Q&A with Dr. Monica Cojocaru
Dr. Monica Cojocaru has been appointed the Interim Associate Dean of Research and Graduate Studies in CEPS.
Congratulations to Dr. Monica Cojocaru on her appointment to Interim Associate Dean of Research and Graduate Studies for the College of Engineering and Physical Sciences.
Cojocaru joined the University of Guelph in the Department of Mathematics and Statistics in 2003, where she is now a professor and has served as Graduate Program Coordinator. We had the opportunity to speak with her about her goals as the Associate Dean and her research.
As the Associate Dean of Research for the College of Engineering and Physical Sciences what do you hope to accomplish during your term?
First, I hope to keep some current best practices in good running condition and even strengthen the many accomplishments our College has recorded so far in research and development. Next, I hope to help my colleagues with exciting initiatives regarding new/expanding grad student programs, for instance building on the excellence of our Artificial Intelligence (AI) and Machine Learning (ML) Collaborative Specialization and the Masters in Data Science programs, to name a few. Last but not least, I would like to help our College researchers at all career levels get involved in more collaborative grants with colleagues at other universities, both Canadian or international. We have some excellent research and development taking place in our college and I believe there is much more we can accomplish in collaborative research initiatives.
Could you tell us a bit about your research focus?
My area of expertise is the study of applied problems in and outside of equilibrium. The word equilibrium is meaningful for all of us, in many contexts. In our own personal lives, we often talk about equilibrium in terms of a state where we believe our professional, emotional and social lives have reached a good ebb-and-flow. In mathematical modelling and applied sciences, the notion of equilibrium can have several equivalent definitions, depending on the applied field, such as: physical equilibrium, economic market equilibrium, epidemiological equilibrium, Nash equilibrium (which is a game theoretic notion), etc. Equally interesting for research are questions of both existence as well as characterizations of equilibria, not to mention questions on whether these privileged states can even be reached: in other words, when not in equilibrium, what does a system do? In my 20 years in research so far, I tackled these questions with tools from nonlinear analysis, differential equations, optimization, game theory, dynamical systems, agent-based models and data driven modelling.
Some of your research studies the dynamics of human behaviour at both the individual and population levels. Can you walk us through how your research plays into policy development?
Any policy introduced in a population will be as successful as people are willing to adopt it. Some of my research circa 2008-2012 centered around using models of individuals in a population of adopters to determine the state of the adoption of green vehicles – at the time, our definition of a green vehicle was of course a hybrid; now, the same models can be run with the innovative (new) product being the fully electrical cars. In 2008 my colleagues and I advised the City of Guelph on fast-tracking house permits for the “green” builders. In 2010, I was awarded a Fulbright Research Chair position on this green adoption research.
Most recently (this year) I led a team of researchers at Guelph, Montreal, Calgary and UBC Okanagan on an Alliance grant looking at (among other things) whether nonpharmaceutical intervention measures adoption can be quantified regionally, and whether these levels from the pandemic can give us insight into health measures adoption in general, in other possible upcoming scenarios. This sort of research is of interest to the Office of the Chief Medical Officer of Health in Ontario (who supports and wishes to possibly use our results) – as well as broadly being one of the most discussed emerging issues in population health: Behavioural quantification and its public health impact.
One of your areas of focus is using AI methods in generalized Nash games. Could you explain what the generalized Nash games are and how AI can be used?
My most recent focus has been on advancing computational methods for generalized Nash games, specifically heuristics based on AI/machine learning (ML) approaches. As for what is a generalized Nash game, let us think about it in small simple steps: A game is a theoretical model in which several players (two or more) choose concurrent or sequent strategies so that each player achieves their goal. This goal could be winning a game (which one can do in the detriment of their opponent – called zero-sum games), or simply maximizing/minimizing an objective (say two companies who both wish to maximize profit, but money earned by one of them does not rely on the other’s losses).
The players will reach an equilibrium – a so-called Nash equilibrium from the American mathematician John Nash’s work circa 1949-1950 – when they managed to find a pair of strategies whose outcomes satisfy both players to such a degree that, if they were to play again, they would choose the same strategy pair (i.e, they would have no incentive to change strategies). A generalized Nash game (from works of Arrow circa 1951) is a Nash game in which a player’s choice of strategy affects not only the payoff of all other players but also their strategy sets – meaning one player’s choice may not allow certain choices from other players.
A simple illustration of this is the so-called environmental accord model, where several countries (players) agree to an overall cap of general emissions in a common region. If one pollutes more, it will further limit the allowances of all others.
One complex feature of a generalized game is that the solution sets are large, and when one does not know what region of space contains this solution set, this is where computational techniques come in handy.
My interest is to develop computational algorithms where the solution set area for a given game can be searched and approximately described by allowing agents to “learn and adapt” their search until they find the best target area. These techniques could be applicable to games where current optimization techniques do not apply.
What is a recent research project/initiative that you are especially excited about?
I am very excited about a recent collaboration that I started in 2020 that relates my interests in generalized Nash games with the broader numerical optimization community in France. This is a team between myself, trainees and my colleague Dr. Samir Adly (and trainees) at the University of Limoges and the XLIM Institute (hosted by University de Limoges). We are exploring heuristics and traditional techniques to compare and advise practitioners on best methods to solve Nash games.
Are you currently looking for undergraduate, graduate, or postdoctoral students?
I am always looking for new trainees, I find that supervising trainees is one of the most rewarding activities I engage in. My group loves to maintain a very positive space and attitude towards both group and individual research contributions, and we love to hang out socially whenever possible. I love to hear about students’ interests in furthering their mathematical knowledge at any level in their career, my door is always open.
Dr. Monica Cojocaru is a Professor in the Department of Mathematics and Statistics.