Eloïse Berthier

 

Briefly

Since September 2019, I am a Ph.D. student under the supervision of Francis Bach. I work in the SIERRA team in Paris, which is a joint team between Inria Paris, ENS Paris and CNRS. My research focuses on developing efficient algorithms for optimal control and motion planning, with a particular interest in methods which can be applied to robotics, and which come with theoretical guarantees.

Before that, I have worked in the MLO team, under the supervision of Martin Jaggi, on privacy-preserving machine learning.

Contact

  • E-mail: eloise [dot] berthier [at] inria [dot] fr

  • Physical address: Inria Paris, 4th floor, Office C409, 2 rue Simone Iff, 75012 Paris.

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Recent Publications and Preprints

  • E. Berthier, J. Carpentier, F. Bach. Fast and Robust Stability Region Estimation for Nonlinear Dynamical Systems. Preprint, 2020.
    [hal] [Show Abstract]

    Abstract: A linear quadratic regulator can stabilize a nonlinear dynamical system with a local feedback controller around a linearization point, while minimizing a given performance criteria. An important practical problem is to estimate the region of attraction of such a controller, that is, the region around this point where the controller is certified to be valid. This is especially important in the context of highly nonlinear dynamical systems. In this paper, we propose two stability certificates that are fast to compute and robust when the first, or second derivatives of the system dynamics are bounded. Associated with an efficient oracle to compute these bounds, this provides a simple stability region estimation algorithm compared to classic approaches of the state of the art. We experimentally validate that it can be applied to both polynomial and non-polynomial systems of various dimensions, including standard robotic systems, for estimating region of attractions around equilibrium points, as well as for trajectory tracking.

  • E. Berthier, F. Bach. Max-Plus Linear Approximations for Deterministic Continuous-State Markov Decision Processes. IEEE Control Systems Letters, 4(3):767-772, 2020.
    [hal, journal] [Show Abstract]

    Abstract: We consider deterministic continuous-state Markov decision processes (MDPs). We apply a max-plus linear method to approximate the value function with a specific dictionary of functions that leads to an adequate state-discretization of the MDP. This is more efficient than a direct discretization of the state space, typically intractable in high dimension. We propose a simple strategy to adapt the discretization to a problem instance, thus mitigating the curse of dimensionality. We provide numerical examples showing that the method works well on simple MDPs.