2022-05103 - Doctorant F/H Approximation methods for the soundness of control laws derived by machine learning
The offer description below is in French

Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

About the research centre or Inria department

The Inria Rennes - Bretagne Atlantique Centre is one of Inria's eight centres and has more than thirty research teams. The Inria Center is a major and recognized player in the field of digital sciences. It is at the heart of a rich R&D and innovation ecosystem: highly innovative PMEs, large industrial groups, competitiveness clusters, research and higher education players, laboratories of excellence, technological research institute, etc.


The design of controllers for large cyber physical systems (CPS, i.e. systems driven both by physical equations and digital controllers) is challenged today by machine learning approaches, and specifically reinforcement learning. The latter however still fail to provide guarantees on the behavior of the controllers it provides. The objective of this thesis is to explore a range of techniques that would make control design for CPS or any other large-scale complex system sound and scalable. The focus will be on quantitative methods, that provide performance guarantees, for example PAC bounds (probably approximately correct).

Several research directions are envisioned. The main one concerns model approximation. For a given dynamic system with discrete state, like a stochastic automaton, this may mean reducing the size of the state space while preserving as much as possible the distribution over generated runs, which requires computing or estimating distances between models. Starting from a CPS with continuous state variables, this means finding the best discretization with bounded state size. One may as well take as starting point a (possibly infinite) collection of representative runs of that system, or a black box trace generator, and be interested in learning a model from these traces (system identification) in order to capture the most characteristic features of their dynamics. For all these directions, one will be interested both in designing approximation algorithms, in characterizing their convergence properties, and in providing bounds for their accuracy.

A second research direction concerns approximation techniques in view of control design. There, the model (a Markov Decision Process for example) comes as the support to design an efficient control policy, toward some quantitative objective. Optimal control laws generally derive from iterative methods that do not scale up with model dimension, in particular if the latter come from discretization of continuous variables. The objective will be to explore various approximation techniques that would improve scalability, convergence speeds and provide both performance bounds and readability of the control laws. Model approximations are one possible way, but also controller regularization (for example through state aggregation), or approximations in the iterative procedure that yield optimal laws, or even control objective relaxations.

As a possible use-case for the above techniques, we aim at designing distributed controllers for large CPS, for example a fleet of trains on a subway line. The objective will be both to design multi-agent control strategies, to estimate their performances and to verify safety properties like maintaining minimal headways. Applications to other complex mechanical devices are also envisioned, like those of the OpenAi Gym.


This PhD will take place in the SUMO Team at INRIA Rennes (Brittany, France), under the joint supervision of  Loïc Hélouët and Eric Fabre. Funding is secured for this PhD, as a 3 years contract. This research will be connected to the Maveriq ANR project.

Main activities

The activities during this PhD wil consists in : 

  • bibliographical work, 
  • algorithms design and proofs, 
  • paper writing,
  • meetings with the supervisors and with the members of the MAVERIQ ANR
  • attending conferences


The candidate should be fluent in english (written, read spoken). 

It is not necessary to speak french to apply. 

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Possibility of teleworking ( 90 days per year) and flexible organization of working hours
  • partial payment of insurance costs


monthly gross salary amounting to 1982 euros for the first and second years and 2085 euros for the third year