# Convergence of SARSA with linear function approximation: The random horizon case

arXiv: https://arxiv.org/abs/2306.04548 · HTML: https://mlsanity.com/paper/2306.04548/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 7 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [Learning Stochastic Shortest Path with Linear Function Approximation](https://mlsanity.com/paper/2110.12727/) (2021)
- [Regret Bounds for Stochastic Shortest Path Problems with Linear Function Approximation](https://mlsanity.com/paper/2105.01593/) (2021)
- [On the Convergence of SARSA with Linear Function Approximation](https://mlsanity.com/paper/2202.06828/) (2022)
- [Improved No-Regret Algorithms for Stochastic Shortest Path with Linear MDP](https://mlsanity.com/paper/2112.09859/) (2021)

## Abstract (arXiv)

The reinforcement learning algorithm SARSA combined with linear function approximation has been shown to converge for infinite horizon discounted Markov decision problems (MDPs). In this paper, we investigate the convergence of the algorithm for random horizon MDPs, which has not previously been shown. We show, similar to earlier results for infinite horizon discounted MDPs, that if the behaviour policy is varepsilon-soft and Lipschitz continuous with respect to the weight vector of the linear function approximation, with small enough Lipschitz constant, then the algorithm will converge with probability one when considering a random horizon MDP.