Related papers: On the $1/e$-strategy for the best-choice problem …
We present an extensive study of the key problem of online learning where algorithms are allowed to abstain from making predictions. In the adversarial setting, we show how existing online algorithms and guarantees can be adapted to this…
We study a natural online variant of the replacement path problem. The \textit{replacement path problem} asks to find for a given graph $G = (V,E)$, two designated vertices $s,t\in V$ and a shortest $s$-$t$ path $P$ in $G$, a…
Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the…
It has been pointed out by counterexamples in a 2013 paper in the IEEE Transactions on Computers [1], that there is an error in the previously ibid.\ in 2005 published paper [2] on the construction of valid digit selection tables for SRT…
In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting…
This paper has been withdrawn by the corresponding author because the newest version is now published in Journal of Discrete Algorithms.
Concerning Version 1 of ``Worst-case Nonparametric Bounds for the Student T-statistic'', arXiv:2508.13226: The main result there is incorrect. Concerning Version 2 of arXiv:2508.13226: At least the proof of the main result there is…
Given a finite sequence of events and a well-defined notion of events being interesting, the Odds-theorem (Bruss (2000)) gives an online strategy to stop on the last interesting event. It is optimal for independent events. Here we study…
This paper has been withdrawn due to a crucial error in combining the two probability sectors represented in equations 13 and 14. Corrected, one can recover, in the limit of no background, the results of Allen et al. The general result that…
In high-stakes applications, predictive models must not only produce accurate predictions but also quantify and communicate their uncertainty. Reject-option prediction addresses this by allowing the model to abstain when prediction…
This work addresses the classic machine learning problem of online prediction with expert advice. We consider the finite-horizon version of this zero-sum, two-person game. Using verification arguments from optimal control theory, we view…
We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and on…
People are often reluctant to sell a house, or shares of stock, below the price at which they originally bought it. While this is generally not consistent with rational utility maximization, it does reflect two strong empirical regularities…
This paper has been withdrawn by the author, since one of the key results duplicates existing work, as pointed out by a reader. I am currently revising the manuscript.
Strategy improvement is a widely-used and well-studied class of algorithms for solving graph-based infinite games. These algorithms are parameterized by a switching rule, and one of the most natural rules is "all switches" which switches as…
We propose a novel method for selective classification (SC), a problem which allows a classifier to abstain from predicting some instances, thus trading off accuracy against coverage (the fraction of instances predicted). In contrast to…
This paper has been withdrawn by the author due to a crucial error.
I withdraw my paper from arXiv because there is a technical error in the proof of Theorem 1.1. And because of this error, all the results in the paper are untrue. I am very sorry for this.
In this paper, we study the behavior of the Hedge algorithm in the online stochastic setting. We prove that anytime Hedge with decreasing learning rate, which is one of the simplest algorithm for the problem of prediction with expert…
Optimising queries in real-world situations under imperfect conditions is still a problem that has not been fully solved. We consider finding the optimal order in which to execute a given set of selection operators under partial ignorance…