Distributed Model-Free Stochastic Optimization in Wireless Sensor Networks
With the improvement in computer electronics in terms of processing, memory and communication capabilities, it has become possible to scatter tiny embedded devices such as sensor nodes to monitor physical phenomena with greater flexibility. A large number of sensor nodes, communicating over the wireless medium, also allows information gathering with greater accuracy than current systems. This paper presents a new stochastic technique known as Incremental Simultaneous Perturbation Approximation(ISPA) for performing optimization in wireless sensor networks. The proposed algorithm is based on a combination of gradient-based decentralized incremental (GBDI) optimization and Simultaneous Perturbation Stochastic Approximation (SPSA) techniques. The former is based on Incremental Sub-Gradient Optimization (ISGO) techniques that allow the algorithm to be performed in a distributed and collaborative manner. The latter component addresses the limitations of the GBDI component especially in real-world sensor networks. Specifically, the SPSA component is a model-free technique that finds the optimal solution without requiring a functional model such as an input-output relationship and a cost gradient. Simulation results show that the proposed ISPA approach not only achieves distributed optimization in a stochastic environment, but can also be implemented in a practical manner for resource-constrained devices.
KeywordsCost Function Sensor Network Sensor Node Wireless Sensor Network Loss Function
Unable to display preview. Download preview PDF.
- 1.Rabbat, M., Nowak, R.: Distributed Optimization in Sensor Networks. In: Proc. Information Processing in Sensor Networks, Berkeley, CA, USA (2004)Google Scholar
- 2.Nedic, A., Bertsekas, D.: Incremental Subgradient Methods for Non-differentiable Optimization. Technical Report LIDS-P-2460, Massachusetts Institute of Technology, Cambridge, MA, USA (1999)Google Scholar
- 5.Nedic, A., Bertsekas, D.: Convergence rate of incremental subgradient algorithms. In: Uryasev, S., Pardalos, P. (eds.) Stochastic Optimization: Algorithms and Applications, pp. 263–304. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
- 6.Spall, J.C.: A Stochastic Approximation Algorithm for Large-Dimensional Systems in the Kiefer-Wolfowitz Setting. In: Proc. IEEE Conf. on Decision and Control., pp. 1544–1548 (1988)Google Scholar
- 8.Sadegh, P., Spall, J.: Optimal Random Perturbations for Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation. In: Proc. American Control Conf., pp. 3582–3586 (1997)Google Scholar
- 12.Maryak, J.L., Chin, D.C.: Efficient Global Optimization Using SPSA. In: Proc. American Control Conf., pp. 890–894 (1999)Google Scholar
- 14.Wang, I., Spall, J.: A Constrained Simultaneous Perturbation Stochastic Approximation Algorithm Based on Penalty Functions. In: Proc. American Control Conf., pp. 393–399 (1999)Google Scholar