arXiv research

The paper analyzes GTD algorithms with finite-sample bounds.

Paper analyzes Greedy-GQ for reinforcement learning with Markovian noise.

This paper analyzes momentum Q-learning with finite-sample guarantees.

Despite the increasing interest in multi-agent reinforcement learning (MARL) in multiple communities, understanding its theoretical foundation has long been recognized as a challenging problem. In this work, we address this problem by providing a finite-sample analysis for decentralized batch MARL with networked agents…

The paper shows how to learn causal representations with few environments and finite samples.

This study analyzes LTS in sparse models with finite sample error bounds.

New method reduces sample complexity for robust reinforcement learning.

Paper analyzes online tensorial ICA convergence with stochastic approximation.

We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires $k \to \infty$ as the sample size $n \to \in…

Paper analyzes PSGLD for adaptive IRL with finite-sample bounds.

This work analyzes actor-critic methods for faster convergence.

This work analyzes tree-based methods from a ranking perspective, providing insights and new statistics.

This work closes the gap between theory and practice for nICA identifiability.

The paper analyzes off-policy TD-learning using generalized Bellman operators and provides finite-sample bounds.

New analysis shows actor-critic method converges efficiently in practical settings.

We test for departures from normal and independent and identically distributed (NIID) returns, when returns under the alternative hypothesis are self-affine. Self-affine returns are either fractionally integrated and long-range dependent, or drawn randomly from an L-stable distribution with infinite higher-order moment…

A study on a surprising phase transition in model generalization error as parameters approach sample size.

Bitcoin volatility analysis shows decreasing HE with longer sampling periods.

We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to the tensors with the given rank and define a set of polynomials based on the sa…

The paper introduces a frequency-domain estimator for low-order systems from noisy data.

In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the locations of the samples to ens…

The paper studies how more data affects prediction risk in high-dimensional models.

SARSA is an on-policy algorithm to learn a Markov decision process policy in reinforcement learning. We investigate the SARSA algorithm with linear function approximation under the non-i.i.d.\ data, where a single sample trajectory is available. With a Lipschitz continuous policy improvement operator that is smooth eno…

This paper analyzes sampling from heavy-tailed distributions using discretized Itô diffusions.

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalm…

The OLS estimator optimally identifies stable linear systems with a finite number of samples.

Paper introduces a new reinforcement learning method with improved performance.

This work analyzes nonexpansive stochastic approximations with Markovian noise, proving convergence in reinforcement learning.

The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower boun…

We study finite sample properties of estimators of power-law cross-correlations -- detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA) -- with a special focus on short-term memory bias as well as power-law coherency. Presen…

Study on distributional TD learning with linear approximations for better return estimation.

This work uses sampling theory to analyze smoothness and error bounds of finite neural networks.

CNFs learn distributions from samples with error bounds.

New Thompson sampling algorithm reduces regret for exponential family bandits.

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through feature maps; in this way, in addition to treating the consistency of logistic reg…

Paper provides convergence guarantees for off-policy NAC with finite sample complexity.

We adapt a Markov Random Field learning algorithm for continuous variables.

We learn linear models from nonlinear systems using multiple trajectories and regularization.

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are wel…

MF-TRPO optimizes MFGs with finite sample guarantees.

Method constructs nonparametric prediction intervals with finite-sample guarantees.

Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An incomplete $d \times N$ matrix is finitely rank-$r$ completable if there are at …

The paper investigates topic models, ensuring their statistical identifiability and accuracy.

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests. Despite its rich applications, theoretical convergence analysis remains largely ope…

In reinforcement learning (RL) , one of the key components is policy evaluation, which aims to estimate the value function (i.e., expected long-term accumulated reward) of a policy. With a good policy evaluation method, the RL algorithms will estimate the value function more accurately and find a better policy. When th…

Paper analyzes NAC with neural networks for efficient policy optimization.

The paper analyzes how the one-dimensional Wasserstein distance captures pointwise density differences in finite samples.

Unified framework for finite-sample RL algorithms using Lyapunov theory.