About the Project
Most daily-life activities of both humans and machines depend upon a simple yet central set of capacities inherent to humans and recently granted to machines: acquisition of information, information processing, and decision making. The acquisition of information as well as information processing are studied by mathematicians and engineers within the framework of information theory. Alternatively, decision-making processes are studying within the foundations of game theory and control theory. Surprisingly, the progress toward a unified mathematical theory including the advances in information theory, game theory and control theory are relatively minor. Most of the current literature is developed under the assumption that decision makers possess complete information in order to make decisions and interact with each other. The most comprehensive developments suggest Bayesian approaches to model via priors the lack of information. Nonetheless, within the current Bayesian approach, the impact of perturbations to the state of knowledge either because of loss or acquisition of additional data is difficult to quantify.
The main objective of this thesis is to unify existing results obtained independently in the fields of mathematics and engineering for the study of the behaviour of humans and machines under the assumption that information is not perfect but rather acquired through systems with limited acquisition capabilities such as biological sensors, e.g., eyes, hears, skin, etc, and electronic sensors, e.g., cameras, communication systems, data collectors, etc. Essentially, this thesis seeks to quantify the notion of incomplete information using information measures such that decision-making processes can be quantitatively studied and, for instance, the probability of making mistakes or making decisions that may harm individual interests can be precisely estimated as a function of the distortion on the random variables describing the environment. Hence, the findings of this thesis would lead to clear answers to questions of the form: Given the available information about the random variables describing the environment, what is the probability of making a decision that might induce a regret to the decision maker? Given the rate at which information about the environment is received, what is the minimum time interval that minimizes the probability of regret?
This PhD position is opened within the collaboration between The University of Sheffield (TUOS) and INRIA in the areas of Information Sciences and Systems. The candidate will be based in Sheffield, UK, but mobility between the INRIA-Nice and the Department of Automatic Control and Systems Engineering of The University of Sheﬃeld is expected. The PhD student will be supervised by Dr. Iñaki Esnaola (Sheﬃeld) and Prof. Samir M. Perlaza (INRIA). The research topic lies in the broad intersection of information theory, game theory, and artificial intelligence.
Applicants can apply for a Scholarship from the University of Sheffield but should note that competition for these Scholarships is highly competitive. It will be possible to make Scholarship applications from the Autumn with a strict deadline in late January 2020. Specific information is available at: