Minimum Number Of Queries Research Articles

Perfect Distinguishability of Quantum Operations

We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretly selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and thus complete the characterization of the perfect distinguishability of quantum operations. We further design an optimal protocol which can achieve the perfect discrimination between two quantum operations by a minimal number of queries. Interestingly, we find that an optimal perfect discrimination between two isometries is always achievable without auxiliary systems or entanglement.

Randomized algorithms for the majority problem

Abstract In the majority problem, we are given n balls coloured black or white and we are allowed to query whether two balls have the same colour or not. The goal is to find a ball of majority colour in the minimum number of queries. The answer is known to be n − B ( n ) , where B ( n ) is the number of 1's in the binary representation of n. In [G. De Marco and A. Pelc, Randomized algorithms for determining the majority on graphs, Combin. Probab. Comput. 15 (2006), 823–834], De Marco and Pelc proved that even if we use a randomized algorith which is allowed to fail with probability at most e, we still need linear expected time to determine a ball in majority colour. We prove that any such algorithm has expected running time at least ( 2 3 − δ ( e ) ) n , where δ ( e ) → 0 as e → 0 . Moreover, we provide a randomized algorithm showing that this result is best possible.

On randomized algorithms for the majority problem

In the majority problem, we are given n balls coloured black or white and we are allowed to query whether two balls have the same colour or not. The goal is to find a ball of majority colour in the minimum number of queries. The answer is known to be n − B ( n ) where B ( n ) is the number of 1’s in the binary representation of n . In this paper we study randomized algorithms for determining majority, which are allowed to err with probability at most ε . We show that any such algorithm must have expected running time at least ( 2 3 − o ( 1 ) ) n . Moreover, we provide a randomized algorithm which shows that this result is best possible. These extend a result of De Marco and Pelc [G. De Marco, A. Pelc, Randomized algorithms for determining the majority on graphs, Combin. Probab. Comput. 15 (2006) 823–834].

Apprentissage actif dans les processus décisionnels de Markov partiellement observables L'algorithme MEDUSA

We study a problem inspired from robotics in which we want to find an optimal policy to learn a Partially Observable Markov Decision Process (POMDP) when the agent only has an imperfect model of its environment. To help the agent in its task we assume the availability of an external operator (an oracle), that can provide information about the underlying state. We present the algorithm MEDUSA, which improves an initial POMDP model using experimentation through the environment and a minimum number of queries. We also show how MEDUSA handles non-stationary environments and how it can withstand noise in the query answer.

Learning from labeled and unlabeled data using a minimal number of queries

The considerable time and expense required for labeling data has prompted the development of algorithms which maximize the classification accuracy for a given amount of labeling effort. On the one hand, the effort has been to develop the so-called "active learning" algorithms which sequentially choose the patterns to be explicitly labeled so as to realize the maximum information gain from each labeling. On the other hand, the effort has been to develop algorithms that can learn from labeled as well as the more abundant unlabeled data. Proposed in this paper is an algorithm that integrates the benefits of active learning with the benefits of learning from labeled and unlabeled data. Our approach is based on reversing the roles of the labeled and unlabeled data. Specifically, we use a Genetic Algorithm (GA) to iteratively refine the class membership of the unlabeled patterns so that the maximum a posteriori (MAP) based predicted labels of the patterns in the labeled dataset are in agreement with the known labels. This reversal of the role of labeled and unlabeled patterns leads to an implicit class assignment of the unlabeled patterns. For active learning, we use a subset of the GA population to construct multiple MAP classifiers. Points in the input space where there is maximal disagreement amongst these classifiers are then selected for explicit labeling. The learning from labeled and unlabeled data and active learning phases are interlaced and together provide accurate classification while minimizing the labeling effort.

Security in statistical databases for queries with small counts

The security problem of statistical databases containing anonymous but individual records which may be evaluated by queries about sums and averages is considered. A model, more realistic than the previous ones, is proposed, in which nonexisting records for some keys can be allowed. Under the assumption that the system protects the individual's information by the well-known technique which avoids publishing summaries with small counts, several properties about the system and a necessary and sufficient condition for compromising the database have been derived. The minimum number of queries needed to compromise the database is also discussed.