Postdoc on “Distributed Optimization in Dynamic Wireless Networks” at INRIA Maestro team, Sophia Antipolis, France

Dear all,
the following postdoc position is available with start
date in a couple of months (the time needed to accomplish
all the administrative formalities).

TITLE: Distributed Optimization in Dynamic Wireless Networks

CANDIDATE’S BACKGROUND:
The candidate should have a solid background on probability,
graph theory and optimization and good programming skills.

CONTEXT:
The applicant will be part of INRIA Maestro team and will
work in the framework of INRIA and Alcatel-Lucent Bell Labs
joint laboratory.
MAESTRO is an INRIA project-team (created on October 1st,
2003) whose permanent members are located in Sophia
Antipolis, in Avignon and in Montpellier.
The ambition of MAESTRO is to provide the community with
methods and tools for the performance evaluation,
optimization and control of networks. More precisely, the
objectives of MAESTRO are:
* to develop mathematical and software tools for
evaluating the performance, optimizing and controlling
discrete-event systems, including networks and their
applications;
* to evaluate the performance and to control
communication networks (protocols, architectures,
applications) and, primarily, IP networks.
http://www-sop.inria.fr/maestro/

SALARY:
25600 euros net per year

DURATION:
One year

CONTACT:
Giovanni Neglia, giovanni.neglia@inria.fr,
http://www-sop.inria.fr/members/Giovanni.Neglia/

TOPIC DESCRIPTION:
Future wireless networks may require autonomic operation
features in order to cope with a high number of users and a
fast changing scenario. In fact, the time a central
authority would need to discover network operation
conditions and enforce particular behaviours at the nodes
would be in many application scenarios much longer than the
network dynamics timescales. Then, nodes need to be able to
derive local policies in oder to achieve a global desired
performance.
This problem can be considered as a distributed stochastic
optimal control problem or a team theory problem: we have
multiple controllers (the nodes) with a common objective.
The challenge arises from the fact that nodes in general do
not have an exact knowledge of the status of the system
because this is distributed, large and because the spreading
of information may be significantly limited by intermittent
connectivity. Hence each node can only rely on some belief
about the status of the system to take its decisions. In
such a context, optimal policies may be identified only for
specific structures of the information available at the
agent (full, sampled, delayed…) and their complexities
depend on the information structure too. Moreover, not only
the current state of the system, but also the network
scenario itself (e.g. the total number of nodes, their
connectivity, the consequences of each action) can be
unknown to the nodes. In such cases it is needed that nodes
learn online about the dynamic environment through
trial-and-error interactions.
We want to address the problem of distributed optimization
in such a scenario. We start considering the case when the
nodes collaborate to minimize the sum of local objective
functions, depending in general on some parameters or
actions of all the nodes in the network. If the local
objective functions are convex, it can be adopted a recently
proposed computation framework that relies on local
sub-gradient methods and consensus algorithms to average
each node information [Nedic2009]. For example the
dissemination of dynamic content in a Delay Tolerant Network
falls in this scenario [Iaonnidis2009].
Existing convergence results for this framework can be
applied only in the case of synchronous node operation and
simple network dynamics without memory. We will address both
these issues studying the convergence to the optimal
solution for a more general class of dynamics and under
asynchronous operation. Some preliminary results are in
[Masiero2010].
Moreover, we want to investigate also the speed of
convergence of this distributed optimization approach, that
is determined by its two components: the consensus algorithm
and the gradient algorithm.
A third research direction is to determine if the local
sub-gradient can be replaced by local derivative-free
approaches [Conn2009] in the cases when the performance
metric to optimize is unknown, so that it is not possible to
calculate a gradient or even a sub-gradient.

[Ioannidis2009] S. Ioannidis, A. Chaintreau, and L.
Massoulie, “Optimal and Scalable Distribution of Content
Updates over a Mobile Social Network,” in proceedings of
IEEE INFOCOM 2009, Rio de Janeiro, Brazil, Apr. 2009, pp.
1422–1430.
[Nedic2009] A. Nedic and A. Ozdaglar, “Distributed
Subgradient Methods for Multi-agent Optimization,” LIDS
report 2755, IEEE Transactions on Automatic Control, vol.
54, no. 1, pp. 48-61, 2009.
[Masiero2010] R. Masiero, G. Neglia, Distributed
Sub-gradient Method for Delay Tolerant Networks, in
proceedings of IEEE INFOCOM 2010 (Miniconf), Shangai, China,
April 2010.
[Conn2009] A. R. Conn, K. Scheinberg, L. N. Vicente,
Introduction to Derivative-Free Optimization, Society for
Industrial and Applied Mathematics. 2009

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