Related papers: Rational Decisions, Random Matrices and Spin Glass…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
Recent advancements in Large Language Models (LLMs) have demonstrated remarkable capabilities in various domains. However, effective decision-making relies heavily on strong reasoning abilities. Reasoning is the foundation for…
In this talk we review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
We study the problem of finding the optimal assortment that maximizes expected revenue under the decision forest model, a recently proposed nonparametric choice model that is capable of representing any discrete choice model and in…
This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
We provide a strategy to find in few elementary calculations the critical exponents of the overlaps for dilute spin glasses, in absence of external field. Such a strategy is based on the expansion of a suitably perturbed average of the…
Starting from preferences on N proposed policies obtained via questionnaires from a sample of the electorate, an Ising spin-glass model in a field can be constructed from which a political party could find the subset of the proposed…
This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…
Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…
Causality is receiving increasing attention in the Recommendation Systems (RSs) community, which has realised that RSs could greatly benefit from causality to transform accurate predictions into effective and explainable decisions. Indeed,…
This paper considers the problem of learning safe policies in the context of reinforcement learning (RL). In particular, we consider the notion of probabilistic safety. This is, we aim to design policies that maintain the state of the…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as…
Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical…
Selective rationalization aims to produce decisions along with rationales (e.g., text highlights or word alignments between two sentences). Commonly, rationales are modeled as stochastic binary masks, requiring sampling-based gradient…
This paper studies an optimal investing problem for a retiree facing longevity risk and living standard risk. We formulate the investing problem as a portfolio choice problem under a time-varying risk capacity constraint. We derive the…
In this paper we look at a class of random optimization problems. We discuss ways that can help determine typical behavior of their solutions. When the dimensions of the optimization problems are large such an information often can be…