Related papers: Robust Algorithms for Online Convex Problems via P…
We study the online convex covering problem and online convex packing problem. The (offline) convex covering problem is modeled by the following convex program: $\min_{x \in R_+^n} f(x) \ \text{s.t}\ A x \ge 1$, where $f : R_+^n \mapsto…
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…
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…
We study a continuous-time primal-dual algorithm for distributed optimization with nonconvex local cost functions over weight-unbalanced digraphs, and analyze its performance from a dissipativity-based perspective. We first reformulate the…
In this work, we introduce a learning model designed to meet the needs of applications in which computational resources are limited, and robustness and interpretability are prioritized. Learning problems can be formulated as constrained…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
We study the robustness of accelerated first-order algorithms to stochastic uncertainties in gradient evaluation. Specifically, for unconstrained, smooth, strongly convex optimization problems, we examine the mean-squared error in the…
We study the problems of distributed online and bandit convex optimization against an adaptive adversary. We aim to minimize the average regret on $M$ machines working in parallel over $T$ rounds with $R$ intermittent communications.…
Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a…
Proximal splitting algorithms are well suited to solving large-scale nonsmooth optimization problems, in particular those arising in machine learning. We propose a new primal-dual algorithm, in which the dual update is randomized;…
We revisit the concept of "adversary" in online learning, motivated by solving robust optimization and adversarial training using online learning methods. While one of the classical setups in online learning deals with the "adversarial"…
In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…
Learning-augmented algorithms have been extensively studied across the computer science community in the recent years, driven by advances in machine learning predictors, which can provide additional information to augment classical…
We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists…
Online optimisation revolves around new data being introduced into a problem while it is still being solved; think of deep learning as more training samples become available. We adapt the idea to dynamic inverse problems such as video…
We describe a primal-dual framework for the design and analysis of online convex optimization algorithms for {\em drifting regret}. Existing literature shows (nearly) optimal drifting regret bounds only for the $\ell_2$ and the…
Entropy regularized Markov decision processes have been widely used in reinforcement learning. This paper is concerned with the primal-dual formulation of the entropy regularized problems. Standard first-order methods suffer from slow…
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…