Related papers: Semiconcavity and Sensitivity Analysis in Mean-Fie…
Since the early nineties, it has been observed that the Schroedinger bridge problem can be formulated as a stochastic control problem with atypical boundary constraints. This in turn has a fluid dynamic counterpart where the flow of…
Impractical assumptions, an inherently myopic nature, and the crucial role of the initial design, all together contribute to making theoretical convergence proofs of little value in real-life Bayesian Optimization applications. In this…
We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the…
This paper studies a mean field game inspired by crowd motion in which agents evolve in a compact domain and want to reach its boundary minimizing the sum of their travel time and a given boundary cost. Interactions between agents occur…
Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by recasting deep learning as an optimal control problem on…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. This paper studies the stability properties of the mean-field approximation when the target…
We consider extended mean-field control problems with multi-dimensional singular controls. A key challenge when analysing singular controls are jump costs. When controls are one-dimensional, jump costs are most naturally computed by linear…
This paper aims to improve the reliability of optimal control using models constructed by machine learning methods. Optimal control problems based on such models are generally non-convex and difficult to solve online. In this paper, we…
In this paper, we provide a convergence rate for particle approximations of a class of second-order PDEs on Wasserstein space. We show that, up to some error term, the infinite-dimensional inf(sup)-convolution of the finite-dimensional…
In the Maslov idempotent probability calculus, expectations of random variables are defined so as to be linear with respect to max-plus addition and scalar multiplication. This paper considers control problems in which the objective is to…
We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable agents whose behaviors can be collectively modeled as a…
We analyze optimal transport problems with additional entropic cost evaluated along curves in the Wasserstein space which join two probability measures $m_0,m_1$. The effect of the additional entropy functional results into an elliptic…
This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…
We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…
In this paper we establish an attainability result for the minimum time function of a control problem in the space of probability measures endowed with Wasserstein distance. The dynamics is provided by a suitable controlled continuity…
Inverse problems in physical or biological sciences often involve recovering an unknown parameter that is random. The sought-after quantity is a probability distribution of the unknown parameter, that produces data that aligns with…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state…