My past research have primarily been at the intersection between game theory, optimization, control. In the past I have worked on or have been interested in the following topics:
optimal control, calculus of variations, and differential games,
optimization on manifolds,
all areas of machine learning and their interfaces with game theory,
online learning and bandit algorithms for multi-agent systems,
MDP-based reinforcement learning and inverse reinforcement learning/reward-learning,
generative adversarial networks and generative adversarial imitation learning,
metric geometry and metric learning,
information theory and information geometry,
computational social science/sociology/psychological/behavioral science.
Things I have been working on recently
Control
I have tried at various points to incorporate geometry in my past work on game dynamics. There has been some new results on applying differential geometry and geometric control to game dynamics by Krishnaprasad et al. I am spending time to study geometric control in depth.
I am also interested some recent results on Fenchel duality theory in control. As well I am becoming very interested in calculus of variations.
Optimization
I am mostly spending time studying computational complexity in the context of optimization and games. This started when I was digging into some results on L0 minimization in compressed sensing and was unsatisfied with how the reduction argument was presented.
I am becoming very interested in third-order-in-space methods (Helly's method), Forward-Forward propagation algorithm and efficient implementation of second-order methods in machine learning, e.g,. KFAC.
Machine learning
I occasionally read up some new techniques or modifications related to the transformer model, e.g., LoRA or the more recent Mamba model.
I am gradually becoming interested in diffusion process, particularly langevin equations. I think these equations are directly related to my past research, but I didn't get around to sufficiently review measure theory and Ito calculus to appreciate those results.
Robotics
I am quite interested in how recent applications involving these robots work. The common denominator seems to be Sim2Real imitation learning-type algorithm behind the scenes but I haven't been following this area for a while now.
Outside from these ideas which are all adjacent to my previous areas of research, I strongly hold the belief that we need to explore ideas which are outside of our comfort zone, not purely confined by our previous training or discipline. I am constantly seeking opportunities that allows for this type of exploration. For example, I have been previously quite interested in biology, in particular neuroscience and physiology, I would be quite happy to do research on these areas. I'm also drawn to more exotic applications such as animal communication, extraterrestrial exploration, kinetic art, artificial life, and I follow people who are working on these topics.
Some thoughts on sociology and computational social science
The type of research I have felt most passionate about is applying computational techniques to analyze people, groups and society.
Society is paradoxically one of the simplest as well as the most complex system in existence. It is simple because society operate on simple principles (e.g., energy conservation and evolutionary mechanism) that produce routinely predictable macro-outcomes. It is also complex because these rules and outcomes are obfuscated through many layers of mediums such as our own perceptions and the media. It is difficult not to view society as having a well-defined mathematical structure. Social theories are descriptions of feedback systems.
I believe a truly intelligent AI system is one that is capable of objectively analyze the human experience and critique social structures. I don't think we will ever reach there.
I view my past works in control and games as a potential foray into my long-term vision, which is to algorthmatize research from the ''soft sciences'' and develop technology or analytical models or predictions that can aid people working in the area of public health, therapy, social work and social policy.