Minimum Number Of Queries Research Articles

Efficient Ensemble Adversarial Attack for a Deep Neural Network (DNN)-Based Unmanned Aerial Vehicle (UAV) Vision System

In recent years, unmanned aerial vehicles (UAVs) vision systems based on deep neural networks (DNNs) have made remarkable advancements, demonstrating impressive performance. However, due to the inherent characteristics of DNNs, these systems have become increasingly vulnerable to adversarial attacks. Traditional black-box attack methods typically require a large number of queries to generate adversarial samples successfully. In this paper, we propose a novel adversarial attack technique designed to achieve efficient black-box attacks with a minimal number of queries. We define a perturbation generator that first decomposes the image into four frequency bands using wavelet decomposition and then searches for adversarial perturbations across these bands by minimizing a weighted loss function on a set of fixed surrogate models. For the target victim model, the perturbation images generated by the perturbation generator are used to query and update the weights in the loss function, as well as the weights for different frequency bands. Experimental results show that, compared to state-of-the-art methods on various image classifiers trained on ImageNet (such as VGG-19, DenseNet-121, and ResNext-50), our method achieves a success rate over 98% for targeted attacks and nearly a 100% success rate for non-targeted attacks with only 1–2 queries per image.

Diagonalization Games

We study several variants of a combinatorial game which is based on Cantor’s diagonal argument. The game is between two players called Kronecker and Cantor. The names of the players are motivated by the known fact that Leopold Kronecker did not appreciate Georg Cantor’s arguments about the infinite, and even referred to him as a “scientific charlatan.” In the game Kronecker maintains a list of m binary vectors, each of length n, and Cantor’s goal is to produce a new binary vector which is different from each of Kronecker’s vectors, or prove that no such vector exists. Cantor does not see Kronecker’s vectors but he is allowed to ask queries of the form What is bit number j of vector number i? What is the minimal number of queries with which Cantor can achieve his goal? How much better can Cantor do if he is allowed to pick his queries adaptively, based on Kronecker’s previous replies? The case when m = n is solved by diagonalization using n (nonadaptive) queries. We study this game more generally, and prove an optimal bound in the adaptive case and nearly tight upper and lower bounds in the nonadaptive case.

On the Rényi–Ulam game with restricted size queries

We investigate the following version of the well-known Rényi–Ulam game. Two players – the Questioner and the Responder – play against each other. The Responder thinks of a number from the set {1,…,n}, and the Questioner has to find this number. To do this, he can ask whether a chosen set of at most k elements contains the thought number. The Responder answers with YES or NO immediately, but during the game, he may lie at most ℓ times. The minimum number of queries needed for the Questioner to surely find the unknown element is denoted by RUℓk(n). First, we develop a highly effective tool that we call Convexity Lemma. By using this lemma, we give a general lower bound of RUℓk(n) and an upper bound which differs from the lower one by at most 2ℓ+1. We also give its exact value when n is sufficiently large compared to k. With these, we managed to improve and generalize the results obtained by Meng, Lin, and Yang in a 2013 paper about the case ℓ=1.

Active Learning for Contextual Search with Binary Feedback

In this paper, we study the learning problem in contextual search, which is motivated by applications such as crowdsourcing and personalized medicine experiments. In particular, for a sequence of arriving context vectors, with each context associated with an underlying value, the decision maker either makes a query at a certain point or skips the context. The decision maker will only observe the binary feedback on the relationship between the query point and the value associated with the context. We study a probably approximately correct learning setting, where the goal is to learn the underlying mean value function in context with a minimum number of queries. To address this challenge, we propose a trisection search approach combined with a margin-based active learning method. We show that the algorithm only needs to make [Formula: see text] queries to achieve an ε-estimation accuracy. This sample complexity significantly reduces the required sample complexity in the passive setting where neither sample skipping nor query selection is allowed, which is at least [Formula: see text]. This paper was accepted by J. George Shanthikumar, data science. Funding: X. Chen and Q. Liu were supported by the National Science Foundation [Grant IIS-1845444].

Sequential metric dimension for random graphs

AbstractIn the localization game on a graph, the goal is to find a fixed but unknown target node$v^\star$with the least number of distance queries possible. In thejth step of the game, the player queries a single node$v_j$and receives, as an answer to their query, the distance between the nodes$v_j$and$v^\star$. The sequential metric dimension (SMD) is the minimal number of queries that the player needs to guess the target with absolute certainty, no matter where the target is.The term SMD originates from the related notion of metric dimension (MD), which can be defined the same way as the SMD except that the player’s queries are non-adaptive. In this work we extend the results of Bollobás, Mitsche, and Prałat [4] on the MD of Erdős–Rényi graphs to the SMD. We find that, in connected Erdős–Rényi graphs, the MD and the SMD are a constant factor apart. For the lower bound we present a clean analysis by combining tools developed for the MD and a novel coupling argument. For the upper bound we show that a strategy that greedily minimizes the number of candidate targets in each step uses asymptotically optimal queries in Erdős–Rényi graphs. Connections with source localization, binary search on graphs, and the birthday problem are discussed.

