Quantum mechanics and photonics share mathematical equivalence. By carefully exploiting the interplay between optical index, gain and loss in the complex dielectric permittivity plane, optics has become an ideal platform to explore some exotic quantum concepts, such as topological physics and parity-time (PT) symmetry.

The theory of learning in games emerged to understand how repeated interactions among independent individuals can lead to certain equilibrium behaviors in the long run. Stochastic stability is a popular solution concept to explain the long term behavior for a class of learning dynamics called stochastic learning dynamics. In this talk, I will first establish that stochastic stability may not be a complete solution concept for stochastic learning dynamics.

When navigation algorithms realize their potential, autonomous driving will usher a new era of mobility, providing cheaper mobility to the elderly, the disabled and the young. It will reduce car ownership, increase fuel efficiency and reduce traffic jams. The navigation problem needs to be solved efficiently. It is well understood that slower reaction time in driving can be fatal. For the self-driving cars to be safe, the navigation algorithms have to be optimized without compromising accuracy. I will talk about optimizing algorithms in the navigation pipeline.

In many practical problems from online advertisement to healthcare and computational finance, it is extremely important to have guarantees on the performance and other characteristics of the policy generated by our algorithms. This reduces the risk of deploying our policy and helps us to convince the product (hospital, investment) managers that it is not going to harm their business. In the first part of the talk, we provide an overview of our work on learning safe and risk-sensitive policies in sequential decision-making problems. The notion of safety studied here is “safety w.r.t.