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The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose an impressively…
We consider combinatorial semi-bandits over a set of arms ${\cal X} \subset \{0,1\}^d$ where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound $R(T) = {\cal O}\Big( {d (\ln…
The inductive matrix completion (IMC) problem is to recover a low rank matrix from few observed entries while incorporating prior knowledge about its row and column subspaces. In this work, we make three contributions to the IMC problem:…
We introduce GLR-klUCB, a novel algorithm for the piecewise iid non-stationary bandit problem with bounded rewards. This algorithm combines an efficient bandit algorithm, kl-UCB, with an efficient, parameter-free, changepoint detector, the…
The Combinatorial Multi-Armed Bandit problem is a sequential decision-making problem in which an agent selects a set of arms on each round, observes feedback for each of these arms and aims to maximize a known reward function of the arms it…
The Wasserstein metric is broadly used in optimal transport for comparing two probabilistic distributions, with successful applications in various fields such as machine learning, signal processing, seismic inversion, etc. Nevertheless, the…
We consider a kernelized bandit problem with a compact arm set ${X} \subset \mathbb{R}^d $ and a fixed but unknown reward function $f^*$ with a finite norm in some Reproducing Kernel Hilbert Space (RKHS). We propose a class of…
We study the computational complexity of several polynomial-time-solvable graph problems parameterized by vertex integrity, a measure of a graph's vulnerability to vertex removal in terms of connectivity. Vertex integrity is the smallest…
There has been substantial research on sub-linear time approximate algorithms for Maximum Inner Product Search (MIPS). To achieve fast query time, state-of-the-art techniques require significant preprocessing, which can be a burden when the…
Witnessing subsystems for probabilistic reachability thresholds in discrete Markovian models are an important concept both as diagnostic information on why a property holds, and as input to refinement algorithms. We present SWITSS, a tool…
We consider the Gittins index for a normal distribution with unknown mean $\theta$ and known variance where $\theta$ has a normal prior. In addition to presenting some monotonicity properties of the Gittins index, we derive an approximation…
We study the bit complexity of two methods, related to the Euclidean algorithm, for computing cubic and quartic analogs of the Jacobi symbol. The main bottleneck in such procedures is computation of a quotient for long division. We give…
We address the problem of opportunistic multiuser scheduling in downlink networks with Markov-modeled outage channels. We consider the scenario in which the scheduler does not have full knowledge of the channel state information, but…
Given a multiset $S$ of $n$ positive integers and a target integer $t$, the subset sum problem is to decide if there is a subset of $S$ that sums up to $t$. We present a new divide-and-conquer algorithm that computes all the realizable…
We describe an algorithm for computing Schur indices of irreducible characters of a finite group $G$, based on computations within $G$ and its subgroups and with their character tables. The algorithm has been implemented within \Magma\ and…
We study replicable algorithms for stochastic multi-armed bandits (MAB) and linear bandits with UCB (Upper Confidence Bound) based exploration. A bandit algorithm is $\rho$-replicable if two executions using shared internal randomness but…
Let $G$ be a finite group and let $H$ be a proper subgroup of $G$ of minimal index. By applying an old result of Y. Berkovich, we provide a polynomial algorithm for computing $|G : H|$ for a permutation group $G$. Moreover, we find $H$…
The Kirchhoff index, which is the sum of the resistance distance between every pair of nodes in a network, is a key metric for gauging network performance, where lower values signify enhanced performance. In this paper, we study the problem…
We consider the question introduced by \cite{Mason2020} of identifying all the $\varepsilon$-optimal arms in a finite stochastic multi-armed bandit with Gaussian rewards. We give two lower bounds on the sample complexity of any algorithm…
We study the best-arm identification problem in multi-armed bandits with stochastic, potentially private rewards, when the goal is to identify the arm with the highest quantile at a fixed, prescribed level. First, we propose a (non-private)…