Research shows necessary conditions for optimal Markov policies in distribution steering, suggesting a new heuristic approach.
We study a class of distribution-steering problems from a variational point of view. Under some differentiability assumptions, we derive necessary conditions for optimal Markov policies in the spirit of the Lagrange multiplier approach. We also provide a heuristic gradient-based method derived from the variational principle.
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Corella et al. (2025) studied this question.
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