389 research outputs found
Privacy-Preserving Distributed Optimization and Learning
Distributed optimization and learning has recently garnered great attention
due to its wide applications in sensor networks, smart grids, machine learning,
and so forth. Despite rapid development, existing distributed optimization and
learning algorithms require each agent to exchange messages with its neighbors,
which may expose sensitive information and raise significant privacy concerns.
In this survey paper, we overview privacy-preserving distributed optimization
and learning methods. We first discuss cryptography, differential privacy, and
other techniques that can be used for privacy preservation and indicate their
pros and cons for privacy protection in distributed optimization and learning.
We believe that among these approaches, differential privacy is most promising
due to its low computational and communication complexities, which are
extremely appealing for modern learning based applications with high dimensions
of optimization variables. We then introduce several differential-privacy
algorithms that can simultaneously ensure privacy and optimization accuracy.
Moreover, we provide example applications in several machine learning problems
to confirm the real-world effectiveness of these algorithms. Finally, we
highlight some challenges in this research domain and discuss future
directions.Comment: Accepted as a chapter in the Encyclopedia of Systems and Control
Engineering published by Elsevie
Homomorphic Sensing of Subspace Arrangements
Homomorphic sensing is a recent algebraic-geometric framework that studies
the unique recovery of points in a linear subspace from their images under a
given collection of linear maps. It has been successful in interpreting such a
recovery in the case of permutations composed by coordinate projections, an
important instance in applications known as unlabeled sensing, which models
data that are out of order and have missing values. In this paper, we provide
tighter and simpler conditions that guarantee the unique recovery for the
single-subspace case, extend the result to the case of a subspace arrangement,
and show that the unique recovery in a single subspace is locally stable under
noise. We specialize our results to several examples of homomorphic sensing
such as real phase retrieval and unlabeled sensing. In so doing, in a unified
way, we obtain conditions that guarantee the unique recovery for those
examples, typically known via diverse techniques in the literature, as well as
novel conditions for sparse and unsigned versions of unlabeled sensing.
Similarly, our noise result also implies that the unique recovery in unlabeled
sensing is locally stable.Comment: 18 page
Classical and quantum Merlin-Arthur automata
We introduce Merlin-Arthur (MA) automata as Merlin provides a single
certificate and it is scanned by Arthur before reading the input. We define
Merlin-Arthur deterministic, probabilistic, and quantum finite state automata
(resp., MA-DFAs, MA-PFAs, MA-QFAs) and postselecting MA-PFAs and MA-QFAs
(resp., MA-PostPFA and MA-PostQFA). We obtain several results using different
certificate lengths.
We show that MA-DFAs use constant length certificates, and they are
equivalent to multi-entry DFAs. Thus, they recognize all and only regular
languages but can be exponential and polynomial state efficient over binary and
unary languages, respectively. With sublinear length certificates, MA-PFAs can
recognize several nonstochastic unary languages with cutpoint 1/2. With linear
length certificates, MA-PostPFAs recognize the same nonstochastic unary
languages with bounded error. With arbitrarily long certificates, bounded-error
MA-PostPFAs verify every unary decidable language. With sublinear length
certificates, bounded-error MA-PostQFAs verify several nonstochastic unary
languages. With linear length certificates, they can verify every unary
language and some NP-complete binary languages. With exponential length
certificates, they can verify every binary language.Comment: 14 page
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