Control and estimation of multi-agent systems via structured multi-marginal optimal transport
Event details
| Date | 11.04.2025 |
| Hour | 11:00 › 12:00 |
| Speaker | Professor Johan Karlsson KTH Royal Institute of Technology, Sweden |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract
The optimal mass transport problem is a classical problem in mathematics, and dates back to 1781 and work by G. Monge where he formulated an optimization problem for minimizing the cost of transporting soil for construction of forts and roads. Historically the optimal mass transport problem has been widely used in economics in, e.g., planning and logistics. In the last two decades there has been a rapid development of the area, leading to a mature framework for optimal mass transport with computationally efficient algorithms that can be used to address many problems in applied mathematics.
In this talk, I will give an overview of the multi-marginal optimal mass transport framework and show how it can be applied to address and solve a range of problems in control and estimation of multi-agent systems. The optimal transport framework allows for replacing the standard state space formalist, where a state evolve over time, to a setting where instead densities or multi-agent systems evolve over time. In this setting we can formulate and solve a large set of problems, e.g., with given dynamics of the underlying agents, multiple classes of agents, nonlocal interactions, and include constraints between different time points such as origin destination constraints. We will also consider computational methods, and motivated by Sinkhorn's method for the standard optimal transport problems, it can be shown that dual coordinate ascent is a computationally efficient approach for this class of problems.
Short bio:
Johan Karlsson is professor in optimization and systems theory at KTH Royal Institute of Technology. He received an MSc and a PhD degree from KTH in 2003 and 2008, respectively. From 2009 to 2011, he was with Sirius International, and from 2011 to 2013 he was a postdoc at University of Florida. From 2013 he joined the Department of Mathematics, KTH, as a faculty. He is also affiliated with Digital Futures. His current research interests include optimal transport, methods for large scale optimization, and inverse problems, for applications in control theory, network problems, and remote sensing.
The optimal mass transport problem is a classical problem in mathematics, and dates back to 1781 and work by G. Monge where he formulated an optimization problem for minimizing the cost of transporting soil for construction of forts and roads. Historically the optimal mass transport problem has been widely used in economics in, e.g., planning and logistics. In the last two decades there has been a rapid development of the area, leading to a mature framework for optimal mass transport with computationally efficient algorithms that can be used to address many problems in applied mathematics.
In this talk, I will give an overview of the multi-marginal optimal mass transport framework and show how it can be applied to address and solve a range of problems in control and estimation of multi-agent systems. The optimal transport framework allows for replacing the standard state space formalist, where a state evolve over time, to a setting where instead densities or multi-agent systems evolve over time. In this setting we can formulate and solve a large set of problems, e.g., with given dynamics of the underlying agents, multiple classes of agents, nonlocal interactions, and include constraints between different time points such as origin destination constraints. We will also consider computational methods, and motivated by Sinkhorn's method for the standard optimal transport problems, it can be shown that dual coordinate ascent is a computationally efficient approach for this class of problems.
Short bio:
Johan Karlsson is professor in optimization and systems theory at KTH Royal Institute of Technology. He received an MSc and a PhD degree from KTH in 2003 and 2008, respectively. From 2009 to 2011, he was with Sirius International, and from 2011 to 2013 he was a postdoc at University of Florida. From 2013 he joined the Department of Mathematics, KTH, as a faculty. He is also affiliated with Digital Futures. His current research interests include optimal transport, methods for large scale optimization, and inverse problems, for applications in control theory, network problems, and remote sensing.
Practical information
- General public
- Free
Organizer
- Professor Maryam Kamgarpour
Contact
- chantal.demont@epfl.ch barbara.schenkel@epfl.ch