Karthik Gopalakrishnan

I am a postdoctoral scholar in the Autonomous Systems Lab at Stanford University, advised by Prof. Marco Pavone. I am also affiliated with the Center for Automotive Research at Stanford.

I develop methodologies to design, analyze, and operate mobility systems. I am particularly interested in settings with multiple objectives, competition and strategic decision-making by agents, uncertainty and imperfect information, data-privacy considerations, equity cocnerns, and safety-critical requirements. Typically, this involves combining classical techniques from operations research and control theory, with more recent tools from machine learning, differential privacy, and cryptography.

I obtained my PhD in Aeronautics and Astronautics from MIT and was advised by Prof. Hamsa Balakrishnan at the DINaMo lab. My doctoral research focused on scheduling and planning problems in air transportation systems. Prior to that, I obtained my SM from MIT and B.Tech. from the Indian Institute of Technology Madras (where I received the HAL prize and the Institute Silver Medal for my academic performance).

My work has recieved several best paper awards [1, 2, 3, 4, 5, 6] including the Kevin Corker Award for the best paper in the ATM Seminar 2021 [7].

news

Apr 27, 2023	InforMARL, a scalable graph RL framework for multiagent navigation is accepted at ICML 2023! Check out the website
Jan 19, 2023	Our online learning algorithm for setting system-optimal road tolls under unknown preferences was accepted in AISTATS 2023.
Nov 15, 2022	InforMARL, a scalable graph RL framework for multiagent navigation was presented at the workshop on Strategic Multi agent Interactions at CoRL.
Oct 28, 2022	Check our our preprint on learning differentially private network routing policies.
Sep 30, 2022	Our work on privacy-preserving location sharing got published in ITSC

selected publications

AISTATS

Online Learning for Traffic Routing under Unknown Preferences

Jalota, Devansh, Gopalakrishnan, Karthik, Azizan, Navid, Johari, Ramesh, and Pavone, Marco

International Conference on Artificial Intelligence and Statistics (AISTATS) 2023

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In transportation networks, users typically choose routes in a decentralized and self-interested manner to minimize their individual travel costs, which, in practice, often results in inefficient overall outcomes for society. As a result, there has been a growing interest in designing road tolling schemes to cope with these efficiency losses and steer users toward a system-efficient traffic pattern. However, the efficacy of road tolling schemes often relies on having access to complete information on users’ trip attributes, such as their origin-destination (O-D) travel information and their values of time, which may not be available in practice. Motivated by this practical consideration, we propose an online learning approach to set tolls in a traffic network to drive heterogeneous users with different values of time toward a system-efficient traffic pattern. In particular, we develop a simple yet effective algorithm that adjusts tolls at each time period solely based on the observed aggregate flows on the roads of the network without relying on any additional trip attributes of users, thereby preserving user privacy. In the setting where the O-D pairs and values of time of users are drawn i.i.d. at each period, we show that our approach obtains an expected regret and road capacity violation of O(\sqrtT), where T is the number of periods over which tolls are updated. Our regret guarantee is relative to an offline oracle that has complete information on users’ trip attributes. We further establish a Ω(\sqrtT) lower bound on the regret of any algorithm, which establishes that our algorithm is optimal up to constants. Finally, we demonstrate the superior performance of our approach relative to several benchmarks on a real-world transportation network, thereby highlighting its practical applicability.
ICML

Scalable Multi-Agent Reinforcement Learning through Intelligent Information Aggregation

Nayak, Siddharth, Choi, Kenneth, Ding, Wenqi, Dolan, Sydney, Gopalakrishnan, Karthik, and Balakrishnan, Hamsa

International Conference on Machine Learning 2023

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We consider the problem of multi-agent navigation and collision avoidance when observations are limited to the local neighborhood of each agent. We propose InforMARL, a novel architecture for multi-agent reinforcement learning (MARL) which uses local information intelligently to compute paths for all the agents in a decentralized manner. Specifically, InforMARL aggregates information about the local neighborhood of agents for both the actor and the critic using a graph neural network and can be used in conjunction with any standard MARL algorithm. We show that (1) in training, InforMARL has better sample efficiency and performance than baseline approaches, despite using less information, and (2) in testing, it scales well to environments with arbitrary numbers of agents and obstacles.
ITSC

Private and Decentralized Location Sharing for Congestion-Aware Routing

Tsao, Matthew, Yang, Kaidi, Gopalakrishnan, Karthik, and Pavone, Marco

IEEE International Transportation Systems Conference 2022

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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. Unfortunately, in practice many advertising companies offer to buy such data for the sake of targeted advertisements. 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. 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.
AnnRev

Control and optimization of air traffic networks

Gopalakrishnan, Karthik, and Balakrishnan, Hamsa

Annual Review of Control, Robotics, and Autonomous Systems 2021

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The air transportation system connects the world through the transport of goods and people. However, operational inefficiencies such as flight delays and cancellations are prevalent, resulting in economic and environmental impacts. In the first part of this article, we review recent advances in using network analysis techniques to model the interdependencies observed in the air transportation system and to understand the role of airports in connecting populations, serving air traffic demand, and spreading delays. In the second part, we present some of our recent work on using operational data to build dynamical system models of air traffic delay networks. We show that Markov jump linear system models capture many of the salient characteristics of these networked systems. We illustrate how these models can be validated and then used to analyze system properties such as stability and to design optimal control strategies that limit the propagation of disruptions in air traffic networks.
MobiSys

Throughput-fairness tradeoffs in mobility platforms

Balasingam, Arjun, Gopalakrishnan, Karthik, Mittal, Radhika, Arun, Venkat, Saeed, Ahmed, Alizadeh, Mohammad, Balakrishnan, Hamsa, and Balakrishnan, Hari

Proceedings of the 19th Annual International Conference on Mobile Systems, Applications, and Services 2021

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This paper studies the problem of allocating tasks from different customers to vehicles in mobility platforms, which are used for applications like food and package delivery, ridesharing, and mobile sensing. A mobility platform should allocate tasks to vehicles and schedule them in order to optimize both throughput and fairness across customers. However, existing approaches to scheduling tasks in mobility platforms ignore fairness. We introduce Mobius, a system that uses guided optimization to achieve both high throughput and fairness across customers. Mobius supports spatiotemporally diverse and dynamic customer demands. It provides a principled method to navigate inherent tradeoffs between fairness and throughput caused by shared mobility. Our evaluation demonstrates these properties, along with the versatility and scalability of Mobius, using traces gathered from ridesharing and aerial sensing applications. Our ridesharing case study shows that Mobius can schedule more than 16,000 tasks across 40 customers and 200 vehicles in an online manner.