相关论文: Online Adjoint Methods for Optimization of PDEs
We propose a new discrete-time online parameter estimation algorithm that combines two different aspects, one that adds momentum, and another that includes a time-varying learning rate. It is well known that recursive least squares based…
We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…
We propose a new multistep deep learning-based algorithm for the resolution of moderate to high dimensional nonlinear backward stochastic differential equations (BSDEs) and their corresponding parabolic partial differential equations (PDE).…
Online decision making aims to learn the optimal decision rule by making personalized decisions and updating the decision rule recursively. It has become easier than before with the help of big data, but new challenges also come along.…
When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…
Online optimization problems arise in many resource allocation tasks, where the future demands for each resource and the associated utility functions change over time and are not known apriori, yet resources need to be allocated at every…
We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to…
This paper studies the problem of controlling linear dynamical systems subject to point-wise-in-time constraints. We present an algorithm similar to online gradient descent, that can handle time-varying and a priori unknown convex cost…
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…
This paper considers online convex optimization with time-varying constraint functions. Specifically, we have a sequence of convex objective functions $\{f_t(x)\}_{t=0}^{\infty}$ and convex constraint functions…
In the past few years, Online Convex Optimization (OCO) has received notable attention in the control literature thanks to its flexible real-time nature and powerful performance guarantees. In this paper, we propose new step-size rules and…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
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…
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,…
We present a series of results regarding conceptually simple algorithms for bipartite matching in various online and related models. We first consider a deterministic adversarial model. The best approximation ratio possible for a one-pass…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
Reduced-order modeling lies at the interface of numerical analysis and data-driven scientific computing, providing principled ways to compress high-fidelity simulations in science and engineering. We propose a training framework that…
In the setting of online algorithms, the input is initially not present but rather arrive one-by-one over time and after each input, the algorithm has to make a decision. Depending on the formulation of the problem, the algorithm might be…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
We incorporate future information in the form of the estimated value of future gradients in online convex optimization. This is motivated by demand response in power systems, where forecasts about the current round, e.g., the weather or the…