Related papers: Controlling tail risk in two-slope ski rental
The classical ski-rental problem admits a textbook 2-competitive deterministic algorithm, and a simple randomized algorithm that is $\frac{e}{e-1}$-competitive in expectation. The randomized algorithm, while optimal in expectation, has a…
The learning-augmented multi-option ski rental problem generalizes the classical ski rental problem in two ways: the algorithm is provided with a prediction on the number of days we can ski, and the ski rental options now come with a…
The ski rental problem is a canonical model for online decision-making under uncertainty, capturing the fundamental trade-off between repeated rental costs and a one-time purchase. While classical algorithms focus on worst-case competitive…
The classical 'buy or rent' ski-rental problem was recently considered in the setting where multiple experts (such as Machine Learning algorithms) advice on the length of the ski season. Here, robust algorithms were developed with improved…
We consider the {\em multi-shop ski rental} problem. This problem generalizes the classic ski rental problem to a multi-shop setting, in which each shop has different prices for renting and purchasing a pair of skis, and a \emph{consumer}…
In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a one-time setup cost (``buying…
In this paper, we study the two-level ski-rental problem,where a user needs to fulfill a sequence of demands for multiple items by choosing one of the three payment options: paying for the on-demand usage (i.e., rent), buying individual…
In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the…
We study the design of risk-sensitive online algorithms, in which risk measures are used in the competitive analysis of randomized online algorithms. We introduce the CVaR$_\delta$-competitive ratio ($\delta$-CR) using the conditional…
We revisit the central online problem of ski rental in the "algorithms with predictions" framework from the point of view of distributional predictions. Ski rental was one of the first problems to be studied with predictions, where a…
This paper introduces a novel multi-agent ski-rental problem that generalizes the classical ski-rental dilemma to a group setting where agents incur individual and shared costs. In our model, each agent can either rent at a fixed daily…
Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…
We consider a variant of the classic Ski Rental online algorithm with applications to machine learning. In our variant, we allow the skier access to a black-box machine-learning algorithm that provides an estimate of the probability that…
We study stochastic convex optimization (SCO) with heavy-tailed gradients under pure $\varepsilon$-differential privacy (DP). Instead of assuming a bound on the worst-case Lipschitz parameter of the loss, we assume only a bounded $k$-th…
We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…
In this paper we propose a problem-driven scenario generation approach to the single-period portfolio selection problem which use tail risk measures such as conditional value-at-risk. Tail risk measures are useful for quantifying potential…
We revisit the classic ski rental problem through the lens of Bayesian decision-making and machine-learned predictions. While traditional algorithms minimize worst-case cost without assumptions, and recent learning-augmented approaches…
We study the optimal trade-off between expectation and tail risk for regret distribution in the stochastic multi-armed bandit model. We fully characterize the interplay among three desired properties for policy design: worst-case…
We study convex optimization problems under differential privacy (DP). With heavy-tailed gradients, existing works achieve suboptimal rates. The main obstacle is that existing gradient estimators have suboptimal tail properties, resulting…
We study the stochastic multi-armed bandit problem and design new policies that enjoy both worst-case optimality for expected regret and light-tailed risk for regret distribution. Specifically, our policy design (i) enjoys the worst-case…