A stochastic approximation algorithm for stochastic semidefinite programming

Motivated by applications to multi-antenna wireless networks, we propose a distributed and asynchronous algorithm for stochastic semidefinite programming. This algorithm is a stochastic approximation of a continous- time matrix exponential scheme regularized by the addition of an entropy-like term to the problem's objective function. We show that the resulting algorithm converges almost surely to an $\varepsilon$-approximation of the optimal solution requiring only an unbiased estimate of the gradient of the problem's stochastic objective. When applied to throughput maximization in wireless multiple-input and multiple-output (MIMO) systems, the proposed algorithm retains its convergence properties under a wide array of mobility impediments such as user update asynchronicities, random delays and/or ergodically changing channels. Our theoretical analysis is complemented by extensive numerical simulations which illustrate the robustness and scalability of the proposed method in realistic network conditions.Comment: 25 pages, 4 figure

Trace checking of Metric Temporal Logic with Aggregating Modalities using MapReduce

Modern complex software systems produce a large amount of execution data, often stored in logs. These logs can be analyzed using trace checking techniques to check whether the system complies with its requirements specifications. Often these specifications express quantitative properties of the system, which include timing constraints as well as higher-level constraints on the occurrences of significant events, expressed using aggregate operators. In this paper we present an algorithm that exploits the MapReduce programming model to check specifications expressed in a metric temporal logic with aggregating modalities, over large execution traces. The algorithm exploits the structure of the formula to parallelize the evaluation, with a significant gain in time. We report on the assessment of the implementation - based on the Hadoop framework - of the proposed algorithm and comment on its scalability.Comment: 16 pages, 6 figures, Extended version of the SEFM 2014 pape

Scather: programming with multi-party computation and MapReduce

We present a prototype of a distributed computational infrastructure, an associated high level programming language, and an underlying formal framework that allow multiple parties to leverage their own cloud-based computational resources (capable of supporting MapReduce [27] operations) in concert with multi-party computation (MPC) to execute statistical analysis algorithms that have privacy-preserving properties. Our architecture allows a data analyst unfamiliar with MPC to: (1) author an analysis algorithm that is agnostic with regard to data privacy policies, (2) to use an automated process to derive algorithm implementation variants that have different privacy and performance properties, and (3) to compile those implementation variants so that they can be deployed on an infrastructures that allows computations to take place locally within each participant’s MapReduce cluster as well as across all the participants’ clusters using an MPC protocol. We describe implementation details of the architecture, discuss and demonstrate how the formal framework enables the exploration of tradeoffs between the efficiency and privacy properties of an analysis algorithm, and present two example applications that illustrate how such an infrastructure can be utilized in practice.This work was supported in part by NSF Grants: #1430145, #1414119, #1347522, and #1012798