Related papers: Fenchel Duals for Drifting Adversaries

To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms…

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…

In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…

We study offline reinforcement learning (RL) with linear MDPs under the infinite-horizon discounted setting which aims to learn a policy that maximizes the expected discounted cumulative reward using a pre-collected dataset. Existing…

Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better…

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…

The goal of a learner in standard online learning is to maintain an average loss close to the loss of the best-performing single function in some class. In many real-world problems, such as rating or ranking items, there is no single best…

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…

Fast changing states or volatile environments pose a significant challenge to online optimization, which needs to perform rapid adaptation under limited observation. In this paper, we give query and regret optimal bandit algorithms under…

We provide theoretical analyses for two algorithms that solve the regularized optimal transport (OT) problem between two discrete probability measures with at most $n$ atoms. We show that a greedy variant of the classical Sinkhorn…

Offline Reinforcement Learning (RL) aims to learn a near-optimal policy from a fixed dataset of transitions collected by another policy. This problem has attracted a lot of attention recently, but most existing methods with strong…

We study geometric duality for convex vector optimization problems. For a primal problem with a $q$-dimensional objective space, we formulate a dual problem with a $(q+1)$-dimensional objective space. Consequently, different from an…

We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…

This paper proposes a primal-dual framework to learn a stable estimator for linear constrained estimation problems leveraging the moving horizon approach. To avoid the online computational burden in most existing methods, we learn a…

We reinterpret some online greedy algorithms for a class of nonlinear "load-balancing" problems as solving a mathematical program online. For example, we consider the problem of assigning jobs to (unrelated) machines to minimize the sum of…

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…

The theory of deep learning focuses almost exclusively on supervised learning, non-convex optimization using stochastic gradient descent, and overparametrized neural networks. It is common belief that the optimizer dynamics, network…

We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…

In this paper, we address tracking of a time-varying parameter with unknown dynamics. We formalize the problem as an instance of online optimization in a dynamic setting. Using online gradient descent, we propose a method that sequentially…