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In this paper, we analyze the continuous armed bandit problems for nonconvex cost functions under certain smoothness and sublevel set assumptions. We first derive an upper bound on the expected cumulative regret of a simple bin splitting…
Counterfactual explanations provide a potentially significant solution to the Explainable AI (XAI) problem, but good, native counterfactuals have been shown to rarely occur in most datasets. Hence, the most popular methods generate…
In the stochastic submodular cover problem, the goal is to select a subset of stochastic items of minimum expected cost to cover a submodular function. Solutions in this setting correspond to sequential decision processes that select items…
Currency arbitrage leverages price discrepancies in currency exchange rates across different currency pairs to gain risk-free profits. It involves multiple trading, where short-lived price discrepancies require real-time, high-speed…
We formulate and solve a variant of the quickest detection problem which features false negatives. A standard Brownian motion acquires a drift at an independent exponential random time which is not directly observable. Based on the…
We present a family of quantum money schemes with classical verification which display a number of benefits over previous proposals. Our schemes are based on hidden matching quantum retrieval games and they tolerate noise up to 23%, which…
Designed to compete with fiat currencies, bitcoin proposes it is a crypto-currency alternative. Bitcoin makes a number of false claims, including: solving the double-spending problem is a good thing; bitcoin can be a reserve currency for…
In this note, we introduce a distributed twist on the classic coupon collector problem: a set of $m$ collectors wish to each obtain a set of $n$ coupons; for this, they can each sample coupons uniformly at random, but can also meet in…
Counterfactual explanations (CEs) offer a human-understandable way to explain decisions by identifying specific changes to the input parameters of a base or present model that would lead to a desired change in the outcome. For optimization…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
This paper analyzes a necessary and sufficient condition for the change-making problem to be solvable with a greedy algorithm. The change-making problem is to minimize the number of coins used to pay a given value in a specified currency…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…
We consider a generalisation of the classical coupon collector's problem, in which at each time step a collector either receives a new copy of a randomly chosen coupon, or loses all their previously collected copies of that coupon. We…
We study counterfactual regression, which aims to map input features to outcomes under hypothetical scenarios that differ from those observed in the data. This is particularly useful for decision-making when adapting to sudden shifts in…
In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
Many evolutionary and constructive heuristic approaches have been introduced in order to solve the Traveling Thief Problem (TTP). However, the accuracy of such approaches is unknown due to their inability to find global optima. In this…
We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well…
We study a counterfactual mean-variance optimization, where the mean and variance are defined as functionals of counterfactual distributions. The optimization problem defines the optimal resource allocation under various constraints in a…