MPPI is recovered as unit-step preconditioned gradient descent on a reduced free-energy objective over parametric sampling distributions, with descent guarantees when the preconditioned Hessian is bounded.
CoVO-MPC: Theoretical analysis of sampling- based MPC and optimal covariance design
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Model Predictive Path Integral Control as Preconditioned Gradient Descent
MPPI is recovered as unit-step preconditioned gradient descent on a reduced free-energy objective over parametric sampling distributions, with descent guarantees when the preconditioned Hessian is bounded.