Second-Order Smooth Planning with Optimal-Transport Bellman Smoothing
Quick summary
arXiv:2609.06484v1 Announce Type: cross Abstract: Planning with a generative model aims to estimate the value of a state using as few simulator calls as possible. SmoothCruiser achieves problem-independent complexity $\widetilde O(\varepsilon^{-4})$ by exploiting the smoothness of the entropy-regularized Bellman backup, but its estimator is only first-order. We show that the sample-complexity exponent of SmoothCruiser-type planners is governed by the order $\beta$ of the local Taylor remainder, giving oracle complexity $\widetilde O(\varepsilon^{-(2+2/(\beta-1))})$: the first-order case $\beta
Key takeaways
- arXiv:2609.06484v1 Announce Type: cross Abstract: Planning with a generative model aims to estimate the value of a state using as few simulator calls as possible.
- SmoothCruiser achieves problem-independent complexity $\widetilde O(\varepsilon^{-4})$ by exploiting the smoothness of the entropy-regularized Bellman backup, but its estimator is only first-order.
- We show that the sample-complexity exponent of SmoothCruiser-type planners is governed by the order $\beta$ of the local Taylor remainder, giving oracle complexity $\widetilde O(\varepsilon^{-(2+2/(\beta-1))})$: the first-order case $\beta
Why it matters
“Second-Order Smooth Planning with Optimal-Transport Bellman Smoothing” should be evaluated beyond branding and benchmark scores. Its practical importance will emerge in task accuracy, latency, unit cost, safety and integration with real workflows.
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