The SOLACE seminar is held on Thursdays at 2pm at the
Laboratory of Analysis and Architecture of Systems (LAAS).
During the academic year 2024–2025, the seminar is organized by
Céline Comte and Thomas Hira.
The Cost of Randomness and Value of Information in Resource Allocation
Itai Gurvich – September 10, 12, and 19, 2024
The mini-course covers a family of dynamic resource allocation problems. In these, requests arrive over the time. Accepting a request generates a reward and requires the use of a collection of (possibly reusable) resources. Benchmarks (upper bounds on collected rewards) help in designing “good” online control policies. Two natural benchmarks are the so-called fluid benchmark---where, effectively, randomness is ignored---and the offline benchmark where there is a “prophet” that can see the future and, in particular, has more information than the online controller. The development of online algorithms is practically useful but also brings about a mathematical understanding of the cost of randomness and the value of information in these resource allocation problems. If online can do almost as well as the offline prophet, this means that future information is of little value. If the offline controller---who has information but still faces randomness---can achieve the fluid upper bound, it means that the cost of randomness is limited.
We will cover different mathematical frameworks to study these problems as well as various examples and applications.
Principal Component Analysis in the Pseudo-Riemannian Wasserstein Space: A Review
Elsa Cazelles – September 5, 2024
In this talk, I will present different ways of conducting principal component analysis of datasets whose elements are probability distributions. For that purpose, I will consider the pseudo-Riemannian structure of the space of probability distributions (with moments of order 2) endowed with the Wasserstein metric. The nice geometric properties (such as the existence of geodesics) of the Wasserstein space do not, however, allow applying classical statistical learning tools such as PCA for Hilbert spaces. Using techniques borrowed from Riemannian geometry or redefining projections are all tools to produce a meaningful second order statistical analysis of a dataset of probability measures.
