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We introduce and study the Group Square-Root Lasso (GSRL) method for estimation in high dimensional sparse regression models with group structure. The new estimator minimizes the square root of the residual sum of squares plus a penalty…

Leveraging offline data is a promising way to improve the sample efficiency of online reinforcement learning (RL). This paper expands the pool of usable data for offline-to-online RL by leveraging abundant non-curated data that is…

Here we develop variants of SGD (stochastic gradient descent) with an adaptive step size that make use of the sampled loss values. In particular, we focus on solving a finite sum-of-terms problem, also known as empirical risk minimization.…

We present an approach for continual learning (CL) that is based on fully probabilistic (or generative) models of machine learning. In contrast to, e.g., GANs that are "generative" in the sense that they can generate samples, fully…

Many stochastic optimization algorithms work by estimating the gradient of the cost function on the fly by sampling datapoints uniformly at random from a training set. However, the estimator might have a large variance, which inadvertently…

Importance sampling (IS) represents a fundamental technique for a large surge of off-policy reinforcement learning approaches. Policy gradient (PG) methods, in particular, significantly benefit from IS, enabling the effective reuse of…

We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by…

First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…

It is challenging to recover the large-scale internet traffic data purely from the link measurements. With the rapid growth of the problem scale, it will be extremely difficult to sustain the recovery accuracy and the computational cost. In…

This paper proposes an improved version of the current online learning algorithm for a general fuzzy min-max neural network (GFMM) to tackle existing issues concerning expansion and contraction steps as well as the way of dealing with…

Online decision-making problem requires us to make a sequence of decisions based on incremental information. Common solutions often need to learn a reward model of different actions given the contextual information and then maximize the…

In this paper, we propose the generalized mixed reduced rank regression method, GMR$^3$ for short. GMR$^3$ is a regression method for a mix of numeric, binary, and ordinal response variables. The predictor variables can be a mix of binary,…

Deep reinforcement learning (DRL) has significantly advanced the field of combinatorial optimization (CO). However, its practicality is hindered by the necessity for a large number of reward evaluations, especially in scenarios involving…

GRPO has emerged as a prominent reinforcement learning algorithm for post-training LLMs. Unlike critic-based methods, GRPO computes advantages by estimating the \emph{value baselines} from group-level statistics, eliminating the need for a…

This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a…

Randomized algorithms that base iteration-level decisions on samples from some pool are ubiquitous in machine learning and optimization. Examples include stochastic gradient descent and randomized coordinate descent. This paper makes…

Group distributionally robust optimization (GDRO) aims to develop models that perform well across $m$ distributions simultaneously. Existing GDRO algorithms can only process a fixed number of samples per iteration, either 1 or $m$, and…

Federated learning (FL) is an emerging technique for training machine learning models using geographically dispersed data collected by local entities. It includes local computation and synchronization steps. To reduce the communication…

Federated Learning (FL) typically aggregates client model parameters using a weighting approach determined by sample proportions. However, this naive weighting method may lead to unfairness and degradation in model performance due to…

Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…