Provably Efficient and Agile Randomized Q-Learning

He Wang, Xingyu Xu, Yuejie Chi
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2377-2385, 2026.

Abstract

While Bayesian-based exploration often demonstrates superior empirical performance compared to bonus-based methods in model-based reinforcement learning (RL), its theoretical understanding remains limited for model-free settings. Existing provable algorithms either suffer from computational intractability or rely on stage-wise policy updates which reduce responsiveness and slow down the learning process. In this paper, we propose a novel variant of Q-learning algorithm, referred to as RandomizedQ, which integrates sampling-based exploration with agile, step-wise, policy updates, for episodic tabular RL. We establish a sublinear regret bound $\widetilde{O}(\sqrt{H^5SAT})$, where $S$ is the number of states, $A$ is the number of actions, $H$ is the episode length, and $T$ is the total number of episodes. In addition, we present a logarithmic regret bound $ O\left(\frac{H^6SA}{\Delta_{\min}}\log^5(SAHT)\right)$ when the optimal Q-function has a positive sub-optimality $\Delta_{\min}$. Empirically, RandomizedQ exhibits outstanding performance compared to existing Q-learning variants with both bonus-based and Bayesian-based exploration on standard benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-wang26e, title = { Provably Efficient and Agile Randomized Q-Learning }, author = {Wang, He and Xu, Xingyu and Chi, Yuejie}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2377--2385}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/wang26e/wang26e.pdf}, url = {https://proceedings.mlr.press/v300/wang26e.html}, abstract = { While Bayesian-based exploration often demonstrates superior empirical performance compared to bonus-based methods in model-based reinforcement learning (RL), its theoretical understanding remains limited for model-free settings. Existing provable algorithms either suffer from computational intractability or rely on stage-wise policy updates which reduce responsiveness and slow down the learning process. In this paper, we propose a novel variant of Q-learning algorithm, referred to as RandomizedQ, which integrates sampling-based exploration with agile, step-wise, policy updates, for episodic tabular RL. We establish a sublinear regret bound $\widetilde{O}(\sqrt{H^5SAT})$, where $S$ is the number of states, $A$ is the number of actions, $H$ is the episode length, and $T$ is the total number of episodes. In addition, we present a logarithmic regret bound $ O\left(\frac{H^6SA}{\Delta_{\min}}\log^5(SAHT)\right)$ when the optimal Q-function has a positive sub-optimality $\Delta_{\min}$. Empirically, RandomizedQ exhibits outstanding performance compared to existing Q-learning variants with both bonus-based and Bayesian-based exploration on standard benchmarks. } }
Endnote
%0 Conference Paper %T Provably Efficient and Agile Randomized Q-Learning %A He Wang %A Xingyu Xu %A Yuejie Chi %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-wang26e %I PMLR %P 2377--2385 %U https://proceedings.mlr.press/v300/wang26e.html %V 300 %X While Bayesian-based exploration often demonstrates superior empirical performance compared to bonus-based methods in model-based reinforcement learning (RL), its theoretical understanding remains limited for model-free settings. Existing provable algorithms either suffer from computational intractability or rely on stage-wise policy updates which reduce responsiveness and slow down the learning process. In this paper, we propose a novel variant of Q-learning algorithm, referred to as RandomizedQ, which integrates sampling-based exploration with agile, step-wise, policy updates, for episodic tabular RL. We establish a sublinear regret bound $\widetilde{O}(\sqrt{H^5SAT})$, where $S$ is the number of states, $A$ is the number of actions, $H$ is the episode length, and $T$ is the total number of episodes. In addition, we present a logarithmic regret bound $ O\left(\frac{H^6SA}{\Delta_{\min}}\log^5(SAHT)\right)$ when the optimal Q-function has a positive sub-optimality $\Delta_{\min}$. Empirically, RandomizedQ exhibits outstanding performance compared to existing Q-learning variants with both bonus-based and Bayesian-based exploration on standard benchmarks.
APA
Wang, H., Xu, X. & Chi, Y.. (2026). Provably Efficient and Agile Randomized Q-Learning . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2377-2385 Available from https://proceedings.mlr.press/v300/wang26e.html.

Related Material