aiqbench analysis
This paper is a theoretical study of reinforcement learning, proving sample-complexity bounds for an asynchronous Q-learning method that stays robust to mismatch between simulated and real environments. The bounds are near-minimax-optimal under a total-variation uncertainty set, and the work targets the realistic case of learning from a single Markovian trajectory. For practitioners, the main takeaway is a model-free robust method with provable guarantees, though the results are asymptotic and up to logarithmic factors, so empirical validation still matters.
Provably Efficient Q-learning for Robust Reinforcement Learning
arXiv:2610.35656v1 Announce Type: cross Abstract: Standard reinforcement learning (RL) algorithms based on Markov Decision Processes (MDPs) are vulnerable to sim-to-real gaps. To address this issue, distributionally robust RL algorithms based on robust MDPs (RMDPs) have been proposed, for ensuring that agents can perform reliably to unpredictable conditions in real-world environments. Despite of the rich literature, \revision{an efficient model-free method is still lacking} for robust RL, particularly for Markovian data, which is more relevant in practical applications. In this work, we take a step towards settling this problem by proposing a sample efficient (asynchronous Q-learning) algorithm for robust RL. In particular, consider a $\gamma$-discounted infinite-horizon RMDP with state space $\mathcal{S}$ and action space $\mathcal{A}$, where the uncertainty set is specified by the total variation (TV) distance with uncertainty level $\sigma$. Assuming access to a single trajectory of Markovian samples induced by a behavior policy and the nominal transition kernel, the sample complexity of the proposed Q-learning algorithm --- to achieve an entrywise $\varepsilon$-approximation of the optimal Q-function --- is bounded by $$ \frac{1}{\mu_{\mathsf{min}}\varepsilon^2(1-\gamma)^3\max\{1-\gamma,\sigma\}} + \frac{t_{\mathsf{mix}}}{\mu_{\mathsf{min}}(1-\gamma)} $$ up to logarithmic factors. Here, $t_{\mathsf{mix}}$ and $\mu_{\mathsf{min}}$ denote the mixing time and the minimum state-action occupancy probability of the sample trajectory, respectively. This result is nearly minimax optimal, with an additional factor of $\frac{1}{1-\gamma}$. Moreover, it achieves a significant improvement over existing bounds.
Abstract:Standard reinforcement learning (RL) algorithms based on Markov Decision Processes (MDPs) are vulnerable to sim-to-real gaps. To address this issue, distributionally robust RL algorithms based on robust MDPs (RMDPs) have been proposed, for ensuring that agents can perform reliably to unpredictable conditions in real-world environments. Despite of the rich literature, \revision{an efficient model-free method is still lacking} for robust RL, particularly for Markovian data, which is more relevant in practical applications. In this work, we take a step towards settling this problem by proposing a sample efficient (asynchronous Q-learning) algorithm for robust RL. In particular, consider a $\gamma$-discounted infinite-horizon RMDP with state space $\mathcal{S}$ and action space $\mathcal{A}$, where the uncertainty set is specified by the total variation (TV) distance with uncertainty level $\sigma$. Assuming access to a single trajectory of Markovian samples induced by a behavior policy and the nominal transition kernel, the sample complexity of the proposed Q-learning algorithm --- to achieve an entrywise $\varepsilon$-approximation of the optimal Q-function --- is bounded by $$ \frac{1}{\mu_{\mathsf{min}}\varepsilon^2(1-\gamma)^3\max\{1-\gamma,\sigma\}} + \frac{t_{\mathsf{mix}}}{\mu_{\mathsf{min}}(1-\gamma)} $$ up to logarithmic factors. Here, $t_{\mathsf{mix}}$ and $\mu_{\mathsf{min}}$ denote the mixing time and the minimum state-action occupancy probability of the sample trajectory, respectively. This result is nearly minimax optimal, with an additional factor of $\frac{1}{1-\gamma}$. Moreover, it achieves a significant improvement over existing bounds.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Statistics Theory (math.ST)
arXiv:2610.35656 [stat.ML]
(or arXiv:2610.35656v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.35656 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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