My research interests are in developing efficient algorithms for automated decision making in complex physical, cyber-physical and social systems. In this effort, I draw on tools from a variety of disciplines including stochastic control theory, convex and nonlinear optimization, game theory, economics and machine learning. In recent years, I have focussed on challenging problems arising in large scale infrastructure systems.
Here is a recent CV .
Click on the topics below to see highlights from my recent research (click to expand). A comprehensive list of papers is available here .
Robustness of infrastructure networks
Most infrastructure networks (including the power grid, water and natural gas distribution networks) can be described as dynamical systems with nonlinear dynamics and uncertain inputs (
(for example, wind and solar forecast errors in the power grid). A natural first step towards understanding these stochastic nonlinear systems is to study their equibria: These are typically
solutions to some nonlinear system of equations $F(x)=s$ where $ x $ denotes the physical state variables (voltages or pressures, for example) and $ s $ denotes the inputs
(power generation/consumption at all nodes in the power grid). There are typically engineering constraints on the state variables $ x \in X$ and hence it is of interest to understand whether the
system $F(x)=s$ has a solution with $x \in X$ ($X$ can denote minimum/maximum voltage/pressure levels for example). Since $F$ is a nonlinear map, this is typically a difficult problem (determining existence of a solution to a system of nonlinear equations within a certain set)
and, unsurprisingly, is NP-hard in general.
However, for real phyiscal systems, there is additional structure to both $F$ and $X$ that can be exploited to solve these problems efficiently. We develop an approach to solve $F(x)=s,x \in X$
given $s$, under certain conditions that are satisfied often for real power systems Graphical models for infrastructure network analysis
Graphical models have proven to be a powerful tool in machine learning and artificial intelligence - they are a means to
compactly represent high dimensional probability distributions and reason about them efficiently. We show how to use graphical models to derive efficient approximation algorithms for the mixed-integer nonlinear optimization problems arising in power distribution networks Incentive driven dynamics in markets
Fisher markets are a simple model of exchange markets that have received a lot of attention in the computer science literature on algorithmic game theory. One of the recent celebrated
results from algorithmic game theory include combinatorial algorithms for computing market equilibria in Fisher markets. In parallel, there is a long history of work in the economics
literature addressing various price update dynamics that converge to market equilibria in Fisher markets (and more general markets). However, most of these price update rules do not have a
rational justification - ie, there is no explanation for why participants in an actual market would follow them. In recent work, I proved that under certain assumptions, a very natural set of
rationally justified price update dynamics converge to equilibria in Fisher markets. THe dynamics we consider are based on recursive belief formation (a merchant thinks about what other merchants might do, and
what they might in turn think about other merchants, etc.). For a very general notion of the belief formation procedure, we show that the market dyanmics based on price updates computed using these
beliefs are guaranteed to converge to the market equilibirum at a fast rate (which can be quantified)