Related papers: Offline-online approximation of multiscale eigenva…
Large scale nonlinear classification is a challenging task in the field of support vector machine. Online random Fourier feature map algorithms are very important methods for dealing with large scale nonlinear classification problems. The…
We propose a data-driven approach to solve multiscale elliptic PDEs with random coefficients based on the intrinsic low dimension structure of the underlying elliptic differential operators. Our method consists of offline and online stages.…
Recent work has shown that offline reinforcement learning (RL) can be formulated as a sequence modeling problem (Chen et al., 2021; Janner et al., 2021) and solved via approaches similar to large-scale language modeling. However, any…
We propose a local Legendre frame (LLF) method for function approximation from equispaced data on a finite interval. Motivated by the difficulty of stable high-order polynomial approximation at equispaced points, especially in the presence…
We introduce a novel spatial discretization technique for the reliable and efficient simulation of magnetization dynamics governed by the Landau-Lifshitz (LL) equation. The overall discretization error is systematically decomposed into…
In this paper a novel numerical approximation of parametric eigenvalue problems is presented. We motivate our study with the analysis of a POD reduced order model for a simple one dimensional example. In particular, we introduce a new…
In the last decades, due to the huge technological growth observed, it has become increasingly common that a collection of temporal data rapidly accumulates in vast amounts. This provides an opportunity for extracting valuable information…
We consider online learning with linear models, where the algorithm predicts on sequentially revealed instances (feature vectors), and is compared against the best linear function (comparator) in hindsight. Popular algorithms in this…
Offline reinforcement learning (offline RL), which aims to find an optimal policy from a previously collected static dataset, bears algorithmic difficulties due to function approximation errors from out-of-distribution (OOD) data points. To…
Projection-based reduced order models rely on offline-online model decomposition, where the data-based energetic spatial basis is used in the expensive offline stage to obtain equations of reduced states that evolve in time during the…
In this paper, the online variants of the classical Frank-Wolfe algorithm are considered. We consider minimizing the regret with a stochastic cost. The online algorithms only require simple iterative updates and a non-adaptive step size…
In offline reinforcement learning (RL), we seek to utilize offline data to evaluate (or learn) policies in scenarios where the data are collected from a distribution that substantially differs from that of the target policy to be evaluated.…
We consider the offline constrained reinforcement learning (RL) problem, in which the agent aims to compute a policy that maximizes expected return while satisfying given cost constraints, learning only from a pre-collected dataset. This…
Offline Reinforcement Learning (RL) faces distributional shift and unreliable value estimation, especially for out-of-distribution (OOD) actions. To address this, existing uncertainty-based methods penalize the value function with…
We introduce a transformation framework that can be utilized to develop online algorithms with low $\epsilon$-approximate regret in the random-order model from offline approximation algorithms. We first give a general reduction theorem that…
Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on-line stage, the precomputed problem-dependent solution…
We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the…
We propose a novel and robust online function-on-scalar regression technique via geometric median to learn associations between functional responses and scalar covariates based on massive or streaming datasets. The online estimation…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…