1. Distributed optimization And In-Network Computation Over Multi-hop Wireless Networks
( Joint work with Prof. V. S. Borkar and Prof. D. Manjunath, EE Dept., IIT Bombay)
We consider distributed minimization of a sum of convex functions by a set of distributed nodes. Each variable of the objective function is associated with one node and each node is associated with one component of the sum. Further, each component depends only on some ‘local’ variables of the node, i.e., variables associated with the node and its neighbors. Nodes communicate over a multi-hop wireless network and act as a distributed computing system subject to communication constraints imposed by the wireless network. The problem is motivated by several specific sensor network problems. We formulate the problem of optimizing the transmission schedule subject to constraints imposed by wireless transmission, so as to maximize the speed of convergence.
2. Online Regression Over a Wireless Network
In this problem, we study online in-network regression over wireless networks. We model the distributed regression as a least square problem and perform the computation over an overlay computational structure that is identical to the multilayer backpropagation of neural networks. The overlay is aligned to the physical topology of the network. The sources of the explanatory (input) and response (output) variables are assumed distributed. Since the wireless network imposes constraints on the allowable simultaneous transmissions, the updates to the estimates of the regression coefficients are necessarily asynchronous. The scheme is analyzed as a stochastic gradient descent algorithm. We also propose the scheduling scheme which respects wireless constraints and dynamically
chooses the message passing sequence to speed up the rate of convergence of algorithm.
Work in Progress:
3. Mathematical Modeling of Online Recommendation System
( Joint work with Prof. D. Manjunath, EE Dept. IIT Bombay)
a) Revenue Maximization and Optimal Personalized Online Recommendation Mechanism
Recommendation engine contains set of resources in its database, for instance, list of websites. Each websites have different topics on it e.g. news site thehindu.com contains a topics on politics, sports, healths, etc. Recommendation engine has an objective to maximize
the revenue via recommending websites to the user e.g. youtube recommends videos to the user. We are interested to answer following questions.
1. Under the assumption that user interest known to recommendation, we formulate optimization problem as revenue maximization. What is optimal recommendation strategy which maximizes the revenue of recommendation engine?
2. Under assumption that user interests unknown to recommendation engine, what is recommendation strategy to which maximizes the revenue of recommendation engine?
b) On-line Recommendation and Multi-Armed Bandit Problem
4. Asynchronous In-Network Computation Over Large Networks
Wireless sensor networks plays significant role in measuring environment and performing communication and computation. It has constraints of limited battery storage. This poses challenge on measurement data transmission to sink node or center node and perform function computation. To resolve the issue, distributed in-network processing and optimization is natural to study. Thus we formulate distributed convex optimization as sum of convex function associated with each sensor nodes having constraints on its data sets. We propose asynchronous distributed projection algorithm in wireless constraint network to optimize the convex function.