# Finite-Time Error Analysis of Soft Q-Learning: Switching System Approach

arXiv: https://arxiv.org/abs/2403.06366 · HTML: https://mlsanity.com/paper/2403.06366/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 11 Mar 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 18 of 18)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [Bridging the Gap Between Value and Policy Based Reinforcement Learning](https://mlsanity.com/paper/1702.08892/) (2017)
- [A unified view of entropy-regularized Markov decision processes](https://mlsanity.com/paper/1705.07798/) (2017)
- [Equivalence Between Policy Gradients and Soft Q-Learning](https://mlsanity.com/paper/1704.06440/) (2017)
- [Finite-Time Analysis of Asynchronous Stochastic Approximation and Q-Learning](https://mlsanity.com/paper/2002.00260/) (2020)
- [Stochastic approximation with cone-contractive operators: Sharp ℓ_∞-bounds for Q-learning](https://mlsanity.com/paper/1905.06265/) (2019)
- [A Dual Approach to Constrained Markov Decision Processes with Entropy Regularization](https://mlsanity.com/paper/2110.08923/) (2021)
- [Multiagent Soft Q-Learning](https://mlsanity.com/paper/1804.09817/) (2018)
- [Neural Temporal-Difference and Q-Learning Provably Converge to Global Optima](https://mlsanity.com/paper/1905.10027/) (2019)
- [A Discrete-Time Switching System Analysis of Q-learning](https://mlsanity.com/paper/2102.08583/) (2021)
- [Final Iteration Convergence Bound of Q-Learning: Switching System Approach](https://mlsanity.com/paper/2205.05455/) (2022)
- [On the Convergence of Approximate and Regularized Policy Iteration Schemes](https://mlsanity.com/paper/1909.09621/) (2019)
- [Temporal-Difference Value Estimation via Uncertainty-Guided Soft Updates](https://mlsanity.com/paper/2110.14818/) (2021)

## Built on by (most cited first, 3 of 3)

- [Causality-informed Anomaly Detection in Partially Observable Sensor Networks: Moving beyond Correlations](https://mlsanity.com/paper/2507.09742/) (2025)
- [Finite-Time Analysis of Q-Value Iteration for General-Sum Stackelberg Games](https://mlsanity.com/paper/2604.04394/) (2026)
- [Fast Rates for Offline Q-Learning with KL Regularization](https://mlsanity.com/paper/2610.18839/) (2026)

## Abstract (arXiv)

Soft Q-learning is a variation of Q-learning designed to solve entropy regularized Markov decision problems where an agent aims to maximize the entropy regularized value function. Despite its empirical success, there have been limited theoretical studies of soft Q-learning to date. This paper aims to offer a novel and unified finite-time, control-theoretic analysis of soft Q-learning algorithms. We focus on two types of soft Q-learning algorithms: one utilizing the log-sum-exp operator and the other employing the Boltzmann operator. By using dynamical switching system models, we derive novel finite-time error bounds for both soft Q-learning algorithms. We hope that our analysis will deepen the current understanding of soft Q-learning by establishing connections with switching system models and may even pave the way for new frameworks in the finite-time analysis of other reinforcement learning algorithms.