My research focuses on the mathematical foundations of decision-making, particularly in contexts involving multiple objectives and interacting agents. I work at the intersection of set-valued analysis, game theory, and reinforcement learning, aiming to develop theoretical tools that better reflect the complexity of modern decision systems.
One major line of my work concerns set-valued HJB equations. These generalize classical control theory by allowing for multiple simultaneous objectives. With collaborators, I have extended stochastic calculus to this setting and currently developing viscosity solutions and game-theoretic extensions involving Nash equilibria. These tools offer a promising framework for reasoning about high-dimensional tradeoffs in decision-making problems.
In parallel, I am working to unify reinforcement learning and game theory by introducing a formal notion of agent architecture.Traditional game theory often treats agents as abstract strategy sets, but real agents have internal architectures that shape how they learn and adapt. By formalizing agent design, I aim to unify perspectives from reinforcement learning and game theory under a shared framework.
These research directions come together in applications like algorithmic collusion and financial decision-making, where both multi-objective tradeoffs and strategic interaction are central. Ultimately, my goal is to advance a unified theory that bridges abstract mathematics with emerging challenges in intelligent decision-making systems.