Related papers: Robust Kernel-based Distribution Regression
Sample reweighting is one of the most widely used methods for correcting the error of least squares learning algorithms in reproducing kernel Hilbert spaces (RKHS), that is caused by future data distributions that are different from the…
Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…
The sim-to-real gap, which represents the disparity between training and testing environments, poses a significant challenge in reinforcement learning (RL). A promising approach to addressing this challenge is distributionally robust RL,…
In dynamic programming (DP) and reinforcement learning (RL), an agent learns to act optimally in terms of expected long-term return by sequentially interacting with its environment modeled by a Markov decision process (MDP). More generally…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of…
This article extends the optimal covariance steering (CS) problem for discrete time linear stochastic systems modeled using moment-based ambiguity sets. To hedge against the uncertainty in the state distributions while performing covariance…
Distributionally robust optimization (DRO) is a powerful technique to train robust models against data distribution shift. This paper aims to solve regularized nonconvex DRO problems, where the uncertainty set is modeled by a so-called…
Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…
To train machine learning models that are robust to distribution shifts in the data, distributionally robust optimization (DRO) has been proven very effective. However, the existing approaches to learning a distributionally robust model…
Distributional reinforcement learning (DRL) is a recent reinforcement learning framework whose success has been supported by various empirical studies. It relies on the key idea of replacing the expected return with the return distribution,…
This paper concerns the central issues of model robustness and sample efficiency in offline reinforcement learning (RL), which aims to learn to perform decision making from history data without active exploration. Due to uncertainties and…
Recently, (Blanchet, Kang, and Murhy 2016, and Blanchet, and Kang 2017) showed that several machine learning algorithms, such as square-root Lasso, Support Vector Machines, and regularized logistic regression, among many others, can be…
A key task in actuarial modelling involves modelling the distributional properties of losses. Classic (distributional) regression approaches like Generalized Linear Models (GLMs; Nelder and Wedderburn, 1972) are commonly used, but…
Density ratio estimation (DRE) is a fundamental machine learning technique for capturing relationships between two probability distributions. State-of-the-art DRE methods estimate the density ratio using neural networks trained with loss…
We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate $X$ from the response $Y$, given the projection of…
To address the needs of modeling uncertainty in sensitive machine learning applications, the setup of distributionally robust optimization (DRO) seeks good performance uniformly across a variety of tasks. The recent multi-distribution…
This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…