Related papers: A Nonstochastic Control Approach to Optimization

We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…

In this paper, we consider the problem of distributed online convex optimization, where a group of agents collaborate to track the global minimizers of a sum of time-varying objective functions in an online manner. Specifically, we propose…

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…

We consider the decision-making framework of online convex optimization with a very large number of experts. This setting is ubiquitous in contextual and reinforcement learning problems, where the size of the policy class renders…

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…

Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline.…

In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…

This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…

Temporal point processes have been widely applied to model event sequence data generated by online users. In this paper, we consider the problem of how to design the optimal control policy for point processes, such that the stochastic…

This paper proposes a data-driven framework to solve time-varying optimization problems associated with unknown linear dynamical systems. Making online control decisions to regulate a dynamical system to the solution of an optimization…

Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…

Control of complex systems involves both system identification and controller design. Deep neural networks have proven to be successful in many identification tasks, however, from model-based control perspective, these networks are…

Policy gradients methods apply to complex, poorly understood, control problems by performing stochastic gradient descent over a parameterized class of polices. Unfortunately, even for simple control problems solvable by standard dynamic…

In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…

Batch training of machine learning models based on neural networks is now well established, whereas to date streaming methods are largely based on linear models. To go beyond linear in the online setting, nonparametric methods are of…

We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed…

The article examines in some detail the convergence rate and mean-square-error performance of momentum stochastic gradient methods in the constant step-size and slow adaptation regime. The results establish that momentum methods are…