Section: Application Domains

Application Domains

Applications of black-box algorithms occur in various domains. Industry but also researchers in other academic domains have therefore a great need to apply black-box algorithms on a daily basis. We see this as a great source of motivation to design better methods. Applications not only allow us to backup our methods and understand what are the relevant features to solve a real-world problem but also help identify novel difficulties or set priorities in terms of algorithm design.

Asides from the two applications to Machine Learning that we detail below, we however do not target a specific application domain and we are interested in possible black-box applications stemming from various origins. This is for us intrinsic to the nature of the methods we develop that are general purpose algorithms. Hence our strategy with respect to applications can be seen as opportunistic and our main selection criteria when approached by colleagues who want to develop a collaboration around an application is whether we judge the application interesting: that is the application brings new challenges and/or gives us the opportunity to work on topics we already intended to work on.

The three concrete applications related to industrial collaborations we are currently dealing with are:

• With EDF R&D through the design and placement of bi-facial photovoltaic panel for the postdoc of Asma Atamna funded by the PGMO project.

• With Thales for the thesis of Konstantinos Varelas (DGA-CIFRE thesis) related to the design of radars (shape optimization of the wave form). This thesis investigates the development of large-scale variants of CMA-ES.

• With Storengy, a subsidiary of Engie specialized in gas storage for the thesis of Cheikh Touré. Different multi-objective applications are considered in this context but the primary motivation of Storengy is to get at their disposal a better multi-objective variant of CMA-ES which is the main objective of the developments within the thesis.

Additionally, there are two specific types of applications stemming from Machine Learning we would like to focus on: problems with non-differentiable loss that can occur in reinforcement learning and hyperparameter tuning problems. For the first class of problems the motivation comes from the paper [36] where different reinforcement learning problems are addressed and the weights of neural networks are adjusted using evolution strategies. Those problems are large-scale (in [36] up to ${10}^6$ weights are adjusted), and the large-scale variants of CMA-ES we want to investigate might be relevant in this case. For the second class of problems (hyperparameter tuning problems), standard approches to handle those problems are Bayesian optimization algorithms but despite the tremendous effort for developing Bayesian optimization techniques and having implementations of Bayesian optimization algorithms within libraries, pure random search is still often used for training neural networks. One reason is that pure random search is intrinsically parallel [18]. This suggests that methods like CMA-ES—that are also intrinsically parallel—can be also advantageously used for hyperparameter tuning: this was demonstrated to tune deep neural networks in [32]. One limitation though of the CMA-ES algorithm is that it cannot deal with categorical/integer and continuous variables at the same time. This motivates us to investigate the development of CMA-ES variants that are able to deal with mixed variables.

When dealing with single applications, the results observed are difficult to generalize: typically not many methods are tested on a single application as tests are often time consuming and performed in restrictive settings. Yet, if one circumvent the problem of confidentiality of data and of criticality for companies to publish their applications, real-world problems could become benchmarks as any other analytical function. This would allow to test wider ranges of methods on the problems and to find out whether analytical benchmarks properly capture real-world problem difficulties. We will thus seek to incorporate real-world problems within the COCO platform. This is a recurrent demand by researchers in optimization. As far as confidentiality of data are concerned, our preliminary discussions with industrials allow us to be optimistic that we can convince industrials to propose real-world problems with anonymized (and uncritical) data that still capture the essence of the underlying real-world problem.