2024年2月28日（水） WeSCoS Colloquium＃07「Chance constrained probabilistic measure optimization: towards probabilistic decision-making」（瀋 迅 大阪大学 大学院工学研究科 助教）を開催します。※要事前申し込み
＃07：Chance constrained probabilistic measure optimization: towards probabilistic decision-making
報告者：瀋 迅 (大阪大学 大学院工学研究科 助教）
Choosing decision variables deterministically (deterministic decision-making) can be regarded as a particular case of choosing decision variables probabilistically (probabilistic decision-making). It is necessary to investigate whether probabilistic decision-making can further improve the expected decision-making performance than deterministic decision-making when chance constraints exist. This talk introduces the problem formulation of Chance Constrained Probability Measure Optimization (CCPMO) to realize optimal probabilistic decision-making under chance constraints. We prove the existence of the optimal solution to CCPMO. It is further shown that there is an optimal solution of CCPMO with the probability measure concentrated on two decisions, leading to an equivalently reduced problem of CCPMO. The reduced problem still has chance constraints due to uncertain disturbance. We then propose the sample-based smooth approximation method to solve the reduced problem. Samples of model uncertainties are used to establish an approximate problem of the reduced problem. Algorithms for general nonlinear programming problems can solve the approximate problem. The solution of the approximate problem is an approximate solution of CCPMO. A numerical example of controlling a quadrotor in turbulent conditions has been conducted to validate the proposed probabilistic decision-making under chance constraints. Furthermore, we also discuss the extension of CCPMO to reduce the stochastic policy of safe reinforcement learning with chance constrained into a flipped policy, which reduces the complexity of the stochastic policy dramatically.