Research

Planning with Temporal Logic Specifications

Autonomous agents often operate in environments where the state is partially observed. In addition to maximizing their cumulative reward, agents must execute complex tasks with rich temporal and logical structures. These tasks can be expressed using temporal logic languages like finite linear temporal logic (LTLf ). We provide a structured framework for designing agent policies that maximize the reward while ensuring that the probability of satisfying the temporal logic specification is sufficiently high.

Publications:

• K. Kalagarla, D. Kartik, D. Shen, R. Jain, A. Nayyar and P. Nuzzo, "Optimal Control of Partially Observable Markov Decision Processes with Finite Linear Temporal Logic Constraints", Uncertainty in Artificial Intelligence, August 2022. Arxiv Preprint

Multi-Agent Coordination and Communication

In a multi-agent system, agents may know their local state, but they may not know the other agents' local states. Communicating their local states with each other can reduce uncertainty and help them coordinate better. However, communication may be expensive. This leads to a joint communication and control strategy design problem. We showed that this problem can be formulated as a POMDP (which can be solved using standard solvers). We are currently working on designing strategies that are robust to adversaries that may eavesdrop or disrupt the communication.

Publications:

• D. Kartik, S. Sudhakara, R. Jain and A. Nayyar, "Optimal Communication and Control Strategies for a Multi-Agent System in the Presence of an Adversary", Control and Decision Conference (CDC), December 2022. (Accepted)

• S. Sudhakara, D. Kartik, R. Jain and A. Nayyar, "Optimal communication and control strategies in a multi-agent MDP problem", IEEE Transactions on Automatic Control, April 2021. (Submitted) Arxiv Preprint

Stochastic Games

Cyber-physical systems are typically subject to adversarial attacks. Thus we need to design systems that can adapt to such attacks and ensure a certain degree of robustness. Such problems can be modeled as stochastic zero-sum games. We are particularly interested in solving games in which the attacker and the defender use different information to make their moves. Such games of asymmetric information are notoriously hard problems. For several kinds of information structures, we provide methodologies for finding values and min-max strategies.

Publications:

• D. Kartik, A. Nayyar and U. Mitra, "Stochastic Zero-sum Games between Teams: Behavioral Strategies", IEEE Transactions on Automatic Control, December 2021. (Submitted)

• D. Kartik, A. Nayyar and U. Mitra, "Common Information Belief based Dynamic Programs for Stochastic Zero-sum Games with Competing Teams", American Control Conference (ACC), June 2022 . Arxiv Preprint

• D. Kartik and A. Nayyar, "Upper and Lower Values in Zero-sum Stochastic Games with Asymmetric Information", Dynamic Games and Applications, October 2019. Full version

• D. Kartik and A. Nayyar, "Zero-sum Stochastic Games with Asymmetric Information", 58th Conference on Decision and Control (CDC), December 2019

• D. Kartik and A. Nayyar, "Equivalent Static and Dynamic Games". 50th Annual Asilomar Conference on Signals, Systems and Computers (Asilomar), November 2016

Active Hypothesis Testing

We frequently encounter scenarios wherein we are interested in deducing whether one of several hypotheses is true. We may have access to multiple sources of data and we would like to gather data from the most informative sources for optimal performance (measured with respect to probability of arriving at incorrect conclusions). Such problems are referred to as active hypothesis testing problems.

Classical approaches for active hypothesis testing use randomized strategies. Although these randomized strategies are asymptotically optimal, their non-asymptotic performance is not great. We observed that there are simple deterministic strategies that are also asymptotically optimal and have superior performance in the non-asymptotic regime. Our main goal is to formalize the approach for designing deterministic strategies and characterize associated performance gains.

Publications:

• D. Kartik, and U. Mitra, "Active Hypothesis Testing and Anomaly Detection", Transactions on Signal Processing, September 2021. (Accepted)

• D. Kartik, A. Nayyar and U. Mitra, "Testing for Anomalies: Active Strategies and Non-asymptotic Analysis", International Symposium on Information Theory (ISIT), July 2020. Full version

• D. Kartik, A. Nayyar and U. Mitra, "Fixed-horizon Active Hypothesis Testing", IEEE Transactions on Automatic Control, November 2019. Full version

• D. Kartik, A. Nayyar and U. Mitra, "Active Hypothesis Testing: Beyond Chernoff-Stein", International Symposium on Information Theory (ISIT), July 2019. Full version

• D. Kartik, A. Nayyar and U.Mitra, "Sequential Experiment Design for Hypothesis Verification", 52nd Annual Asilomar Conference on Signals, Systems and Computers (Asilomar), October 2018. Full version

• D. Kartik, E. Sabir, U. Mitra and P. Natarajan, "Policy Design for Active Sequential Hypothesis Testing Using Deep Learning", 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton), October 2018. Full version

• D. Kartik and U. Mitra, "Non-parametric Active Target Localization: Exploiting Unimodality and Separability", 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), October 2017.