Q-Learning with Shift-Aware Upper Confidence Bound in Non-Stationary Reinforcement Learning
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arXiv
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| Format: | Preprint |
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2025
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| author | Bui, Ha Manh Parker, Felix Ghobadi, Kimia Liu, Anqi |
| author_facet | Bui, Ha Manh Parker, Felix Ghobadi, Kimia Liu, Anqi |
| contents | We study the Non-Stationary Reinforcement Learning (RL) under distribution shifts in both finite-horizon episodic and infinite-horizon discounted Markov Decision Processes (MDPs). In the finite-horizon case, the transition functions may suddenly change at a particular episode. In the infinite-horizon setting, such changes can occur at an arbitrary time step during the agent's interaction with the environment. While the Q-learning Upper Confidence Bound algorithm (QUCB) can discover a proper policy during learning, due to the distribution shifts, this policy can exploit sub-optimal rewards after the shift happens. To address this issue, we propose Density-QUCB (DQUCB), a shift-aware Q-learning UCB algorithm, which uses a transition density function to detect distribution shifts, then leverages its likelihood to enhance the uncertainty estimation quality of Q-learning UCB, resulting in a balance between exploration and exploitation. Theoretically, we prove that our oracle DQUCB achieves a better regret guarantee than QUCB. Empirically, our DQUCB enjoys the computational efficiency of model-free RL and outperforms QUCB baselines by having a lower regret across RL tasks, as well as a COVID-19 patient hospital allocation task using a Deep-Q-learning architecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Q-Learning with Shift-Aware Upper Confidence Bound in Non-Stationary Reinforcement Learning Bui, Ha Manh Parker, Felix Ghobadi, Kimia Liu, Anqi Machine Learning We study the Non-Stationary Reinforcement Learning (RL) under distribution shifts in both finite-horizon episodic and infinite-horizon discounted Markov Decision Processes (MDPs). In the finite-horizon case, the transition functions may suddenly change at a particular episode. In the infinite-horizon setting, such changes can occur at an arbitrary time step during the agent's interaction with the environment. While the Q-learning Upper Confidence Bound algorithm (QUCB) can discover a proper policy during learning, due to the distribution shifts, this policy can exploit sub-optimal rewards after the shift happens. To address this issue, we propose Density-QUCB (DQUCB), a shift-aware Q-learning UCB algorithm, which uses a transition density function to detect distribution shifts, then leverages its likelihood to enhance the uncertainty estimation quality of Q-learning UCB, resulting in a balance between exploration and exploitation. Theoretically, we prove that our oracle DQUCB achieves a better regret guarantee than QUCB. Empirically, our DQUCB enjoys the computational efficiency of model-free RL and outperforms QUCB baselines by having a lower regret across RL tasks, as well as a COVID-19 patient hospital allocation task using a Deep-Q-learning architecture. |
| title | Q-Learning with Shift-Aware Upper Confidence Bound in Non-Stationary Reinforcement Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.03181 |