Non-stationary Stochastic Optimization

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said change, and study how restrictions on this budget impact achievable performance. We identify sharp conditions under which it is possible to achieve long-run-average optimality and more refined performance measures such as rate optimality that fully characterize the complexity of such problems. In doing so, we also establish a strong connection between two rather disparate strands of literature: adversarial online convex optimization; and the more traditional stochastic approximation paradigm (couched in a non-stationary setting). This connection is the key to deriving well performing policies in the latter, by leveraging structure of optimal policies in the former. Finally, tight bounds on the minimax regret allow us to quantify the "price of non-stationarity," which mathematically captures the added complexity embedded in a temporally changing environment versus a stationary one

Influence de la gouvernance d’entreprise sur l’évolution du périmètre d’activité

L’objectif de cette recherche est d’expliquer l’évolution du périmètre d’activité de l’entreprise par la variation de son système de gouvernance. Nous proposons un modèle de recherche qui met en exergue l’impact des différents mécanismes de gouvernance sur les décisions du dirigeant et les conséquences sur l’évolution du périmètre d’activité de la firme. Ce modèle démontre que suivant la configuration du système de gouvernance de l’entreprise, le dirigeant optera soit pour la diversification, soit pour le recentrage d’activité. La variation du périmètre d’activité et son efficacité en termes de création ou de destruction de valeur résulteraient donc de l’interaction entre le dirigeant et les différents mécanismes de gouvernance de l’entreprise

Fundamental Limits for Light Absorption and Scattering Induced by Cooperative Electromagnetic Coupling

Absorption and scattering of electromagnetic waves by dielectric media are of fundamental importance in many branches of physics. In this Letter we analytically derived the ultimate upper limits for the absorbed and scattered powers by any system of optical resonators in mutual interaction. We show that these bounds depend only on the geometric configuration given an incident field. We give the conditions to fullfill to reach these limits paving so a way for a rational design of optimal metamaterials