We study infinite-horizon average-reward reinforcement learning (RL) for Lipschitz MDPs and develop an algorithm ZoRL that discretizes the state-action space adaptively and zooms into promising regions of the state-action space. We show that its regret can be bounded as $\mathcal{\tilde{O}}\big(T^{1 - d_{\text{eff.}}^{-1}}\big)$, where $d_{\text{eff.}} = 2d_\mathcal{S} + d_z + 3$, $d_\mathcal{S}$ is the dimension of the state space, and $d_z$ is the zooming dimension. $d_z$ is a problem-dependent quantity, which allows us to conclude that if MDP is benign, then its regret will be small. We note that the existing notion of zooming dimension for average reward RL is defined in terms of policy coverings, and hence it can be huge when the policy class is rich even though the underlying MDP is simple, so that the regret upper bound is nearly $O(T)$. The zooming dimension proposed in the current work is bounded above by $d$, the dimension of the state-action space, and hence is truly adaptive, i.e., shows how to capture adaptivity gains for infinite-horizon average-reward RL. ZoRL outperforms other state-of-the-art algorithms in experiments; thereby demonstrating the gains arising due to adaptivity.

Watermarking is broadly utilized to protect ownership of shared data while preserving data utility. However, existing watermarking methods for tabular datasets fall short on the desired properties (detectability, non-intrusiveness, and robustness) and only preserve data utility from the perspective of data statistics, ignoring the performance of downstream ML models trained on the datasets. Can we watermark tabular datasets without significantly compromising their utility for training ML models while preventing attackers from training usable ML models on attacked datasets? In this paper, we propose a hypothesis testing-based watermarking scheme, TabularMark. Data noise partitioning is utilized for data perturbation during embedding, which is adaptable for numerical and categorical attributes while preserving the data utility. For detection, a custom-threshold one proportion z-test is employed, which can reliably determine the presence of the watermark. Experiments on real-world and synthetic datasets demonstrate the superiority of TabularMark in detectability, non-intrusiveness, and robustness.