Samir M. Perlaza | Princeton University | Electrical and Computer Engineering

I am interested in theoretical and practical aspects of game theory and information theory. The application domains that motivate my research include statistical machine learning, decision making, communication systems, and electric power systems.

Selected Research Areas

Statistical Empirical Risk Minimization and Generalization Capabilities of Machine Learning Algorithms

I am interested in the empirical risk minimization (ERM) problem when the optimization domain is a given set of probability measures over the set of models. A solution to this problem is a probability measure from which models can be sampled from to perform a machine learning task, e.g., a classification or a regression. A popular probability measure that arises from the ERM, subject to particular regularizations, is the Gibbs probability measure, which leads to the well-known Gibbs algorithm in statistical machine learning. The key challenge in this problem is the inclusion of previous knowledge about the models via regularizations of the ERM to enhance the generalization capabilities of machine learning algorithms. My research focuses on the study of the statistical properties of the random variables representing the training loss and test loss, when models are sampled from probability measures that are solutions to ERM problems subject to particular regularizations. The main feature of this research effort is that contrary to the main stream in the community, this analysis is made for fixed training datasets, which provides new and insightful mathematical tools for the analysis of generalization capabilities of machine learning algorithms.

Selected (Recent) Results:
- ‘‘Empirical Risk Minimization with Relative Entropy Regularization’’, with Gaetan Bisson, Iñaki Esnaola, Alain Jean-Marie, Stefano Rini.
  Research Report, INRIA, No. RR-9454, Sophia Antipolis, France, Feb., 2022.
- ‘‘Empirical Risk Minimization with f-Divergence Regularization in Statistical Learning’’, with Francisco Daunas, Iñaki Esnaola, and H. Vincent Poor.
  Research Report, INRIA, No. RR-9521, Sophia Antipolis, France, Oct., 2023".
- ‘‘The Worst-Case Data-Generating Probability Measure’’, with Xinying Zou, Iñaki Esnaola, and Eitan Altman.
  Research Report, INRIA, No. RR-9515, Sophia Antipolis, France, Aug., 2023".

Machine Learning and Decision Making with Noisy Observations

Recently, we have introduced a new formulation of zero-sum games (ZSG), which is particularly suited for studying decision making problems in which decision makers observe each other decisions subject to some degree of distorsion. Such a distorsion is modelled using the notion of channel, as in the realm of information theory. This provide the flexibility to consider effects such as quantization due to data acquisition via digital systems, additive noise due to privacy concerns, etc. Under these conditions, we have shown that the equilibrium of this game always exists and is often different from the Nash and Stackelberg equilibria. My research focuses on the analysis of the efect of the channel in the behavior of the decision makers. More specifically, my objective is to quantify, using information measures, the benefit or the loss for a given player due the distorsion in its observations.
Selected (Recent) Results:
- ‘‘2 × 2 Zero-Sum Games with Commitments and Noisy Observations’’, with Ke Sun and Alain Jean-Marie.
  Research Report, INRIA, No. RR-9505, Sophia Antipolis, France, May., 2023.

Samir M. Perlaza | Princeton University | Electrical and Computer Engineering

Research

Selected Research Areas

Teaching

Academic Appointments

Education

Editorial Boards

International Research Projects

Acknowledgments and Awards