Parallel Deterministic and Stochastic Global Minimization of Functions with Very Many Minima

The optimization of three problems with high dimensionality and many local minima are investigated under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO package, and QNSTOP, a new algorithm developed at Indiana University

Newton based Stochastic Optimization using q-Gaussian Smoothed Functional Algorithms

We present the first q-Gaussian smoothed functional (SF) estimator of the Hessian and the first Newton-based stochastic optimization algorithm that estimates both the Hessian and the gradient of the objective function using q-Gaussian perturbations. Our algorithm requires only two system simulations (regardless of the parameter dimension) and estimates both the gradient and the Hessian at each update epoch using these. We also present a proof of convergence of the proposed algorithm. In a related recent work (Ghoshdastidar et al., 2013), we presented gradient SF algorithms based on the q-Gaussian perturbations. Our work extends prior work on smoothed functional algorithms by generalizing the class of perturbation distributions as most distributions reported in the literature for which SF algorithms are known to work and turn out to be special cases of the q-Gaussian distribution. Besides studying the convergence properties of our algorithm analytically, we also show the results of several numerical simulations on a model of a queuing network, that illustrate the significance of the proposed method. In particular, we observe that our algorithm performs better in most cases, over a wide range of q-values, in comparison to Newton SF algorithms with the Gaussian (Bhatnagar, 2007) and Cauchy perturbations, as well as the gradient q-Gaussian SF algorithms (Ghoshdastidar et al., 2013).Comment: This is a longer of version of the paper with the same title accepted in Automatic

Distributed self-tuning of sensor networks

This work is motivated by the need for an ad hoc sensor network to autonomously optimise its performance for given task objectives and constraints. Arguing that communication is the main bottleneck for distributed computation in a sensor network we formulate two approaches for optimisation of computing rates. The first is a team problem for maximising the minimum communication throughput of sensors and the second is a game problem in which cost for each sensor is a measure of its communication time with its neighbours. We investigate adaptive algorithms using which sensors can tune to the optimal channel attempt rates in a distributed fashion. For the team problem, the adaptive scheme is a stochastic gradient algorithm derived from the augmented Lagrangian formulation of the optimisation problem. The game formulation not only leads to an explicit characterisation of the Nash equilibrium but also to a simple iterative scheme by which sensors can learn the equilibrium attempt probabilities using only the estimates of transmission and reception times from their local measurements. Our approach is promising and should be seen as a step towards developing optimally self-organising architectures for sensor networks

Symmetric confidence regions and confidence intervals for normal map formulations of stochastic variational inequalities

Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method to build asymptotically exact confidence regions and confidence intervals for the solution of the normal map formulation, based on the asymptotic distribution of SAA solutions. The confidence regions are single ellipsoids with high probability. We also discuss the computation of simultaneous and individual confidence intervals

IPA-based tuning of queue admission control under imperfect information

Includes bibliographical references (p. 14-16).Supported by the NSF. ECS-8552419Daniel Chonghwan Lee

Stochastic Dynamic Cache Partitioning for Encrypted Content Delivery

In-network caching is an appealing solution to cope with the increasing bandwidth demand of video, audio and data transfer over the Internet. Nonetheless, an increasing share of content delivery services adopt encryption through HTTPS, which is not compatible with traditional ISP-managed approaches like transparent and proxy caching. This raises the need for solutions involving both Internet Service Providers (ISP) and Content Providers (CP): by design, the solution should preserve business-critical CP information (e.g., content popularity, user preferences) on the one hand, while allowing for a deeper integration of caches in the ISP architecture (e.g., in 5G femto-cells) on the other hand. In this paper we address this issue by considering a content-oblivious ISP-operated cache. The ISP allocates the cache storage to various content providers so as to maximize the bandwidth savings provided by the cache: the main novelty lies in the fact that, to protect business-critical information, ISPs only need to measure the aggregated miss rates of the individual CPs and do not need to be aware of the objects that are requested, as in classic caching. We propose a cache allocation algorithm based on a perturbed stochastic subgradient method, and prove that the algorithm converges close to the allocation that maximizes the overall cache hit rate. We use extensive simulations to validate the algorithm and to assess its convergence rate under stationary and non-stationary content popularity. Our results (i) testify the feasibility of content-oblivious caches and (ii) show that the proposed algorithm can achieve within 10\% from the global optimum in our evaluation

Optimization with Discrete Simultaneous Perturbation Stochastic Approximation Using Noisy Loss Function Measurements

Discrete stochastic optimization considers the problem of minimizing (or maximizing) loss functions defined on discrete sets, where only noisy measurements of the loss functions are available. The discrete stochastic optimization problem is widely applicable in practice, and many algorithms have been considered to solve this kind of optimization problem. Motivated by the efficient algorithm of simultaneous perturbation stochastic approximation (SPSA) for continuous stochastic optimization problems, we introduce the middle point discrete simultaneous perturbation stochastic approximation (DSPSA) algorithm for the stochastic optimization of a loss function defined on a p-dimensional grid of points in Euclidean space. We show that the sequence generated by DSPSA converges to the optimal point under some conditions. Consistent with other stochastic approximation methods, DSPSA formally accommodates noisy measurements of the loss function. We also show the rate of convergence analysis of DSPSA by solving an upper bound of the mean squared error of the generated sequence. In order to compare the performance of DSPSA with the other algorithms such as the stochastic ruler algorithm (SR) and the stochastic comparison algorithm (SC), we set up a bridge between DSPSA and the other two algorithms by comparing the probability in a big-O sense of not achieving the optimal solution. We show the theoretical and numerical comparison results of DSPSA, SR, and SC. In addition, we consider an application of DSPSA towards developing optimal public health strategies for containing the spread of influenza given limited societal resources