In this talk, I will present our work on uncertainty management in two different contexts. First, we consider the classical multi-armed bandit problem, where the goal is to choose the optimal option (arm) among a basket of options via exploration, but with two novel twists: (i) we allow the reward/cost distributions to be unbounded or even heavy-tailed, and (ii) the optimal arm is to be chosen in a risk-aware manner. In this setting, we devise analytically tractable algorithms that are entirely environment oblivious, i.e., the algorithm is not aware of any information on the reward distributions, including bounds on the moments/tails, or the suboptimality gaps across arms. Second, we consider the problem of sizing storage for reliable integration of renewables into the power grid. Formally, we characterize the reliability of a renewable generator bundled with a battery. Our results shed light on the fundamental limits of reliability achievable, and also guide the sizing of the storage required in order to meet a given reliability target. Using this framework, we also explore the statistical economies of scale in battery sizing that are achievable by sharing the battery between different renewable generators. Theoretical results, as well as an extensive case study using real-world data, demonstrate the tremendous economies achievable via battery sharing.
Jayakrishnan Nair is an Assistant Professor of Electrical Engineering at IIT Bombay. His research draws on tools from queueing theory, applied probability, game theory, and control theory to address performance evaluation and design issues in networks, service systems, and smart power grids.