Active-Learning a Convex Body in Low Dimensions

Consider a set $$P\subseteq \mathbb {R}^d$$ of n points, and a convex body $$C$$ provided via a separation oracle. The task at hand is to decide for each point of $$P$$ if it is in $$C$$ using the fewest number of oracle queries. We show that one can solve this problem in two and three dimensions using queries, where is the size of the largest subset of points of $$P$$ in convex position. In 2D, we provide an algorithm that efficiently generates these adaptive queries. Furthermore, we show that in two dimensions one can solve this problem using oracle queries, where is a lower bound on the minimum number of queries that any algorithm for this specific instance requires. Finally, we consider other variations on the problem, such as using the fewest number of queries to decide if $$C$$ contains all points of $$P$$ . As an application of the above, we show that the discrete geometric median of a point set P in $$\mathbb {R}^2$$ can be computed in expected time.

Decoding from Pooled Data: Sharp Information-Theoretic Bounds

Consider a population consisting of n individuals, each of whom has one of d types (e.g. their blood type, in which case d=4). We are allowed to query this database by specifying a subset of the population, and in response we observe a noiseless histogram (a d-dimensional vector of counts) of types of the pooled individuals. This measurement model arises in practical situations such as pooling of genetic data and may also be motivated by privacy considerations. We are interested in the number of queries one needs to unambiguously determine the type of each individual. In this paper, we study this information-theoretic question under the random, dense setting where in each query, a random subset of individuals of size proportional to n is chosen. This makes the problem a particular example of a random constraint satisfaction problem (CSP) with a "planted" solution. We establish almost matching upper and lower bounds on the minimum number of queries m such that there is no solution other than the planted one with probability tending to 1 as n tends to infinity. Our proof relies on the computation of the exact "annealed free energy" of this model in the thermodynamic limit, which corresponds to the exponential rate of decay of the expected number of solution to this planted CSP. As a by-product of the analysis, we show an identity of independent interest relating the Gaussian integral over the space of Eulerian flows of a graph to its spanning tree polynomial.

Exact learning from an honest teacher that answers membership queries

Given a teacher that holds a function f:X→R from some class of functions C. The teacher can receive from the learner an element d in the domain X (a query) and returns the value of the function in d, f(d)∈R. The learner goal is to find f with a minimum number of queries, optimal time complexity, and optimal resources.In this survey, we present some of the results known from the literature, different techniques used, some new problems, and open problems.

Sequential plan recognition: An iterative approach to disambiguating between hypotheses

Plan recognition algorithms output hypotheses about an agent's plans from its observed actions. Due to imperfect knowledge about the agent's behavior and the environment, it is often the case that there are multiple hypotheses about an agent's plans that are consistent with the observations, though only one of these hypotheses is correct. This paper addresses the problem of how to disambiguate between hypotheses during the recognition process, by querying the acting agent about whether a given plan is part of the correct hypothesis. The main contribution is a sound and complete process for reducing the set of possible hypotheses called Sequential Plan Recognition (SPR). SPR iteratively queries the user and revises the set of possible hypotheses according to the outcome of the query. Several policies are provided for choosing which plans to query the agent. These policies address the problem of how to reduce the number of hypotheses during the recognition process using a minimal number of queries. The proposed policies include policies that use maximum likelihood and information gain measures.The paper provides a complexity analysis of the SPR process and the proposed query policies. It demonstrate its efficiency on two known domains from the literature, describing how performance and runtime are affected by features in the domain. Our results can inform the design of future plan recognition systems that interleave the recognition process with intelligent interventions of their users.

Finding a non-minority ball with majority answers

Suppose we are given a set of n balls {b1,…,bn} each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls {bi1,bi2,bi3}. As an answer to such a query we obtain (the index of) a majority ball, that is, a ball whose color is the same as the color of another ball from the triple. Our goal is to find a non-minority ball, that is, a ball whose color occurs at least n2 times among the n balls. We show that the minimum number of queries needed to solve this problem is Θ(n) in the adaptive case and Θ(n3) in the non-adaptive case. We also consider some related problems.

Finding a majority ball with majority answers

Suppose we are given a set of n balls {b1,…,bn} each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls {bi1,bi2,bi3}. As an answer to such a query we obtain (the index of) a majority ball, that is, a ball whose color is the same as the color of another ball from the triple. Our goal is to find a non-minority ball, that is, a ball whose color occurs at least n2 times among the n balls. We show that the minimum number of queries needed to solve this problem is Θ(n) in the adaptive case and Θ(n3) in the non-adaptive case.

