# Path Integral Control and State Dependent Feedback

arXiv: https://arxiv.org/abs/1406.4026 · HTML: https://mlsanity.com/paper/1406.4026/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2014.

## Built on by (most cited first, 12 of 12)

- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Paths](https://mlsanity.com/paper/2207.02149/) (2022)
- [Inference via Interpolation: Contrastive Representations Provably Enable Planning and Inference](https://mlsanity.com/paper/2403.04082/) (2024)
- [Reinforcement learning of rare diffusive dynamics](https://mlsanity.com/paper/2105.04321/) (2021)
- [Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions](https://mlsanity.com/paper/2206.03369/) (2022)
- [Deriving time-averaged active inference from control principles](https://mlsanity.com/paper/2208.10601/) (2022)
- [Myopically Verifiable Probabilistic Certificates for Safe Control and Learning](https://mlsanity.com/paper/2404.16883/) (2024)
- [Interacting Particle Systems for Fast Linear Quadratic RL](https://mlsanity.com/paper/2406.11057/) (2024)
- [Control, Transport and Sampling: Towards Better Loss Design](https://mlsanity.com/paper/2405.13731/) (2024)
- [Path Integral Value Matching for Linear Quadratic Stochastic Optimal Control](https://mlsanity.com/paper/2608.10777/) (2026)

## Abstract (arXiv)

In this paper we address the problem to compute state dependent feedback controls for path integral control problems. To this end we generalize the path integral control formula and utilize this to construct parameterized state dependent feedback controllers. In addition, we show a novel relation between control and importance sampling: better control, in terms of control cost, yields more efficient importance sampling, in terms of effective sample size. The optimal control provides a zero-variance estimate.