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Distributed Optimization Methods for Smart Cyber-Physical Networks

Periodic Reporting for period 4 - OPT4SMART (Distributed Optimization Methods for Smart Cyber-Physical Networks)

Reporting period: 2020-01-01 to 2021-09-30

Smart communicating devices with their sensing, computing and control capabilities promise to make our society more intelligent, energy-efficient, safe and secure. To achieve these goals the main challenge is to exploit these powerful, but unstructured, computational resources. The most natural, and widely implemented, centralized computation model is not applicable to this extremely complex system in which processors are spatially distributed and interact through asynchronous and unreliable communication. Thus, a novel peer-to-peer distributed computational model is emerging as a new opportunity in which a problem is solved cooperatively by peers, rather than by a unique provider that knows and owns all data. Scientists and analysts agree that today’s goal is to get full value from the available massive data. Optimization is a key part of this process, since it is a building block in several learning, decision making and control problems for complex cyber-physical networks. Very-large scale and dynamic optimization problems need to be solved in several domains as, e.g. big-data analytics, energy networks, smart mobility, and cooperative robotics.
The OPT4SMART project has a twofold ambitious goal: (i) to set-up a novel, comprehensive methodological framework to solve distributed optimization problems in peer-to-peer networks, and (ii) to provide numerical methods and toolboxes, based on this framework, to solve distributed estimation, learning, decision and control problems in complex cyber-physical networks. We aim at pursuing this twofold objective by developing interdisciplinary methodologies arising from a synergic combination of optimization, control-systems, and graph theories. The envisioned distributed methods should solve general classes of problems, as nonconvex and mixed-integer, and work under time-varying and possibly asynchronous communication models.
The OPT4SMART project has successfully reached breakthrough results establishing a fundamental research framework for distributed optimization and developing numerical methods and toolboxes for applications in cyber-physical networks.

In the construction of a fundamental research framework for distributed optimization general classes of optimization problems have been identified to model distributed (machine/deep) learning, estimation, decision, and control problems in several domains as, e.g. big-data analytics, energy systems and cooperative robotics.

Distributed methods have been proposed to solve (stochastic) convex, nonconvex and mixed-integer problems under several communication models including (stochastic) time-varying, asynchronous and unreliable networks. Moreover, big-data problems have been successfully addressed with applications, e.g. in (deep) learning training problems and in control of spatially distributed systems. Moreover, the challenge of dynamic (online) optimization problems was successfully addressed with results in personalized learning, smart energy networks and cooperative robotics.

Two toolboxes, Disropt and ChoiRbot (available open source) have been developed to implement on realistic platforms distributed optimization and cooperative robotics tasks.

Disropt is a Python package providing full-fledged functionalities to design distributed optimization algorithms over networks. The toolbox also allows users to implement deep learning training methods in a distributed way and is compatible with state of art platforms (as, e.g. TensorFlow). The toolbox also gives the possibility to run numerical tests on supercomputing platforms.

ChoiRbot is based on the novel Robot Operating System (ROS) 2 and provides a fully-functional toolset to execute complex distributed multi-robot tasks, either in simulation or experimentally, with a particular focus on networks of heterogeneous robots. The toolbox has been used to implement in realistic simulations and experiments the developed distributed optimization and control methods for multi-robot teams.

The OPT4SMART group has disseminated the novel theories, methodologies and numerical methods in three directions: transfer to the scientific community, training at PhD and Postdoc level, and dissemination to a broad audience. The events related to the project activities have been reported in the News section of the project website.

Besides publications in major journals and conferences, results were disseminated in plenary lectures, round tables and PhD schools as well as in invited sessions and workshops co-organized with international experts.

Finally, OPT4SMART members advertised the main project challenges, topics and outcomes to a broad audience in several events as, e.g. the Researchers’ Nights or the MakerFaire.

In these events the goal was to highlight the potential impact for the society of the methods and technologies developed and under investigation in the OPT4SMART project.
OPT4SMART has given significant contributions to the area of distributed optimization for cyber-physical networks by addressing general optimization set-ups (e.g. stochastic convex, nonconvex and mixed-integer) and various communication frameworks (e.g. time-varying, asynchronous and unreliable). Moreover, big-data and dynamic optimization problems have been addressed in a purely distributed framework.

As for big-data optimization, it had been widely investigated in the parallel optimization literature. Our work on block-wise gradient tracking was the first addressing this challenge in distributed optimization with a proposed solution that extends state-of-art methods for standard consensus optimization. This work paved the way to other works addressing, e.g. stochastic optimization and highlighted interesting connections with deep learning.

The project also contributed to create a new algorithmic framework for distributed optimal control of spatially distributed systems. The main advantage of the proposed approach relies in the intrinsic stability of the optimization procedure inherited by a control feedback.

As for mixed-integer optimization, we have been among the first to propose distributed algorithms working under asynchronous and unreliable communication. Moreover, a distributed primal decomposition framework has given rise to significant improvements with respect to state-of-art solutions even in a parallel set-up. The proposed schemes have been successfully applied to realistic scenarios in smart grids and cooperative robotics.
As for cooperative robotics, distributed methods for pick-up-and-delivery and other decision-making problems have been developed for heterogeneous robot teams and implemented in experimental scenarios including ground and aerial robots.

Two toolboxes, Disropt and CoiRbot, have been developed. They represent important milestones for distributed optimization and cooperative robotics. Disropt is, to the best of our knowledge, the first toolbox allowing researchers to implement distributed algorithms on multi-core machines with processors performing only local computations and communications with neighboring processors. ChoiRbot is to the best of our knowledge, the first robotic platform giving roboticists a set of routines to design realistic simulations and experiments for distributed multi-robot coordination. The toolbox is based on ROS 2, a new version of the widely used operating systems ROS.
Distributed cooperative robotics
Distributed cooperative robotics
Concept of distributed optimization 2
Disropt toolbox
Concept of distributed optimization 1
Distributed computing concept
ChoiRbot toolbox