Control, Transport and Sampling: Towards Better Loss Design
- URL: http://arxiv.org/abs/2405.13731v1
- Date: Wed, 22 May 2024 15:24:48 GMT
- Title: Control, Transport and Sampling: Towards Better Loss Design
- Authors: Qijia Jiang, David Nabergoj,
- Abstract summary: We propose objective functions that can be used to transport $nu$ to $mu$, via optimally controlled dynamics.
We highlight the importance of the pathwise perspective and the role various optimality conditions on the path measure can play for the design of valid training losses.
- Score: 10.732151772173083
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Leveraging connections between diffusion-based sampling, optimal transport, and optimal stochastic control through their shared links to the Schr\"odinger bridge problem, we propose novel objective functions that can be used to transport $\nu$ to $\mu$, consequently sample from the target $\mu$, via optimally controlled dynamics. We highlight the importance of the pathwise perspective and the role various optimality conditions on the path measure can play for the design of valid training losses, the careful choice of which offer numerical advantages in practical implementation.
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