arXiv subjects

Kévin Colin

Publications and source records attributed to Kévin Colin.

4 recordsLinked to original sources

arXiv2024

Regret Minimization in Scalar, Static, Non-linear Optimization Problems

We study the problem of determining an effective exploration strategy in static and non-linear optimization problems, which depend on an unknown scalar parameter to be learned from online collected noisy data. An optimal trade-off between exploration and exploitation is crucial for effective optimization under uncertainties, and to achieve this we consider a cumulative regret minimization approach over a finite horizon, with each time instant in the horizon characterized by a stochastic exploration signal, whose variance is to be designed. We aim to extend the well-established concepts of regret minimization from linear to non-linear systems, with a focus on the subsequent conceptual differences and challenges. Thus, under an idealized assumption on an appropriately defined information function associated with the excitation, we are able to show that an optimal exploration strategy is either to use no exploration at all (called lazy exploration) or adding an exploration excitation only at the first time instant of the horizon (called immediate exploration). A quadratic numerical example is presented to demonstrate the effectiveness of the proposed strategy.

math.OC↗

arXiv2024

Data-driven Bayesian estimation of Monod kinetics

In this paper, we consider the well known problem of non-linear identification of the rates of the reactions involved in cells with Monod functions. In bioprocesses, generating data is very expensive and long and so it is important to incorporate prior knowledge on the Monod kinetic parameters. Bayesian estimation is an elegant estimation technique which deals with parameter estimation with prior knowledge modeled as probability density functions. However, we might not have an accurate knowledge of the kinetic parameters such as interval bounds, especially for newly developed cell lines. Hence, we consider the case when there is no accurate prior information on the kinetic parameters except qualitative knowledge such that their non-negativity. A log-Gaussian prior distribution is considered for the parameters and the mean and variances of these distribution are tuned using the Expectation Maximization algorithm. The algorithm requires to use Metropolis Hastings within Gibbs sampling which can be computationally expensive. We develop a novel variant of the Metropolis-Hastings within Gibbs sampling sampling scheme in order to accelerate and improve on the hyperparameter tuning. We show that it can give better modeling performances on a relatively large-scale simulation example compared to available methods in the literature.

stat.ME↗

arXiv2022

Optimal exploration strategies for finite horizon regret minimization in some adaptive control problems

In this work, we consider the problem of regret minimization in adaptive minimum variance and linear quadratic control problems. Regret minimization has been extensively studied in the literature for both types of adaptive control problems. Most of these works give results of the optimal rate of the regret in the asymptotic regime. In the minimum variance case, the optimal asymptotic rate for the regret is $\log(T)$ which can be reached without any additional external excitation. On the contrary, for most adaptive linear quadratic problems, it is necessary to add an external excitation in order to get the optimal asymptotic rate of $\sqrt{T}$. In this paper, we will actually show from an a theoretical study, as well as, in simulations that when the control horizon is pre-specified a lower regret can be obtained with either no external excitation or a new exploration type termed immediate.

math.OC↗

arXiv2021

Robustness of a feedback optimization scheme with application to bioprocess manufacturing

In this work the robustness of a feedback optimization scheme is discussed. Previously known results in literature, on the convergence to local optima of the optimization problem of interest, are extended to the case where the sensitivities of the steady-state input-output map of the plant present bounded uncertainties. The application of the scheme to a biological setting, with the goal of maximizing the concentration of products of interest in a bioreactor, under a continuous perfusion framework, is suggested and the potential of the approach is exposed by means of a simple synthetic example. This extended version contains also the Numerical data for example in "Robustness of a feedback optimization scheme with application to bioprocess manufacturing" report, for the sake of reproducibility of the results.

math.OC↗