Karthik Gopalakrishnan

Karthik Gopalakrishnan


Karthik is a postdoctoral scholar in ASL at Stanford. He recieved his Ph.D. in Aeronautics and Astronautics from MIT in 2021 and worked on the modeling and control of air transportation networks. His work has recieved several awards from the FAA / Eurocontrol conference in air trasnportation, including the 2021 Kevin Corker award for the best paper in the conference.

Karthik’s current research focuses on developing algorithms that balance multiple objectives such as efficiency, robustness, fairness, and privacy in transportation systems. He is interested in applying these algorithms to design future mobility systems, both in the ground as well as in the air.


ASL Publications

  1. M. Tsao, K. Yang, K. Gopalakrishnan, and M. Pavone, “Private Location Sharing for Decentralized Routing Services,” in Proc. IEEE Int. Conf. on Intelligent Transportation Systems, Macau, China, 2022. (In Press)

    Abstract: Data-driven methodologies offer many exciting upsides, but they also introduce new challenges, particularly in the realm of user privacy. Specifically, the way data is collected can pose privacy risks to end users. In many routing services, a single entity (e.g., the routing service provider) collects and manages user trajectory data. When it comes to user privacy, these systems have a central point of failure since users have to trust that this entity will not sell or use their data to infer sensitive private information. With this as motivation, we study the problem of using location data for routing services in a privacy-preserving way. Rather than having users report their location to a central operator, we present a protocol in which users participate in a decentralized and privacy-preserving computation to estimate travel times for the roads in the network in a way that no individuals’ location is ever observed by any other party. The protocol uses the Laplace mechanism in conjunction with secure multi-party computation to ensure that it is cryptogrpahically secure and that its output is differentially private. The protocol is computationally efficient and does not require specialized hardware; all it needs is GPS, which is included in most mobile devices. A natural question is if privacy necessitates degradation in accuracy or system performance. We show that if a road has sufficiently high capacity, then the travel time estimated by our protocol is provably close to the ground truth travel time. We validate the protocol through numerical experiments which show that using the protocol as a routing service provides privacy guarantees with minimal overhead to user travel time.

    @inproceedings{Tsao2022a,
      author = {Tsao, M. and Yang, K. and Gopalakrishnan, K. and Pavone, M.},
      booktitle = {{Proc. IEEE Int. Conf. on Intelligent Transportation Systems}},
      title = {Private Location Sharing for Decentralized Routing Services},
      year = {2022},
      address = {Macau, China},
      month = oct,
      keywords = {press},
      url = {https://arxiv.org/pdf/2202.13305.pdf}
    }
    
  2. D. Jalota, K. Solovey, K. Gopalakrishnan, S. Zoepf, H. Balakrishnan, and M. Pavone, “When Efficiency meets Equity in Congestion Pricing and Revenue Refunding Schemes,” in ACM Conf. on Equity and Access in Algorithms, Mechanisms, and Optimization, Online, 2021.

    Abstract: Congestion pricing has long been hailed as a means to mitigate traffic congestion; however, its practical adoption has been limited due to the resulting social inequity issue, e.g., low-income users are priced out off certain roads. This issue has spurred interest in the design of equitable mechanisms that aim to refund the collected toll revenues as lump-sum transfers to users. Although revenue refunding has been extensively studied for over three decades, there has been no thorough characterization of how such schemes can be designed to simultaneously achieve system efficiency and equity objectives. In this work, we bridge this gap through the study of congestion pricing and revenue refunding (CPRR) schemes in non-atomic congestion games. We first develop CPRR schemes, which in comparison to the untolled case, simultaneously (i) increase system efficiency and (ii) decrease wealth inequality, while being (iii) user-favorable: irrespective of their initial wealth or values-of-time (which may differ across users) users would experience a lower travel cost after the implementation of the proposed scheme. We then characterize the set of optimal user-favorable CPRR schemes that simultaneously maximize system efficiency and minimize wealth inequality. These results assume a well-studied behavior model of users minimizing a linear function of their travel times and tolls, without considering refunds. We also study a more complex behavior model wherein users are influenced by and react to the amount of refund that they receive. Although, in general, the two models can result in different outcomes in terms of system efficiency and wealth inequality, we establish that those outcomes coincide when the aforementioned optimal CPRR scheme is implemented. Overall, our work demonstrates that through appropriate refunding policies we can achieve system efficiency while reducing wealth inequality.

    @inproceedings{JalotaEtAl2021,
      author = {Jalota, D. and Solovey, K. and Gopalakrishnan, K. and Zoepf, S. and Balakrishnan, H. and Pavone, M.},
      title = {When Efficiency meets Equity in Congestion Pricing and Revenue Refunding Schemes},
      booktitle = {{ACM Conf. on Equity and Access in Algorithms, Mechanisms, and Optimization}},
      year = {2021},
      note = {Submitted},
      address = {Online},
      month = oct,
      owner = {devanshjalota},
      timestamp = {2021-06-22},
      url = {https://dl.acm.org/doi/10.1145/3465416.3483296}
    }