FRE Special Seminar: Aymeric Dieuleveut & Marco Frittelli
RSVP
Aymeric Dieuleveut
Title
Computer-aided Proofs in First-order Optimization Approaches, A Case Study on Error Feedback
Abstract
First-order methods are widely used in optimization and machine learning, and their behavior often analyzed through the spectrum of worst case convergence rates. Obtaining such guarantees is often difficult and both time consuming and error-prone. Starting with the work of Drori and Teboulle (2014), novel techniques have been used to gain numerical insights, leading to the release of various performance estimation (PE) software.
In this talk, I will show how various computer-aided techniques can be used to study first-order optimization methods in a systematic way. From performance estimation problems with automated Lyapunov discovery, to symbolic regression and computer algebra systems, novel tools completely reshape the way we approach theory of optimization.
As a main example, I will focus on error feedback methods used with compressed communication in distributed optimization. While error feedback has been widely studied, existing theory often provides untight (thus unreliable) bounds. I will present tight analyses with matching lower bounds that allow a fair comparison between error feedback schemes and standard compressed gradient descent, and help explain when error feedback is useful and when it is not.
Overall, the talk aims to show how various computer-aided proofs can lead to clearer and more reliable insights into first-order optimization methods.
Marco Frittelli
Professor of Mathematical Finance at the University of Milano
Title
When Cooperation is Beneficial to All Agents
Abstract
This paper advances the theory of Collective Finance, as developed in \cite{BDFFM26}, \cite{DFM25} and \cite{F25}.
Within a general semimartingale framework, we study the relationship between collective market efficiency and individual rationality. We derive necessary and sufficient condition for the existence of (possibly zero-sum) exchanges among agents that strictly increase their indirect utilities and characterize this condition in terms of the compatibility between agents’ preferences and collective pricing measures.
The framework applies to both continuous and discrete-time models and clarifies when cooperation leads to a strict improvement in each participating agent’s indirect utility.
Bio
Marco Frittelli is Professor of Mathematical Finance at the University of Milano, having held positions at Florence, Milano-Bicocca and Urbino Universities and visiting scholar positions in several universities in USA and Europe.
He is a member of the Editorial Board of the SIAM Journal on Financial Mathematics and was member of the Editorial board of The Annals of Applied Probability (2003-2008) and of the Scientific Committee of the Bachelier Finance Society (2004-2008). He was a member of the Expert Group (GEV) of the Italian Evaluation of the Research Quality (VQR-ANVUR).
The research is focused on the application of stochastic analysis and convex analysis in Mathematical Finance and it includes: the fundamental theorem of asset pricing; martingale pricing based on entropy minimization; utility maximization in incomplete markets; utility maximization, indifference pricing and risk measures in Orlicz spaces; convex risk measures; dynamic and law invariant risk measures and risk measures on Moduli; quasiconvex dynamic risk measures; V@R and acceptability indices; model-free arbitrage and robust pricing-hedging duality; pathwise finance; systemic risk and risk transfer equilibrium; conditional systemic risk measures; entropy martingale optimal transport; collective arbitrage, collective completeness and collective risk measures.