Arjun Ramachandra

I am a postdoctoral researcher based in Singapore. My research interest broadly lies at the interface of computer science, probability theory and operations research, focusing on leveraging tools from these areas to tackle complex uncertain optimization problems. I work on multiple research areas with a special focus on distributionally robust optimization, You're welcome to learn more about my work at my webpage and correspond with me.

Submodularity and pairwise independence

  • Karthik Natarajan
  • Arjun Ramachandra
    • Categories Optimization in Data Science, Robust Optimization, Stochastic Programming Tags , , ,

    In this paper, we provide a characterization of the expected value of submodular set functions with pairwise independent random input. The set of pairwise independent (uncorrelated) probability distributions contains the mutually independent distribution and is contained within the set of arbitrarily dependent (correlated) distributions. We study the ratio of the maximum expected value of a … Read more

    Tight Probability Bounds with Pairwise Independence

  • Arjun Ramachandra
  • Karthik Natarajan
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Linear Programming Tags , , , , , , , ,

    \(\) While useful probability bounds for \(n\) pairwise independent Bernoulli random variables adding up to at least an integer \(k\) have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several results in this direction. Firstly, when \(k = 1\), the tightest upper bound on the … Read more

    Extremal Probability Bounds in Combinatorial Optimization

  • Divya Padmanabhan
  • Selin Damla Ahipasaoglu
  • Arjun Ramachandra
  • Karthik Natarajan
    • Categories Combinatorial Optimization, Robust Optimization Tags , ,

    In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the marginal distributions of the objective coefficient vector. The bounds are “extremal” since they are valid across all joint … Read more

    Robust Conic Satisficing

  • Arjun Ramachandra
  • Napat Rujeerapaiboon
  • Melvyn Sim
    • Categories Robust Optimization Tags , , ,

    In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we can use to approximately quantify the risk of an evaluation function that depends on both our decision and the uncertainty. This empirical … Read more