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We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function…
This text presents an introduction to an emerging paradigm in control of dynamical systems and differentiable reinforcement learning called online nonstochastic control. The new approach applies techniques from online convex optimization…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
In this paper, we consider the problem of distributed online convex optimization, where a network of local agents aim to jointly optimize a convex function over a period of multiple time steps. The agents do not have any information about…
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…
In this paper we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
Multi-objective Markov decision processes are a special kind of multi-objective optimization problem that involves sequential decision making while satisfying the Markov property of stochastic processes. Multi-objective reinforcement…
A novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in an online manner, where the target and constraint functions are oblivious adversarially generated…
We develop an online gradient algorithm for optimizing the performance of product-form networks through online adjustment of control parameters. The use of standard algorithms for finding optimal parameter settings is hampered by the…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
This paper describes a new online convex optimization method which incorporates a family of candidate dynamical models and establishes novel tracking regret bounds that scale with the comparator's deviation from the best dynamical model in…
We introduce the online stochastic Convex Programming (CP) problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many well-studied problems like online…
Online-learning research has mainly been focusing on minimizing one objective function. In many real-world applications, however, several objective functions have to be considered simultaneously. Recently, an algorithm for dealing with…
We describe a framework for deriving and analyzing online optimization algorithms that incorporate adaptive, data-dependent regularization, also termed preconditioning. Such algorithms have been proven useful in stochastic optimization by…
This paper considers the problem of online trajectory design under time-varying environments. We formulate the general trajectory optimization problem within the framework of time-varying constrained convex optimization and proposed a novel…
This work addresses decentralized online optimization in non-stationary environments. A network of agents aim to track the minimizer of a global time-varying convex function. The minimizer evolves according to a known dynamics corrupted by…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…
As application demands for online convex optimization accelerate, the need for designing new methods that simultaneously cover a large class of convex functions and impose the lowest possible regret is highly rising. Known online…