Related papers: Inexact Online Proximal Mirror Descent for time-va…
In this paper, we propose and analyze algorithms for zeroth-order optimization of non-convex composite objectives, focusing on reducing the complexity dependence on dimensionality. This is achieved by exploiting the low dimensional…
This paper studies bandit convex optimization with constraints, where the learner aims to generate a sequence of decisions under partial information of loss functions such that the cumulative loss is reduced as well as the cumulative…
In this paper, we propose Distributed Mirror Descent (DMD) algorithm for constrained convex optimization problems on a (strongly-)connected multi-agent network. We assume that each agent has a private objective function and a constraint…
We consider the problem of sampling from a posterior distribution arising in Bayesian inverse problems in science, engineering, and imaging. Our method belongs to the family of independence Metropolis-Hastings (IMH) sampling algorithms,…
In this paper, we consider a distributed constrained optimization problem with delayed subgradient information over the time-varying communication network, where each agent can only communicate with its neighbors and the communication…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
In this work, we analyze two of the most fundamental algorithms in geodesically convex optimization: Riemannian gradient descent and (possibly inexact) Riemannian proximal point. We quantify their rates of convergence and produce different…
Online optimization has emerged as powerful tool in large scale optimization. In this paper, we introduce efficient online algorithms based on the alternating directions method (ADM). We introduce a new proof technique for ADM in the batch…
We study three families of online convex optimization algorithms: follow-the-proximally-regularized-leader (FTRL-Proximal), regularized dual averaging (RDA), and composite-objective mirror descent. We first prove equivalence theorems that…
We propose primal-dual stochastic mirror descent for the convex optimization problems with functional constraints. We obtain the rate of convergence in terms of probability of large deviations.
We investigate online convex optimization in changing environments, and choose the adaptive regret as the performance measure. The goal is to achieve a small regret over every interval so that the comparator is allowed to change over time.…
We address the online linear optimization problem with bandit feedback. Our contribution is twofold. First, we provide an algorithm (based on exponential weights) with a regret of order $\sqrt{d n \log N}$ for any finite action set with $N$…
The logarithmic divergence is an extension of the Bregman divergence motivated by optimal transport and a generalized convex duality, and satisfies many remarkable properties. Using the geometry induced by the logarithmic divergence, we…
We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…
Distributed gradient descent algorithms have come to the fore in modern machine learning, especially in parallelizing the handling of large datasets that are distributed across several workers. However, scant attention has been paid to…
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…
This paper addresses the design and analysis of feedback-based online algorithms to control systems or networked systems based on performance objectives and engineering constraints that may evolve over time. The emerging time-varying convex…
We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…
This paper proposes a modular approach that combines the online convex optimization framework and reference governors to solve a constrained control problem featuring time-varying and a priori unknown cost functions. Compared to existing…
In this paper, the mixed equilibrium problem with coupled inequality constraints in dynamic environments is solved by employing a multi-agent system, where each agent only has access to its own bifunction, its own constraint function, and…