We study protocols for verifying approximate optimality of strategies in multi-armed bandits and normal-form games. As the number of actions available to each player is often large, we seek protocols where the number of queries to the utility oracle is sublinear in the number of actions. We prove that such verification is possible for sufficiently smooth strategies that do not put too much probability mass on any specific action and provide protocols for verifying that a smooth policy for a multi-armed bandit is close to optimal. Our verification protocols require provably fewer arm queries than learning. Furthermore, we show how to use cryptographic tools to reduce the communication cost of our protocols. We complement our protocol by proving a nearly tight lower bound on the query complexity of verification in our settings. As an application, we use our bandit verification protocol to build a protocol for verifying approximate optimality of a strong smooth Nash equilibrium, with sublinear query complexity.

As the outputs of generative AI (GenAl) techniques improve in quality, it becomes increasingly challenging to distinguish them from human-created content. Watermarking schemes are a promising approach to address the problem of distinguishing between AI and human-generated content. These schemes embed hidden signals within AI -generated content to enable reliable detection. While watermarking is not a silver bullet for addressing all risks associated with GenAl, it can play a crucial role in enhancing AI safety and trustworthiness by combating misinformation and deception. This paper presents a comprehensive overview of water-marking techniques for GenAl, beginning with the need for watermarking from historical and regulatory perspectives. We formalize the definitions and desired properties of watermarking schemes and examine the key objectives and threat models for existing approaches. Practical evaluation strategies are also explored, providing insights into the development of robust watermarking techniques capable of resisting various attacks. Additionally, we review recent representative works, highlight open challenges, and discuss potential directions for this emerging field. By offering a thorough understanding of watermarking in GenAl, this work aims to guide researchers in advancing watermarking methods and applications, and support policymakers in addressing the broader implications of GenAl.

Zero-knowledge range proofs (ZKRPs) allow a prover to convince a verifier that a secret value lies in a given interval. ZKRPs have numerous applications: from anonymous credentials and auctions, to confidential transactions in cryptocurrencies. At the same time, a plethora of ZKRP constructions exist in the literature, each with its own trade-offs. In this work, we systematize the knowledge around ZKRPs. We create a classification of existing constructions based on the underlying building techniques, and we summarize their properties. We provide comparisons between schemes both in terms of properties as well as efficiency levels, and construct a guideline to assist in the selection of an appropriate ZKRP for different application requirements. Finally, we discuss a number of interesting open research problems.

Recent advances in the capabilities of large language models such as GPT-4 have spurred increasing concern about our ability to detect AI-generated text. Prior works have suggested methods of embedding watermarks in model outputs, by *noticeably* altering the output distribution. We ask: Is it possible to introduce a watermark without incurring *any detectable* change to the output distribution? To this end, we introduce a cryptographically-inspired notion of undetectable watermarks for language models. That is, watermarks can be detected only with the knowledge of a secret key; without the secret key, it is computationally intractable to distinguish watermarked outputs from those of the original model. In particular, it is impossible for a user to observe any degradation in the quality of the text. Crucially, watermarks remain undetectable even when the user is allowed to adaptively query the model with arbitrarily chosen prompts. We construct undetectable watermarks based on the existence of one-way functions, a standard assumption in cryptography.

We show subexponential lower bounds (i.e., 2Ω (nc)) on the smoothed complexity of the classical Howard’s Policy Iteration algorithm for Markov Decision Processes. The bounds hold for the total reward and the average reward criteria. The constructions are robust in the sense that the subexponential bound holds not only on the average for independent random perturbations of the MDP parameters (transition probabilities and rewards), but for all arbitrary perturbations within an inverse polynomial range. We show also an exponential lower bound on the worst-case complexity for the simple reachability objective.

There has been considerable controversy regarding the accuracy and privacy of de-identification mechanisms used in the U.S. Decennial Census. We theoretically and experimentally analyze two such classes of mechanisms, swapping and differential privacy, especially examining their effects on ethnoracial minority groups.We first prove that the expected error of queries made on swapped demographic datasets is greater in sub-populations whose racial distributions differ more from the racial distribution of the global population. We also prove that the probability that m unique entries exist in a sub-population shrinks exponentially as the sub-population size grows. These properties suggest that swapping, which prioritizes unique entries, will produce poor accuracy for minority groups.We then empirically analyze the impact of swapping and differential privacy on the accuracy and privacy of a demographic dataset. We evaluate accuracy in several ways, including methods that stress the effect on minority groups. We evaluate privacy by counting the number of re-identified entries in a simulated linkage attack. Finally, we explore the disproportionate presence of minority groups in identified entries.Our empirical lindings corroborate our theoretical results: for minority representation, the utility of differential privacy is comparable to the utility of swapping, while providing a stronger privacy guarantee. Swapping places a disproportionate privacy burden on minority groups, whereas an ε-differentially private mechanism is ε-differentially private for all subgroups.