Noticias en español
Numerical solution of optimal control problems under uncertainty.
Abstract: The topic of this talk is a class of optimal control problems subject to uncertainty. We highlight some of the difficulties in the infinite-dimensional setting, which is of interest in physics- based models where a control belonging to a Banach space acts on a system described by a partial differential equation (PDE) with random inputs or parameters. We compare numerical approaches based on sample average approximation (SAA) and stochastic approximation (SA). The latter approach can be shown to perform competitively for applications in PDE-constrained optimization and numerical...
Read MoreA stochastic differential Colonel Blotto game in a Stackelberg contract theory setting.
Abstract: The Colonel Blotto game is a resource allocation game where players decide where to focus their forces between different battlefields. We extend the standard Blotto game to a dynamic stochastic setting, in a time-continuous, two-player, zero-sum game. Using the dynamic programming principle, we explicitly characterize some Nash equilibrium strategies as well as the value of the game through a Hamilton-Jacobi-Bellman equation admitting a smooth solution. We formulate the game generally enough to allow for various rewards, as well as various drivers of randomness. We also present an...
Read MoreMean field games with heterogeneity.
Abstract: Mean field games (MFGs) are an extension of interacting particle systems, where the particles are interpreted as rational agents, offering applications in economics, social sciences, or computer science. They can be seen as the limits of large-population stochastic differential games with symmetric agents. In this work, we propose a method to incorporate heterogeneity into MFGs, thus relaxing the symmetry assumptions. We will present the concept of heterogeneous Markovian equilibria and provide a proof of their existence under standard conditions. Our definition of Nash Mean Field...
Read MoreRegret analysis for stochastic optimization problems under parametric models.
Abstract: In this talk, we analyze the growth rate of the regret -or optimality gap- when learning the optimal actions in stochastic optimization problems, formulated in a parametric setting. More precisely, we assume access to samples from random variables whose unknown distribution belongs to a parametric family. For both smooth and non-smooth problems, we describe the asymptotic behavior of the expected optimality gap, and use it to design appropriate estimators. Different examples will be given where explicit calculations are possible.
Read MoreCompletely mixed linear games and irreducibility concepts for Z-transformations over self-dual cones.
Abstract: In the setting of a self-dual cone in a finite-dimensional real inner product space (in particular, over a symmetric cone in an Euclidean Jordan algebra), we consider zero-sum linear games. Motivated by dynamical systems, we concentrate on $Z$-transformations (which are generalizations of $Z$-matrices). It is known that a $Z$-transformation with positive (game) value is completely mixed (thus yielding uniqueness of optimal strategies). The present talk deals with the case of value zero. Motivated by the matrix-game result that a $Z$-matrix with value zero is completely...
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