On competitive recommendations

We are given an unknown binary matrix, where the entries correspond to preferences of users on items. We want to find at least one 1-entry in each row with a minimum number of queries. The number of queries needed heavily depends on the input matrix and a straightforward competitive analysis yields bad results for any online algorithm. Therefore, we analyze our algorithm against a weaker offline algorithm that is given the number of users and a probability distribution according to which the preferences of the users are chosen. We show that our algorithm has an O(nlog2⁡n) overhead in comparison to the weaker offline solution. Furthermore, we show that the corresponding overhead for any online algorithm is Ω(n), which shows that the performance of our algorithm is within an O(log2⁡n) multiplicative factor from optimal in this sense.

Identification of a reversible quantum gate: assessing the resources

We assess the resources needed to identify a reversible quantum gate among a finite set of alternatives, including in our analysis both deterministic and probabilistic strategies. Among the probabilistic strategies, we consider unambiguous gate discrimination—where errors are not tolerated but inconclusive outcomes are allowed—and we prove that parallel strategies are sufficient to unambiguously identify the unknown gate with minimum number of queries. This result is used to provide upper and lower bounds on the query complexity and on the minimum ancilla dimension. In addition, we introduce the notion of generalized t-designs, which includes unitary t-designs and group representations as special cases. For gates forming a generalized t-design we give an explicit expression for the maximum probability of correct gate identification and we prove that there is no gap between the performances of deterministic strategies and those of probabilistic strategies. Hence, evaluating of the query complexity of perfect deterministic discrimination is reduced to the easier problem of evaluating the query complexity of unambiguous discrimination. Finally, we consider discrimination strategies where the use of ancillas is forbidden, providing upper bounds on the number of additional queries needed to make up for the lack of entanglement with the ancillas.

Perfect Strategies for the Ulam-Rényi Game with Multi-interval Questions

We study a new variant of the classical 20 question game with lies (a.k.a. Ulam-Renyi game). The Ulam-Renyi game models the problem of identifying an initially unknown m-bit number by asking subset questions, where up to e of the answers might be mendacious. In the variant considered in this paper, we set an additional constraint on the type of questions, namely, that the subsets they ask for should be the union of at most k intervals for some k>0 fixed beforehand. We show that for any e and m, there exists k only depending on e such that strategies using k-interval question are as powerful (in terms of the minimum number of queries needed) as the best strategies using arbitrary membership questions.

A New Upper Bound on the Query Complexity of Testing Generalized Reed-Muller Codes.

Over a finite field \({\mathbb{F}}_q\) the (n,d,q)-Reed-Muller code is the code given by evaluations of n-variate polynomials of total degree at most d on all points (of \({\mathbb{F}}_q^n\)). The task of testing if a function \(f:{\mathbb{F}}_q^n \to {\mathbb{F}}_q\) is close to a codeword of an (n,d,q)-Reed-Muller code has been of central interest in complexity theory and property testing. The query complexity of this task is the minimal number of queries that a tester can make (minimum over all testers of the maximum number of queries over all random choices) while accepting all Reed-Muller codewords and rejecting words that are δ-far from the code with probability Ω(δ). (In this work we allow the constant in the Ω to depend on d.)

Exact and approximate algorithms for the most connected vertex problem

An (edge) hidden graph is a graph whose edges are notexplicitly given. Detecting the presence of an edge requires an expensive edge probing query. We consider the k Most Connected Vertex ( k -MCV) problem on hidden bipartite graphs. Given a bipartite graph G with independent vertex sets B and W , the goal is to find the k vertices in B with the largest degrees using the minimum number of queries. This problem can be regarded as a top- k extension of semi-join, and is encountered in several applications in practice. If B and W have n and m vertices, respectively, the number of queries needed to solve the problem is nm in the worst case. This, however, is a pessimistic estimate on how many queries are necessary on practical data. In fact, on some inputs, the problem may be settled with only km + n queries, which is significantly lower than nm for k ≪ n . The huge difference between km + n and nm makes it interesting to design an adaptive algorithm that is guaranteed to achieve the best possible performance on every input G . For k ≤ n /2, we give an algorithm that is instance optimal among a broad class of solutions. This means that, for any G , our algorithm can perform more queries than the optimal solution (which is unknown) by only a constant factor, which can be shown at most 2. As a second step, we study an ε-approximate version of the k -MCV problem, where ε is a parameter satisfying 0 < ε < 1. The goal is to return k black vertices b 1 , …, b k such that the degree of b i ( i ≤ k ) can be smaller than t i by a factor of at most ε, where t i , …, t k (in nonascending order) are the degrees of the k most connected black vertices. We give an efficient randomized algorithm that successfully finds the correct answer with high probability. In particular, for a fixed ε and a fixed success probability, our algorithm performs o(nm) queries in expectation for t k = ω(log n ). In other words, whenever t k is greater than log n by more than a constant, our algorithm beats the Ω( nm ) lower bound for solving the k -MCV problem exactly. All the proposed algorithms, despite the complication of their underlying theory, are simple enough for easy implementation in practice. Extensive experiments have confirmed that their performance in reality agrees with our theoretical findings very well.

