Optimization and Game Theory

Optimization is a core methodological discipline that aims to develop analytical and computational methods for solving optimization problems in engineering, data science, and operations research. Research in LIDS focuses on efficient and scalable algorithms for large scale problems, their theoretical understanding, and the deployment of modern optimization techniques to challenging settings in diverse applications ranging from communication networks and power systems to machine learning.

In addition, there is a natural overlap between optimization and control, as much of modern control theory rests on optimization formulations.

Finally the increased interest in systems that involve simultaneous optimization by several, possibly competing agents has led to several research thrusts that rely on game-theoretic approaches.

Sample Activities

  • Distributed nonlinear optimization algorithms
  • Optimization methods for supervised learning
  • Optimization methods that rely on algebraic techniques
  • Optimization in the power grid
  • Reinforcement learning for stochastic optimal control
  • Stochastic gradient descent algorithms and their analysis
  • Cyber-physical systems: architectural design, security and privacy, cross-layer algorithms, and tools for analysis, verification, and performance guarantees
  • Design of incentives and mechanisms in networked, dynamic environments
  • New equilibrium notions and dynamics in games