Heng Huang

Ruibo Chen, Yihan Wu, Xuehao Cui et al.

Watermarking has emerged as a crucial technique for detecting and attributing content generated by large language models. While recent advancements have utilized watermark ensembles to enhance robustness, prevailing methods typically prioritize maximizing the strength of the watermark at every individual layer. In this work, we identify a critical limitation in this "stronger-is-better" approach: strong watermarks significantly reduce the entropy of the token distribution, which paradoxically weakens the effectiveness of watermarking in subsequent layers. We theoretically and empirically show that detectability is bounded by entropy and that watermark ensembles induce a monotonic decrease in both entropy and the expected green-list ratio across layers. To address this inherent trade-off, we propose a general framework that utilizes weaker single-layer watermarks to preserve the entropy required for effective multi-layer ensembling. Empirical evaluations demonstrate that this counter-intuitive strategy mitigates signal decay and consistently outperforms strong baselines in both detectability and robustness.

Anirudh Satheesh, Ziyi Chen, Furong Huang et al.

We study robust Markov decision processes (RMDPs) with general policy parameterization under s-rectangular and non-rectangular uncertainty sets. Prior work is largely limited to tabular policies, and hence either lacks sample complexity guarantees or incurs high computational cost. Our method reduces the average reward RMDPs to entropy-regularized discounted robust MDPs, restoring strong duality and enabling tractable equilibrium computation. We prove novel Lipschitz and Lipschitz-smoothness properties for general policy parameterizations that extends to infinite state spaces. To address infinite-horizon gradient estimation, we introduce a multilevel Monte Carlo gradient estimator with $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity, a factor of $\mathcal{O}(ε^{-2})$ improvement over prior work. Building on this, we design a projected gradient descent algorithm for s-rectangular uncertainty ($\mathcal{O}(ε^{-5})$) and a Frank--Wolfe algorithm for non-rectangular uncertainty ($\mathcal{O}(ε^{-4})$ discounted, $\mathcal{O}(ε^{-10.5})$ average reward), significantly improving prior results in both the discounted setting and average reward setting. Our work is the first one to provide sample complexity guarantees for RMDPs with general policy parameterization beyond $(s, a)$-rectangularity. It also provides the first such guarantees in the average reward setting and improves existing bounds for discounted robust MDPs.