Related papers: When Does the Gittins Policy Have Asymptotically O…

For a stochastic difference equation $D_n=A_nD_{n-1}+B_n$ which stabilises upon time we study tail distribution asymptotics of $D_n$ under the assumption that the distribution of $\log(1+|A_1|+|B_1|)$ is heavy-tailed, that is, all its…

We investigate the right tail behavior of a certain class of GMC ratios, reminiscent of H\"older's inequality. We start with a heuristic argument to justify the optimal exponent in the tail estimate. Since Kahane's convexity inequality does…

We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…

We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior…

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating…

Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful of signals from tens of thousands of predictors in the…

Lost sales inventory models with large lead times, which arise in many practical settings, are notoriously difficult to optimize due to the curse of dimensionality. In this paper we show that when lead times are large, a very simple…

We revisit the problem of stochastic online learning with feedback graphs, with the goal of devising algorithms that are optimal, up to constants, both asymptotically and in finite time. We show that, surprisingly, the notion of optimal…

Suboptimal methods in optimal control arise due to a limited computational budget, unknown system dynamics, or a short prediction window among other reasons. Although these methods are ubiquitous, their transient performance remains…

For a multiclass G/G/1 queue with finite buffers, admission and scheduling control, and holding and rejection costs, we construct a policy that is asymptotically optimal in the heavy traffic limit. The policy is specified in terms of a…

For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system…

The full potential of large pretrained models remains largely untapped in control domains like robotics. This is mainly because of the scarcity of data and the computational challenges associated with training or fine-tuning these large…

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of…

We present upper and lower bounds for the tail distribution of the stationary waiting time $D$ in the stable $GI/GI/s$ FCFS queue. These bounds depend on the value of the traffic load $\rho$ which is the ratio of mean service and mean…

The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm. While many works provide high-probability guarantees, quantifying…

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.

We consider a multi-class G/G/1 queue with a finite shared buffer. There is task admission and server scheduling control which aims to minimize the cost which consists of holding and rejection components. We construct a policy that is…

Inference-time alignment effectively steers large language models (LLMs) by generating multiple candidates from a reference model and selecting among them with an imperfect reward model. However, current strategies face a fundamental…

In many applications, significant correlations between arrivals of load-generating events make the numerical evaluation of the load of a system a challenging problem. Here, we construct very accurate approximations of the workload…

For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…