相关论文: Span-Agnostic Optimal Sample Complexity and Oracle…

The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…

We study the computational complexity of the infinite-horizon discounted-reward Markov Decision Problem (MDP) with a finite state space $|\mathcal{S}|$ and a finite action space $|\mathcal{A}|$. We show that any randomized algorithm needs a…

Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…

Offline Reinforcement Learning (RL) aims to learn a near-optimal policy from a fixed dataset of transitions collected by another policy. This problem has attracted a lot of attention recently, but most existing methods with strong…

In this paper, we focus our attention on the high-dimensional double sparse linear regression, that is, a combination of element-wise and group-wise sparsity. To address this problem, we propose an IHT-style (iterative hard thresholding)…

We consider the optimal sample complexity theory of tabular reinforcement learning (RL) for maximizing the infinite horizon discounted reward in a Markov decision process (MDP). Optimal worst-case complexity results have been developed for…

We introduce SCAL, an algorithm designed to perform efficient exploration-exploitation in any unknown weakly-communicating Markov decision process (MDP) for which an upper bound $c$ on the span of the optimal bias function is known. For an…

We consider the question introduced by \cite{Mason2020} of identifying all the $\varepsilon$-optimal arms in a finite stochastic multi-armed bandit with Gaussian rewards. We give two lower bounds on the sample complexity of any algorithm…

We present the first finite time global convergence analysis of policy gradient in the context of infinite horizon average reward Markov decision processes (MDPs). Specifically, we focus on ergodic tabular MDPs with finite state and action…

We present two Policy Gradient-based algorithms with general parametrization in the context of infinite-horizon average reward Markov Decision Process (MDP). The first one employs Implicit Gradient Transport for variance reduction, ensuring…

In the regression setting, given a set of hyper-parameters, a model-estimation procedure constructs a model from training data. The optimal hyper-parameters that minimize generalization error of the model are usually unknown. In practice…

Sample-efficient exploration is crucial not only for discovering rewarding experiences but also for adapting to environment changes in a task-agnostic fashion. A principled treatment of the problem of optimal input synthesis for system…

This paper investigates the optimization problem of an infinite stage discrete time Markov decision process (MDP) with a long-run average metric considering both mean and variance of rewards together. Such performance metric is important…

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove…

We study the problem of learning policy of an infinite-horizon, discounted cost, Markov decision process (MDP) with a large number of states. We compute the actions of a policy that is nearly as good as a policy chosen by a suitable oracle…

Robust reinforcement learning (RL) under the average-reward criterion is essential for long-term decision-making, particularly when the environment may differ from its specification. However, a significant gap exists in understanding the…

The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…

The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space $\mathcal{S}$ and the action space $\mathcal{A}$ are both finite, to obtain a nearly optimal policy with…

Multi-period mean-variance optimization is a long-standing problem, caused by the failure of dynamic programming principle. This paper studies the mean-variance optimization in a setting of finite-horizon discrete-time Markov decision…

We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…