# Transfer-Entropy-Regularized Markov Decision Processes

arXiv: https://arxiv.org/abs/1708.09096 · HTML: https://mlsanity.com/paper/1708.09096/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2017.

## Built on by (most cited first, 4 of 4)

- [Computing Complexity-aware Plans Using Kolmogorov Complexity](https://mlsanity.com/paper/2109.10303/) (2021)
- [Planning Not to Talk: Multiagent Systems that are Robust to Communication Loss](https://mlsanity.com/paper/2201.06619/) (2022)
- [Entropy-Regularized Partially Observed Markov Decision Processes](https://mlsanity.com/paper/2112.12255/) (2021)
- [Simultaneous Perception-Action Design via Invariant Finite Belief Sets](https://mlsanity.com/paper/2109.05073/) (2021)

## Abstract (arXiv)

We consider the framework of transfer-entropy-regularized Markov Decision Process (TERMDP) in which the weighted sum of the classical state-dependent cost and the transfer entropy from the state random process to the control random process is minimized. Although TERMDPs are generally formulated as nonconvex optimization problems, we derive an analytical necessary optimality condition expressed as a finite set of nonlinear equations, based on which an iterative forward-backward computational procedure similar to the Arimoto-Blahut algorithm is proposed. It is shown that every limit point of the sequence generated by the proposed algorithm is a stationary point of the TERMDP. Applications of TERMDPs are discussed in the context of networked control systems theory and non-equilibrium thermodynamics. The proposed algorithm is applied to an information-constrained maze navigation problem, whereby we study how the price of information qualitatively alters the optimal decision polices.