Group-Based Active Query Selection for Rapid Diagnosis in Time-Critical Situations

In applications such as active learning and disease/fault diagnosis, one often encounters the problem of identifying an unknown object through a minimal number of queries. This problem has been referred to as query learning or object/entity identification. We consider three extensions of this fundamental problem that are motivated by practical considerations in real-world,time-critical identification tasks such as emergency response. First, we consider the problem where the objects are partitioned into groups, and the goal is to identify only the group to which the object belongs. Second, we address the situation where the queries are partitioned into groups, and an algorithm may suggest a group of queries to a human user, who then selects the actual query. Third, we consider the problem of object identification in the presence of persistent query noise, and relate it to group identification. To address these problems we show that a standard algorithm for object identification, known as generalized binary search, may be viewed as a generalization of Shannon-Fano coding. We then extend this result to the group-based settings, leading to new algorithms, whose performance is demonstrated through a logarithmic approximation bound, and through experiments on simulated data and a database used for toxic chemical identification.

Some bounds on the minimum number of queries required for quantum channel perfect discrimination

We prove a lower bound on the $q$-maximal fidelities between two quantum channels $\E_0$ and $\E_1$ and an upper bound on the $q$-maximal fidelities between a quantum channel $\E$ and an identity $\I$. Then we apply these two bounds to provide a simple sufficient and necessary condition for sequential perfect distinguishability between $\E$ and $\I$ and provide both a lower bound and an upper bound on the minimum number of queries required to sequentially perfectly discriminating $\E$ and $\I$. Interestingly, in the $2$-dimensional case, both bounds coincide. Based on the optimal perfect discrimination protocol presented in \cite{DFY09}, we can further generalize the lower bound and upper bound to the minimum number of queries to perfectly discriminating $\E$ and $I$ over all possible discrimination schemes. Finally the two lower bounds are shown remain working for perfectly discriminating general two quantum channels $\E_0$ and $\E_1$ in sequential scheme and over all possible discrimination schemes respectively.

Derandomized Parallel Repetition via Structured PCPs

A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return is allowed to err with some bounded probability. The probability that the verifier accepts a false proof is called the soundness error, and is an important parameter of a PCP system that one seeks to minimize. Constructing PCPs with sub-constant soundness error and, at the same time, a minimal number of queries into the proof (namely two) is especially important due to applications for inapproximability. In this work we construct such PCP verifiers, i.e., PCPs that make only two queries and have sub-constant soundness error. Our construction can be viewed as a combinatorial alternative to the {}``manifold vs. point'' construction, which is the only construction in the literature for this parameter range. The {}``manifold vs. point'' PCP is based on a low degree test, while our construction is based on a direct product test. Our construction of a PCP is based on extending the derandomized direct product test of Impagliazzo, Kabanets and Wigderson (STOC 09) to a derandomized parallel repetition theorem. More accurately, our PCP construction is obtained in two steps. We first prove a derandomized parallel repetition theorem for specially structured PCPs. Then, we show that any PCP can be transformed into one that has the required structure, by embedding it on a de-Bruijn graph.

Discovery of network properties with all-shortest-paths queries

We consider the problem of discovering properties (such as the diameter) of an unknown network G = ( V , E ) with a minimum number of queries. Initially, only the vertex set V of the network is known. Information about the edges and non-edges of the network can be obtained by querying nodes of the network. A query at a node q ∈ V returns the union of all shortest paths from q to all other nodes in V . We study the problem as an online problem–an algorithm does not initially know the edge set of the network, and has to decide where to make the next query based on the information that was gathered by previous queries. We study how many queries are needed to discover the diameter, a minimal dominating set, a maximal independent set, the minimum degree, and the maximum degree of the network. We also study the problem of deciding with a minimum number of queries whether the network is 2-edge or 2-vertex connected. We use the usual competitive analysis to evaluate the quality of online algorithms, i.e., we compare online algorithms with the optimum offline algorithms. For all properties except the maximal independent set, 2-vertex connectivity and minimum/maximum degree, we present and analyze online algorithms. Furthermore we show, for all the aforementioned properties, that “many” queries are needed in the worst case. As our query model delivers more information about the network than the measurement heuristics that are currently used in practice, these negative results suggest that a similar behavior can be expected in realistic settings, or in more realistic models derived from the all-shortest-paths query model.