Related papers: The Adversary Bound Revisited: From Optimal Query …
Given a quantum gate implementing a $d$-dimensional unitary operation $U_d$, without any specific description but $d$, and permitted to use $k$ times, we present a universal probabilistic heralded quantum circuit that implements the exact…
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…
In this paper, we employ a game-theoretic model to analyze the interaction between an adversary and a classifier. There are two classes (i.e., positive and negative classes) to which data points can belong. The adversary is interested in…
Suppose a Bayesian agent seeks to traverse a graph. Each time she crosses an edge, she pays a price. The first time she reaches a node, there is a payoff. She has an opponent who can reduce the payoffs. This paper uses adversarial risk…
Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are…
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…
Random access codes have provided many examples of quantum advantage in communication, but concern only one kind of information retrieval task. We introduce a related task - the Torpedo Game - and show that it admits greater quantum…
In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has…
In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…
An acknowledged weakness of neural networks is their vulnerability to adversarial perturbations to the inputs. To improve the robustness of these models, one of the most popular defense mechanisms is to alternatively maximize the loss over…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
The generation of feasible adversarial examples is necessary for properly assessing models that work in constrained feature space. However, it remains a challenging task to enforce constraints into attacks that were designed for computer…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
Motivated by safety-critical classification problems, we investigate adversarial attacks against cost-sensitive classifiers. We use current state-of-the-art adversarially-resistant neural network classifiers [1] as the underlying models.…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
We study the secure stochastic convex optimization problem. A learner aims to learn the optimal point of a convex function through sequentially querying a (stochastic) gradient oracle. In the meantime, there exists an adversary who aims to…
Adversarial risk quantifies the performance of classifiers on adversarially perturbed data. Numerous definitions of adversarial risk -- not all mathematically rigorous and differing subtly in the details -- have appeared in the literature.…
In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…
We introduce a quantum algorithm integrating counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to tackle combinatorial optimization problems. This approach offers versatility, allowing implementation as either a…