Research Projects || Consultancy Projects || Past Projects
Stochastic control and information Theory
I have a general intellectual interest in all aspects of decisions situations involving multiple decision makers. These problems include stochastic optimal control problems (where the decision makers are controllers), game theory and team theory (decision makers are players), economics (human decision makers!) and information theory (decision makers are encoders, decoders or relays). A key issue that arises in these problems is that of the information structure of the problem. The information structure specifies "who knows what" in at any point of time in a system with multiple decision makers. This issue is largely moot when we have deterministic systems but assumes immense relevance in stochastic systems. All problems here are stochastic control problems with non-classical information structures.
Read more/less
- Finite
blocklength information theory. A novel
approach for deriving unified state-of-the-art
finite-blocklength converse results, or lower bounds on
problems in point-to-point and network information
theory. The approach made an unconventional use of
linear programming relaxations.
Read more/less
Representative publications:
- Sharu Theresa Jose and Ankur A. Kulkarni, "Linear Programming based Converses for Finite Blocklength Lossy Joint Source-Channel Coding", IEEE Transactions on Information Theory, Vol 63, No 11, pp 7066 -- 7094, (2017)
- Sharu Theresa Jose and Ankur A. Kulkarni, "Improved Finite Blocklength Converses for Slepian-Wolf Coding via Linear Programming", under review with the IEEE Transactions on Information Theory, 2018 [arXiv].
- Sharu Theresa Jose and Ankur A. Kulkarni, "A Linear Programming Based Channel Coding Strong Converse for the BSC and BEC", Proceedings of the National Conference on Communications 2017 (Best Paper Award).
- Sharu Theresa Jose and Ankur A. Kulkarni, "New Finite Blocklength Converses for Asymmetric Multiple Access Channels via Linear Programming", to appear in the Proceedings of SPCOM 2018 (Runner-up Best Paper Award).
This work has its origins in stochastic control and can be viewed a generalization of convex-analytic approaches for Markov decision processes. The following papers lay the groundwork for the above results.- Ankur A. Kulkarni and Todd P. Coleman, "An Optimizer’s Approach to Stochastic Control Problems with Nonclassical Information Structures", IEEE Transactions on Automatic Control, Vol 60, No 4, pp 937--949 (2015)
- Sharu Theresa Jose and Ankur A. Kulkarni, "A Linear Programming Relaxation for Stochastic Control Problems with Non-Classical Information Patterns" Proceedings of the IEEE Conference on Decision and Control, 2015.
The following video of a talk I gave at BITS 2018 covers the above story
Funded by: Industrial Research and Consultancy Centre, IIT Bombay.
- Minimax theorems in information theory. We consider finite blocklength communication or state estimation in the presence of a jammer and show approximate minimax theorems in this context.
- Sharu Thereasa Jose and Ankur A. Kulkarni, "On a Game Between a Delay-constrained Communication System and a Finite State Jammer", accepted by IEEE Conference on Decision and Control, 2018.
- Sharu Theresa Jose and Ankur A. Kulkarni, "Shannon meets von Neumann: A Minimax Theorem for Channel Coding in the Presence of a Jammer", under review with the IEEE Transactions on Information Theory, 2018 [arXiv].
- Anuj
S. Vora and Ankur A. Kulkarni, "A
Minimax Theorem for Finite Blocklength Joint
Source-Channel Coding over an AVC", accepted by the
National Conference on Communications, 2019.
Read more/less
Representative publications:
- LQ
problems with near-Gaussian noise.
Initiated a new theme in stochastic control: assessing
sensitivity of classical results in LQG control to core
assumptions, namely the linearity of dynamics, quadratic
cost and Gaussian noise. I showed the surprising but
reassuring result, that the optimal cost of an LQ
problem with static information structure is weakly
continuous with respect to the distribution of the
noise, if one allowed the noise to approach the Gaussian
limit in the sense of a recent central limit theorem of
Eldan and Klartag. I then considered the case of mean
square estimation and showed that while the above
continuity holds for the case of local estimation, the
claim is not automatic for networked estimation, due to
the nonclassicality of the information structure of this
problem.
Read more/less
Representative publications:
- Ankur A. Kulkarni, "Local and Networked Mean Square Estimation with High Dimensional Log-concave Noise", IEEE Transactions on Information Theory, Vol 64, Issue 4, pp 1-15, 2018.
- Ankur A. Kulkarni, "Near-Optimality of Linear Strategies for Static Teams with `Big' Non-Gaussian Noise", accepted by the IEEE Transactions on Automatic Control, 2018.
Funded by: Science and Engineering Research Board, Government of India.
Games on Networks
Games on networks involve decision makers that are situated on nodes of a network. This leads to fascincating connections between properties of the graph and the outcomes of games. I have worked on games of substitutes on networks, including public goods games but am also interested in other network games.
Read more/less
Representative publications:
- Parthe Pandit and Ankur A. Kulkarni, "Refinement of the Equilibrium of Public Goods Games over Networks: Efficiency and Effort of Specialized Equilibria", to appear in the The Journal of Mathematical Economics
- Parthe Pandit and Ankur A. Kulkarni, "A Linear Complementarity Based Characterization of the weighted independence number and the independent domination number in graphs", to appear in Discrete Applied Mathematics, 2018.
- Karan N. Chadha and Ankur A. Kulkarni, "On Independent Cliques and Linear Complementarity Problems", under review with Mathematics of Operations Research, 2018.
SMART Planning and Operations of Grids with Renewables and Storage
Please
see the poster and the video below for details. I am in
charge of the SMART Signalling Framework and also involved
in the SMART Storage Manager and SMART Planning Tool. If
these interest you, please get in touch with me. Main
project website is here.
Representative publications:
- Ankur A. Kulkarni and Anupama Kowli, "Addressing the Free-rider Problem in Voluntary Demand Response Programs", under review for PowerTech 2019.
- Vivek Deulkar, Jayakrishnan Nair and Ankur A. Kulkarni, "Sizing Storage for Reliable Renewable Integration", under review for PowerTech 2019.
Smart Cities, Smart
On-Demand Transportation and the Sharing Economy
I
am interested in a variety of questions involving sizing and
scaling of smart cities. We are approaching this by
developing agent-based models and simulations. We have
presently built a simulator for a fleet of taxis in a Smart
City. It can be used to size fleets and assess impacts of
speeds, congestion, city etc on service reliability. A
project is under review for extending this to other Smart
City infrastructures. Please contact me for more.
Representative
publications:
- Mansi Sood, Sharayu Moharir and Ankur A. Kulkarni, "Pricing and Commission in Two-Sided Markets with Free Upgrades", to appear in the Lecture Notes in Computer Science, 2018.
- Mansi Sood, Ankur A. Kulkarni and Sharayu Moharir, "Platform Competition for Throughput in Two-sided Freelance Markets", to appear in the Proceedings of SPCOM 2018.
- Mansi Sood, Sharayu Moharir and Ankur A. Kulkarni "Pricing in Two-Sided Markets in the Presence of Free Upgrades", accepted by COMSNETS 2018.
Consultancy Projects
Regulation of High Frequency Trading. A Quantitative Framework using Agent-based Modeling.
I have been a consultant to the Technical Advisory Committee of the Securities and Exchange Board of India on devising regulatory strategies for high frequency trading. As a part of this work I designed a quantitative framework based on agent-based modeling and simulation for analyzing and devising scheduling rules (randomization, speed bumps, resting time etc) and information flows (tick-by-tick data feed, colocation access) to ensure a level playing field for all market participants and to control price volatility in the Indian securities market, in the face of high frequency algorithmic trading. More details can be shared on request.