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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…
We study dynamic regret in online convex optimization, where the objective is to achieve low cumulative loss relative to an arbitrary benchmark sequence. By observing that competing with an arbitrary sequence of comparators…
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…
In many sequential decision making applications, the change of decision would bring an additional cost, such as the wear-and-tear cost associated with changing server status. To control the switching cost, we introduce the problem of online…
In online learning an algorithm plays against an environment with losses possibly picked by an adversary at each round. The generality of this framework includes problems that are not adversarial, for example offline optimization, or saddle…
We study dynamic regret minimization in non-stationary online learning, with a primary focus on follow-the-regularized-leader (FTRL) methods. FTRL is important for curved losses and for understanding adaptive optimizers such as Adam, yet…
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…
In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret…
In this paper, we focus on a theory-practice gap for Adam and its variants (AMSgrad, AdamNC, etc.). In practice, these algorithms are used with a constant first-order moment parameter $\beta_{1}$ (typically between $0.9$ and $0.99$). In…
Inspired by online learning, data-dependent regret has recently been proposed as a criterion for controller design. In the regret-optimal control paradigm, causal controllers are designed to minimize regret against a hypothetical optimal…
We propose new algorithms with provable performance for online binary optimization subject to general constraints and in dynamic settings. We consider the subset of problems in which the objective function is submodular. We propose the…
We study the problem of online non-stochastic control (ONC), which is the control of a linear system under adversarial disturbances and adversarial cost functions, with the aim of minimizing the total cost incurred. A recent line of…
In repeated interaction problems with adaptive agents, our objective often requires anticipating and optimizing over the space of possible agent responses. We show that many problems of this form can be cast as instances of online…
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…
An open challenge in supervised learning is \emph{conceptual drift}: a data point begins as classified according to one label, but over time the notion of that label changes. Beyond linear autoregressive models, transfer and meta learning…
Online optimization has emerged as powerful tool in large scale optimization. In this pa- per, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…
This paper considers the distributed online bandit optimization problem with nonconvex loss functions over a time-varying digraph. This problem can be viewed as a repeated game between a group of online players and an adversary. At each…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
We carefully investigate the on-line version of PCA, where in each trial a learning algorithm plays a k-dimensional subspace, and suffers the compression loss on the next instance when projected into the chosen subspace. In this setting, we…