Related papers: Online Alternating Direction Method (longer versio…
In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the…
Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected -- accelerated optimization can…
We revisit multi-agent asynchronous online optimization with delays, where only one of the agents becomes active for making the decision at each round, and the corresponding feedback is received by all the agents after unknown delays.…
Online multi-task learning (OMTL) enhances streaming data processing by leveraging the inherent relations among multiple tasks. It can be described as an optimization problem in which a single loss function is defined for multiple tasks.…
This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
This work focuses on the setting of dynamic regret in the context of online learning with full information. In particular, we analyze regret bounds with respect to the temporal variability of the loss functions. By assuming that the…
Alternating Direction Method of Multipliers (ADMM) is a popular algorithm for distributed learning, where a network of nodes collaboratively solve a regularized empirical risk minimization by iterative local computation associated with…
This article investigates the problem of controlling linear time-invariant systems subject to time-varying and a priori unknown cost functions, state and input constraints, and exogenous disturbances. We combine the online convex…
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…
In online convex optimization, some efficient algorithms have been designed for each of the individual classes of objective functions, e.g., convex, strongly convex, and exp-concave. However, existing regret analyses, including those of…
We propose the algorithms for online convex optimization which lead to cumulative squared constraint violations of the form $\sum\limits_{t=1}^T\big([g(x_t)]_+\big)^2=O(T^{1-\beta})$, where $\beta\in(0,1)$. Previous literature has focused…
The alternating direction method of multipliers (ADMM) is commonly used for distributed model fitting problems, but its performance and reliability depend strongly on user-defined penalty parameters. We study distributed ADMM methods that…
To expand the applicability of decentralized online learning, previous studies have proposed several algorithms for decentralized online continuous submodular maximization (D-OCSM) -- a non-convex/non-concave setting with continuous…
Recently, several universal methods have been proposed for online convex optimization, and attain minimax rates for multiple types of convex functions simultaneously. However, they need to design and optimize one surrogate loss for each…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
We propose an algorithm based on online convex optimization for controlling discrete-time linear dynamical systems. The algorithm is data-driven, i.e., does not require a model of the system, and is able to handle a priori unknown and…
Multi-agent distributed optimization over a network minimizes a global objective formed by a sum of local convex functions using only local computation and communication. We develop and analyze a quantized distributed algorithm based on the…
We consider online optimization problems with time-varying linear equality constraints. In this framework, an agent makes sequential decisions using only prior information. At every round, the agent suffers an environment-determined loss…
Online mirror descent (OMD) and dual averaging (DA) -- two fundamental algorithms for online convex optimization -- are known to have very similar (and sometimes identical) performance guarantees when used with a fixed learning rate. Under…