44,089 research outputs found
Improving Hit-and-Run for global optimization
Improving Hit-and-Run is a random search algorithm for global optimization that at each iteration generates a candidate point for improvement that is uniformly distributed along a randomly chosen direction within the feasible region. The candidate point is accepted as the next iterate if it offers an improvement over the current iterate. We show that for positive definite quadratic programs, the expected number of function evaluations needed to arbitrarily well approximate the optimal solution is at most O(n 5/2 ) where n is the dimension of the problem. Improving Hit-and-Run when applied to global optimization problems can therefore be expected to converge polynomially fast as it approaches the global optimum.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44932/1/10898_2005_Article_BF01096737.pd
A generalization of the Solis-Wets method
In this paper we focus on the application of global stochastic optimization methods to extremum estimators. We propose a general stochastic method the master method which includes several stochastic optimization algorithms as a particular case. The proposed method is sufficiently general to include the Solis-Wets method, the improving hit-and-run algorithm, and a stochastic version of the zigzag algorithm. A matrix formulation of the master method is presented and some specific results are given for the stochastic zigzag algorithm. Convergence of the proposed method is established under a mild set of conditions, and a simple regression model is used to illustrate the method. (C) 2011 Elsevier B.V. All rights reserved
Caching Improvement Using Adaptive User Clustering
In this article we explore one of the most promising technologies for 5G
wireless networks using an underlay small cell network, namely proactive
caching. Using the increase in storage technologies and through studying the
users behavior, peak traffic can be reduced through proactive caching of the
content that is most probable to be requested. We propose a new method, in
which, instead of caching the most popular content, the users within the
network are clustered according to their content popularity and the caching is
done accordingly. We present also a method for estimating the number of
clusters within the network based on the Akaike information criterion. We
analytically derive a closed form expression of the hit probability and we
propose an optimization problem in which the small base stations association
with clusters is optimized
Energy Efficiency in Cache Enabled Small Cell Networks With Adaptive User Clustering
Using a network of cache enabled small cells, traffic during peak hours can
be reduced considerably through proactively fetching the content that is most
probable to be requested. In this paper, we aim at exploring the impact of
proactive caching on an important metric for future generation networks,
namely, energy efficiency (EE). We argue that, exploiting the correlation in
user content popularity profiles in addition to the spatial repartitions of
users with comparable request patterns, can result in considerably improving
the achievable energy efficiency of the network. In this paper, the problem of
optimizing EE is decoupled into two related subproblems. The first one
addresses the issue of content popularity modeling. While most existing works
assume similar popularity profiles for all users in the network, we consider an
alternative caching framework in which, users are clustered according to their
content popularity profiles. In order to showcase the utility of the proposed
clustering scheme, we use a statistical model selection criterion, namely
Akaike information criterion (AIC). Using stochastic geometry, we derive a
closed-form expression of the achievable EE and we find the optimal active
small cell density vector that maximizes it. The second subproblem investigates
the impact of exploiting the spatial repartitions of users with comparable
request patterns. After considering a snapshot of the network, we formulate a
combinatorial optimization problem that enables to optimize content placement
such that the used transmission power is minimized. Numerical results show that
the clustering scheme enable to considerably improve the cache hit probability
and consequently the EE compared with an unclustered approach. Simulations also
show that the small base station allocation algorithm results in improving the
energy efficiency and hit probability.Comment: 30 pages, 5 figures, submitted to Transactions on Wireless
Communications (15-Dec-2016
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Handling boundary constraints for particle swarm optimization in high-dimensional search space
Despite the fact that the popular particle swarm optimizer (PSO) is currently being extensively applied to many real-world problems that often have high-dimensional and complex fitness landscapes, the effects of boundary constraints on PSO have not attracted adequate attention in the literature. However, in accordance with the theoretical analysis in [11], our numerical experiments show that particles tend to fly outside of the boundary in the first few iterations at a very high probability in high-dimensional search spaces. Consequently, the method used to handle boundary violations is critical to the performance of PSO. In this study, we reveal that the widely used random and absorbing bound-handling schemes may paralyze PSO for high-dimensional and complex problems. We also explore in detail the distinct mechanisms responsible for the failures of these two bound-handling schemes. Finally, we suggest that using high-dimensional and complex benchmark functions, such as the composition functions in [19], is a prerequisite to identifying the potential problems in applying PSO to many real-world applications because certain properties of standard benchmark functions make problems inexplicit. © 2011 Elsevier Inc. All rights reserved
Combining Model-Based and Model-Free Updates for Trajectory-Centric Reinforcement Learning
Reinforcement learning (RL) algorithms for real-world robotic applications
need a data-efficient learning process and the ability to handle complex,
unknown dynamical systems. These requirements are handled well by model-based
and model-free RL approaches, respectively. In this work, we aim to combine the
advantages of these two types of methods in a principled manner. By focusing on
time-varying linear-Gaussian policies, we enable a model-based algorithm based
on the linear quadratic regulator (LQR) that can be integrated into the
model-free framework of path integral policy improvement (PI2). We can further
combine our method with guided policy search (GPS) to train arbitrary
parameterized policies such as deep neural networks. Our simulation and
real-world experiments demonstrate that this method can solve challenging
manipulation tasks with comparable or better performance than model-free
methods while maintaining the sample efficiency of model-based methods. A video
presenting our results is available at
https://sites.google.com/site/icml17pilqrComment: Paper accepted to the International Conference on Machine Learning
(ICML) 201
Reinforcement learning based local search for grouping problems: A case study on graph coloring
Grouping problems aim to partition a set of items into multiple mutually
disjoint subsets according to some specific criterion and constraints. Grouping
problems cover a large class of important combinatorial optimization problems
that are generally computationally difficult. In this paper, we propose a
general solution approach for grouping problems, i.e., reinforcement learning
based local search (RLS), which combines reinforcement learning techniques with
descent-based local search. The viability of the proposed approach is verified
on a well-known representative grouping problem (graph coloring) where a very
simple descent-based coloring algorithm is applied. Experimental studies on
popular DIMACS and COLOR02 benchmark graphs indicate that RLS achieves
competitive performances compared to a number of well-known coloring
algorithms
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