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Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…
For a given region, and specified boundary flux and density rate of an extensive property, the optimal flux field that satisfies the balance conditions is considered. The optimization criteria are the $L^{p}$-norm and a Sobolev-like norm of…
We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the square lattice, while in other cases the lattices optimizing the…
Safe exploration is a key to applying reinforcement learning (RL) in safety-critical systems. Existing safe exploration methods guaranteed safety under the assumption of regularity, and it has been difficult to apply them to large-scale…
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…
The specific objective of this paper is to develop a tool that calculates the optimal trajectory of the follower aircraft as it completes a formation rejoin, and then maintains the formation position, defined as a ring of points, until a…
Safety filters provide a practical approach for enforcing safety constraints in autonomous systems. While learning-based tools scale to high-dimensional systems, their performance depends on informative data that includes states likely to…
We develop asymptotically optimal policies for the multi armed bandit (MAB), problem, under a cost constraint. This model is applicable in situations where each sample (or activation) from a population (bandit) incurs a known bandit…
The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is…
We study a scenario where a group of agents, each with multiple heterogeneous sensors are collecting measurements of a vehicle and the measurements are transmitted over a communication channel to a centralized node for processing. The…
In this paper, we study the problem of optimal data collection for policy evaluation in linear bandits. In policy evaluation, we are given a target policy and asked to estimate the expected reward it will obtain when executed in a…
Soft robotic manipulators are attractive for a range of applications such as medical interventions or industrial inspections in confined environments. A myriad of soft robotic manipulators have been proposed in the literature, but their…
Although quality indicators play a crucial role in benchmarking evolutionary multi-objective optimization algorithms, their properties are still unclear. One promising approach for understanding quality indicators is the use of the optimal…
We study bandit best-arm identification with arbitrary and potentially adversarial rewards. A simple random uniform learner obtains the optimal rate of error in the adversarial scenario. However, this type of strategy is suboptimal when the…
We use the exact finite sample likelihood and statistical decision theory to answer questions of ``why?'' and ``what should you have done?'' using data from randomized experiments and a utility function that prioritizes safety over…
We investigate optimal discrimination between two projective quantum measurements on a single qubit. We consider scenario where the measurement that should be identified can be performed twice and we show that adaptive discrimination…
Modern sparse arrays are maximally economic in that they retain just as many sensors required to provide a specific aperture while maintaining a hole-free difference coarray. As a result, these are susceptible to the failure of even a…
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…
This note describes the optimal policy rule, according to the local asymptotic minimax regret criterion, for best arm identification when there are only two treatments. It is shown that the optimal sampling rule is the Neyman allocation,…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…