Related papers: Online Non-convex Optimization with Long-term Non-…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…
We provide an online convex optimization algorithm with regret that interpolates between the regret of an algorithm using an optimal preconditioning matrix and one using a diagonal preconditioning matrix. Our regret bound is never worse…
We study various discrete nonlinear combinatorial optimization problems in an online learning framework. In the first part, we address the question of whether there are negative results showing that getting a vanishing (or even vanishing…
This paper presents a new framework for analyzing and designing no-regret algorithms for dynamic (possibly adversarial) systems. The proposed framework generalizes the popular online convex optimization framework and extends it to its…
We study an algorithmic equivalence technique between non-convex gradient descent and convex mirror descent. We start by looking at a harder problem of regret minimization in online non-convex optimization. We show that under certain…
In this paper, we propose a learning approach to analyze dynamic systems with asymmetric information structure. Instead of adopting a game theoretic setting, we investigate an online quadratic optimization problem driven by system noises…
This paper studies online convex optimization with unknown linear budget constraints, where only the gradient information of the objective and the bandit feedback of constraint functions are observed. We propose a safe and efficient…
We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…
The goal of this work is to accelerate the identification of an unknown ARX system from trajectory data through online input design. Specifically, we present an active learning algorithm that sequentially selects the input to excite the…
This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve…
We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us…
We present the online Newton's method, a single-step second-order method for online nonconvex optimization. We analyze its performance and obtain a dynamic regret bound that is linear in the cumulative variation between round optima. We…
We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we…
We consider online forecasting problems for non-convex machine learning models. Forecasting introduces several challenges such as (i) frequent updates are necessary to deal with concept drift issues since the dynamics of the environment…
Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex…
A constrained version of the online convex optimization (OCO) problem is considered. With slotted time, for each slot, first an action is chosen. Subsequently the loss function and the constraint violation penalty evaluated at the chosen…
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…
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…