4,006 research outputs found
Concurrence of mixed bipartite quantum states in arbitrary dimensions
We derive a lower bound for the concurrence of mixed bipartite quantum
states, valid in arbitrary dimensions. As a corollary, a weaker, purely
algebraic estimate is found, which detects mixed entangled states with positive
partial transpose.Comment: accepted py PR
Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits
Motivated by applications in energy management, this paper presents the
Multi-Armed Risk-Aware Bandit (MARAB) algorithm. With the goal of limiting the
exploration of risky arms, MARAB takes as arm quality its conditional value at
risk. When the user-supplied risk level goes to 0, the arm quality tends toward
the essential infimum of the arm distribution density, and MARAB tends toward
the MIN multi-armed bandit algorithm, aimed at the arm with maximal minimal
value. As a first contribution, this paper presents a theoretical analysis of
the MIN algorithm under mild assumptions, establishing its robustness
comparatively to UCB. The analysis is supported by extensive experimental
validation of MIN and MARAB compared to UCB and state-of-art risk-aware MAB
algorithms on artificial and real-world problems.Comment: 16 page
Poincar\'{e} and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition
In in this paper we establish an explicit and sharp estimate of the spectral
gap (Poincar\'{e} inequality) and the transportation inequality for Gibbs
measures, under the Dobrushin uniqueness condition. Moreover, we give a
generalization of the Liggett's theorem for interacting particle
systems.Comment: Published at http://dx.doi.org/10.1214/009117906000000368 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
General nonexact oracle inequalities for classes with a subexponential envelope
We show that empirical risk minimization procedures and regularized empirical
risk minimization procedures satisfy nonexact oracle inequalities in an
unbounded framework, under the assumption that the class has a subexponential
envelope function. The main novelty, in addition to the boundedness assumption
free setup, is that those inequalities can yield fast rates even in situations
in which exact oracle inequalities only hold with slower rates. We apply these
results to show that procedures based on and nuclear norms
regularization functions satisfy oracle inequalities with a residual term that
decreases like for every -loss functions (), while only
assuming that the tail behavior of the input and output variables are well
behaved. In particular, no RIP type of assumption or "incoherence condition"
are needed to obtain fast residual terms in those setups. We also apply these
results to the problems of convex aggregation and model selection.Comment: Published in at http://dx.doi.org/10.1214/11-AOS965 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
On Robustness in the Gap Metric and Coprime Factor Uncertainty for LTV Systems
In this paper, we study the problem of robust stabilization for linear
time-varying (LTV) systems subject to time-varying normalized coprime factor
uncertainty. Operator theoretic results which generalize similar results known
to hold for linear time-invariant (infinite-dimensional) systems are developed.
In particular, we compute an upper bound for the maximal achievable stability
margin under TV normalized coprime factor uncertainty in terms of the norm of
an operator with a time-varying Hankel structure. We point to a necessary and
sufficient condition which guarantees compactness of the TV Hankel operator,
and in which case singular values and vectors can be used to compute the
time-varying stability margin and TV controller. A connection between robust
stabilization for LTV systems and an Operator Corona Theorem is also pointed
out.Comment: 20 page
Border Basis relaxation for polynomial optimization
A relaxation method based on border basis reduction which improves the
efficiency of Lasserre's approach is proposed to compute the optimum of a
polynomial function on a basic closed semi algebraic set. A new stopping
criterion is given to detect when the relaxation sequence reaches the minimum,
using a sparse flat extension criterion. We also provide a new algorithm to
reconstruct a finite sum of weighted Dirac measures from a truncated sequence
of moments, which can be applied to other sparse reconstruction problems. As an
application, we obtain a new algorithm to compute zero-dimensional minimizer
ideals and the minimizer points or zero-dimensional G-radical ideals.
Experimentations show the impact of this new method on significant benchmarks.Comment: Accepted for publication in Journal of Symbolic Computatio
Concentration for independent random variables with heavy tails
If a random variable is not exponentially integrable, it is known that no
concentration inequality holds for an infinite sequence of independent copies.
Under mild conditions, we establish concentration inequalities for finite
sequences of independent copies, with good dependence in
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