arXiv research

The paper tackles resource allocation for arms with unknown and random rewards, achieving optimal regret bounds.

New method tightens sub-Gaussian concentration inequalities.

The paper tackles best arm identification in contaminated bandits with optimal error guarantees and sample complexity.

This paper extends the MAB problem to consider risk-reward tradeoffs.

Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE -- a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential f…

The paper develops algorithms to minimize misallocation and identify the arm with the highest variance.

Improved statistical efficiency of Thompson Sampling for combinatorial semi-bandits.

LinMED is a new linear bandit algorithm with near-optimal regret bound.

The stochastic multi-armed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper we examine the bandit problem under the weaker assumption that the distributions have moments of order 1+ε, for some $ε\in (0,1]$. Surprisingly, moments of order 2 (i.e., finite variance) are suffi…

Nonparametric Thompson Sampling achieves optimal regret for risk-averse bandits with sub-Gaussian rewards.

A novel algorithm minimizes regret in a multi-agent bandit problem with time-varying random graphs and heterogeneous rewards.

KL-MS improves regret bounds for multi-armed bandits with bounded rewards.

Optimism stabilizes Thompson Sampling for adaptive inference in multi-armed bandits.

GROS combines estimators robustly in metric spaces.

We investigate the optimality of perturbation based algorithms in the stochastic and adversarial multi-armed bandit problems. For the stochastic case, we provide a unified regret analysis for both sub-Weibull and bounded perturbations when rewards are sub-Gaussian. Our bounds are instance optimal for sub-Weibull pertur…

Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration inequalities, which thus lead to over-exploration. In this paper, we propose a n…

New algorithms detect changes in non-stationary MABs for better performance.

Thompson Sampling is a well established approach to bandit and reinforcement learning problems. However its use in continuum armed bandit problems has received relatively little attention. We provide the first bounds on the regret of Thompson Sampling for continuum armed bandits under weak conditions on the function cl…

Unified framework controls false discovery rate in bandit multiple testing.

New algorithm reduces worst-case regret for heavy-tailed bandits.

Global convergence for robust regression problems via IRLS with enhancements.

New method clusters items with bandit feedback without parametric assumptions.

We design and analyze CascadeBAI, an algorithm for finding the best set of $K$ items, also called an arm, within the framework of cascading bandits. An upper bound on the time complexity of CascadeBAI is derived by overcoming a crucial analytical challenge, namely, that of probabilistically estimating the amount of ava…

We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of estimators that achieve sub-Gaussian type deviations even for heavy tailed data. We revisit some of these estimators through the lens of differ…

Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $α$-stable distribution received much interest in the literature. Here, we introduce a type of expectation maximization algorithm that e…

Sharp sub-Gaussian bounds for subsolutions of Trudinger's equation on Riemannian manifolds.

Random linear mappings are widely used in modern signal processing, compressed sensing and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful information. This is done by approximately preserving the distances between data points,…

UCB algorithm adapted for large-scale, non-sub-Gaussian problems.

Proves new concentration inequalities for sub-gaussian and sub-exponential variables.

Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.

We consider $K$-armed stochastic bandits and consider cumulative regret bounds up to time $T$. We are interested in strategies achieving simultaneously a distribution-free regret bound of optimal order $\sqrt{KT}$ and a distribution-dependent regret that is asymptotically optimal, that is, matching the $κ\ln T$ lower b…

A new differentiable UCB algorithm for linear bandits learns adaptive confidence bounds.

New algorithm converts data into sub-gaussian designs efficiently.

Quantum algorithm estimates mean with sub-Gaussian error.

Sharp comparison for sub-Gaussian random variables in convex order.

Thompson Sampling bounds for contextual bandits with sub-Gaussian rewards.

New method reduces summary points for datasets while maintaining quality.

Estimates sub-Gaussian parameter with consistent and optimal rates.

Proposes a new model for clustering with heavier tails.

New study shows mean estimation algorithms can't beat sub-Gaussian rate in general.

New winsorized mean improves robustness to up to 50% contamination.

The paper proves a regret bound for a sub-Gaussian mixture on unbounded data.

Algorithm for low-rank matrix bandits with heavy-tailed rewards, achieving nearly optimal regret bound.

We study the problem of estimating the mean of a random vector $X$ given a sample of $N$ independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of $X$ exists. The estimator is based on a novel concept of a…

Two new algorithms improve robust PCA and Schatten packing.

Paper analyzes SGMs for learning sub-Gaussian distributions without dimensionality constraints.

SVGD algorithm converges at rate 1/sqrt(log log n) for sub-Gaussian distributions.

The paper extends physics-based information maximization to complex bandit problems.