15,515 research outputs found
Quantum algorithm for robust optimization via stochastic-gradient online learning
Optimization theory has been widely studied in academia and finds a large
variety of applications in industry. The different optimization models in their
discrete and/or continuous settings has catered to a rich source of research
problems. Robust convex optimization is a branch of optimization theory in
which the variables or parameters involved have a certain level of uncertainty.
In this work, we consider the online robust optimization meta-algorithm by
Ben-Tal et al. and show that for a large range of stochastic subgradients, this
algorithm has the same guarantee as the original non-stochastic version. We
develop a quantum version of this algorithm and show that an at most quadratic
improvement in terms of the dimension can be achieved. The speedup is due to
the use of quantum state preparation, quantum norm estimation, and quantum
multi-sampling. We apply our quantum meta-algorithm to examples such as robust
linear programs and robust semidefinite programs and give applications of these
robust optimization problems in finance and engineering.Comment: 21 page
Natural evolution strategies and variational Monte Carlo
A notion of quantum natural evolution strategies is introduced, which
provides a geometric synthesis of a number of known quantum/classical
algorithms for performing classical black-box optimization. Recent work of
Gomes et al. [2019] on heuristic combinatorial optimization using neural
quantum states is pedagogically reviewed in this context, emphasizing the
connection with natural evolution strategies. The algorithmic framework is
illustrated for approximate combinatorial optimization problems, and a
systematic strategy is found for improving the approximation ratios. In
particular it is found that natural evolution strategies can achieve
approximation ratios competitive with widely used heuristic algorithms for
Max-Cut, at the expense of increased computation time
Semistochastic Quadratic Bound Methods
Partition functions arise in a variety of settings, including conditional
random fields, logistic regression, and latent gaussian models. In this paper,
we consider semistochastic quadratic bound (SQB) methods for maximum likelihood
inference based on partition function optimization. Batch methods based on the
quadratic bound were recently proposed for this class of problems, and
performed favorably in comparison to state-of-the-art techniques.
Semistochastic methods fall in between batch algorithms, which use all the
data, and stochastic gradient type methods, which use small random selections
at each iteration. We build semistochastic quadratic bound-based methods, and
prove both global convergence (to a stationary point) under very weak
assumptions, and linear convergence rate under stronger assumptions on the
objective. To make the proposed methods faster and more stable, we consider
inexact subproblem minimization and batch-size selection schemes. The efficacy
of SQB methods is demonstrated via comparison with several state-of-the-art
techniques on commonly used datasets.Comment: 11 pages, 1 figur
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