# Sufficient Exploration for Convex Q-learning

arXiv: https://arxiv.org/abs/2210.09409 · HTML: https://mlsanity.com/paper/2210.09409/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 27 references that are in the map.
- First posted on arXiv 17 Oct 2022.

## Builds on (most cited first, 2 of 2)

- [Logistic Q-Learning](https://mlsanity.com/paper/2010.11151/) (2020)
- [A Unified Switching System Perspective and O.D.E. Analysis of Q-Learning Algorithms](https://mlsanity.com/paper/1912.02270/) (2019)

## Built on by (most cited first, 1 of 1)

- [Regularized Q-learning through Robust Averaging](https://mlsanity.com/paper/2405.02201/) (2024)

## Abstract (arXiv)

In recent years there has been a collective research effort to find new formulations of reinforcement learning that are simultaneously more efficient and more amenable to analysis. This paper concerns one approach that builds on the linear programming (LP) formulation of optimal control of Manne. A primal version is called logistic Q-learning, and a dual variant is convex Q-learning. This paper focuses on the latter, while building bridges with the former. The main contributions follow: (i) The dual of convex Q-learning is not precisely Manne's LP or a version of logistic Q-learning, but has similar structure that reveals the need for regularization to avoid over-fitting. (ii) A sufficient condition is obtained for a bounded solution to the Q-learning LP. (iii) Simulation studies reveal numerical challenges when addressing sampled-data systems based on a continuous time model. The challenge is addressed using state-dependent sampling. The theory is illustrated with applications to examples from OpenAI gym. It is shown that convex Q-learning is successful in cases where standard Q-learning diverges, such as the LQR problem.