problems in online learning and captures many of its technical challenges. A recent line of work has looked at online learning through the lens of differential equations and…
In this paper we propose a general methodology to derive regret bounds for randomized multi-armed bandit algorithms. It consists in checking a set of sufficient conditions on the sampling probability of each arm and on the family of…
We consider online optimization in the 1-lookahead setting, where the objective does not decompose additively over the rounds of the online game. The resulting formulation enables us to deal with non-stationary and/or long-term constraints…
We improve the theoretical and empirical performance of neural-network(NN)-based active learning algorithms for the non-parametric streaming setting. In particular, we introduce two regret metrics by minimizing the population loss that are…