# Long-Term Values in Markov Decision Processes, (Co)Algebraically

@inproceedings{Feys2018LongTermVI, title={Long-Term Values in Markov Decision Processes, (Co)Algebraically}, author={Frank M. V. Feys and Helle Hvid Hansen and Lawrence S. Moss}, booktitle={CMCS}, year={2018} }

This paper studies Markov decision processes (MDPs) from the categorical perspective of coalgebra and algebra. Probabilistic systems, similar to MDPs but without rewards, have been extensively studied, also coalgebraically, from the perspective of program semantics. In this paper, we focus on the role of MDPs as models in optimal planning, where the reward structure is central. The main contributions of this paper are (i) to give a coinductive explanation of policy improvement using a new proof…

## 7 Citations

### Co)Algebraic Techniques for Markov Decision Processes

- Computer Science
- 2019

This work is inspired by Bellman’s principle of optimality, which states that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.

### Categorical semantics of compositional reinforcement learning

- Computer ScienceArXiv
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This work develops a framework for a compositional theory of RL using a categorical point of view and investigates sufficient conditions under which learning-by-parts results in the same optimal policy as learning on the whole.

### Value iteration is optic composition

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- 2022

It is shown that value improvement, one of the main steps of dynamic programming, can be naturally seen as composition in a category of optics, and intuitively, the optimal value function is the limit of a chain of optic compositions.

### Introspection Learning.

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- 2019

This paper presents Introspection Learning, an algorithm that allows for the asking of these types of questions of neural network policies, and demonstrates the usefulness of this algorithm both in the context of speeding up training and improving robustness with respect to safety constraints.

### Introspection Learning

- Computer ScienceArXiv
- 2019

This paper presents Introspection Learning, an algorithm that allows for the asking of these types of questions of neural network policies, and demonstrates the usefulness of this algorithm both in the context of speeding up training and improving robustness with respect to safety constraints.

### Representation and Invariance in Reinforcement Learning

- Computer ScienceArXiv
- 2021

This paper lays foundations for studying relative-intelligence-preserving mappability between RL frameworks, and investigates whether or not this is possible depends on the RL frameworks in question and on how intelligence is measured.

### CertRL: formalizing convergence proofs for value and policy iteration in Coq

- Computer ScienceCPP
- 2021

A Coq formalization of two canonical reinforcement learning algorithms: value and policy iteration for finite state Markov decision processes and a contraction property of Bellman optimality operator to establish that a sequence converges in the infinite horizon limit.

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