大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Finite-Horizon Optimal Control for Steering Probability Distributions with Wasserstein Distance

星野健太（京都大学）

1. ホーム
2. セミナー・集中講義
3. セミナー
4. Finite-Horizon Optimal Control for Steering Probability Distributions with Wasserstein Distance

大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第132回

Finite-Horizon Optimal Control for Steering Probability Distributions with Wasserstein Distance

星野健太（京都大学）

The control engineering community has recently devoted much attention to stochastic control problems concerning probability distributions. The goal of the control problems is to steer the marginal probability distributions of a system state to target distributions. Consequently, the problem is formulated as an optimal control problem to minimize the functional to measure the closeness of controlled marginal distributions to target ones. This talk will present the optimal control problem for controlled stochastic systems to steer their marginal distributions using the Wasserstein distance, which is a metric of probability measures, as the cost functional. The talk will focus on an optimality condition and show it as a type of Pontryagin's maximum principle, which is given by forward-backward stochastic differential equations. Additionally, the control problem of probability distributions has a connection to generative models in deep learning. The talk will also introduce potential applications of the optimal control problem to them.