Soft-constrained Schrodinger Bridge: a Stochastic Control Approach

arXiv:2403.01717v1 Announce Type: cross
Abstract: Schr\"{o}dinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process with a pre-specified terminal distribution $\mu_T$. We propose to generalize this stochastic control problem by allowing the terminal distribution to differ from $\mu_T$ but penalizing the Kullback-Leibler divergence between the two distributions. We call this new control problem soft-constrained Schr\"{o}dinger bridge (SSB). The main contribution of this work is a theoretical derivation of …

abstract arxiv bridge continuous control cs.lg diffusion distribution math.oc process stat.co stat.ml stochastic terminal type