We introduce ideal attribution mechanisms, a formal abstraction for reasoning about attribution decisions over strings. At the core of this abstraction lies the ledger, an append-only log of the prompt-response interaction history between a model and its user. Each mechanism produces deterministic decisions based on the ledger and an explicit selection criterion, making it well-suited to serve as a ground truth for attribution. We frame the design goal of watermarking schemes as faithful representation of ideal attribution mechanisms. This novel perspective brings conceptual clarity, replacing piecemeal probabilistic statements with a unified language for stating the guarantees of each scheme. It also enables precise reasoning about desiderata for future watermarking schemes, even when no current construction achieves them, since the ideal functionalities are specified first. In this way, the framework provides a roadmap that clarifies which guarantees are attainable in an idealized setting and worth pursuing in practice.

This work studies the non-monotone DR-submodular Maximization over a ground set of $n$ subject to a size constraint $k$. We propose two approximation algorithms for solving this problem named FastDrSub and FastDrSub++. FastDrSub offers an approximation ratio of $0.044$ with query complexity of $O(n \log(k))$. The second one, FastDrSub++, improves upon it with a ratio of $1/4-ε$ within query complexity of $(n \log k)$ for an input parameter $ε>0$. Therefore, our proposed algorithms are the first constant-ratio approximation algorithms for the problem with the low complexity of $O(n \log(k))$. Additionally, both algorithms are experimentally evaluated and compared against existing state-of-the-art methods, demonstrating their effectiveness in solving the Revenue Maximization problem with DR-submodular objective function. The experimental results show that our proposed algorithms significantly outperform existing approaches in terms of both query complexity and solution quality.

In a supervised online setting, quantifying uncertainty has been proposed in the seminal work of \cite{gibbs2021adaptive}. For any given point-prediction algorithm, their method (ACI) produces a conformal prediction set with an average missed coverage getting close to a pre-specified level $α$ for a long time horizon. We introduce an extended version of this algorithm, called OnlineSCI, allowing the user to additionally select times where such an inference should be made. OnlineSCI encompasses several prominent online selective tasks, such as building prediction intervals for extreme outcomes, classification with abstention, and online testing. While OnlineSCI controls the average missed coverage on the selected in an adversarial setting, our theoretical results also show that it controls the instantaneous error rate (IER) at the selected times, up to a non-asymptotical remainder term. Importantly, our theory covers the case where OnlineSCI updates the point-prediction algorithm at each time step, a property which we refer to as {\it adaptive} capability. We show that the adaptive versions of OnlineSCI can convergence to an optimal solution and provide an explicit convergence rate in each of the aforementioned application cases, under specific mild conditions. Finally, the favorable behavior of OnlineSCI in practice is illustrated by numerical experiments.

We study pure exploration problems where the set of correct answers is possibly infinite, e.g., the regression of any continuous function of the means of the bandit. We derive an instance-dependent lower bound for these problems. By analyzing it, we discuss why existing methods (i.e., Sticky Track-and-Stop) for finite answer problems fail at being asymptotically optimal in this more general setting. Finally, we present a framework, Sticky-Sequence Track-and-Stop, which generalizes both Track-and-Stop and Sticky Track-and-Stop, and that enjoys asymptotic optimality. Due to its generality, our analysis also highlights special cases where existing methods enjoy optimality.

In online selective conformal inference, data arrives sequentially, and prediction intervals are constructed only when an online selection rule is met. Since online selections may break the exchangeability between the selected test datum and the rest of the data, one must correct for this by suitably selecting the calibration data. In this paper, we evaluate existing calibration selection strategies and pinpoint some fundamental errors in the associated claims that guarantee selection-conditional coverage and control of the false coverage rate (FCR). To address these shortcomings, we propose novel calibration selection strategies that provably preserve the exchangeability of the calibration data and the selected test datum. Consequently, we demonstrate that online selective conformal inference with these strategies guarantees both selection-conditional coverage and FCR control. Our theoretical findings are supported by experimental evidence examining tradeoffs between valid methods.

Group-agent reinforcement learning (GARL) is a newly arising learning scenario, where multiple reinforcement learning agents study together in a group, sharing knowledge in an asynchronous fashion. The goal is to improve the learning performance of each individual agent. Under a more general heterogeneous setting where different agents learn using different algorithms, we advance GARL by designing novel and effective group-learning mechanisms. They guide the agents on whether and how to learn from action choices from the others, and allow the agents to adopt available policy and value function models sent by another agent if they perform better. We have conducted extensive experiments on a total of 43 different Atari 2600 games to demonstrate the superior performance of the proposed method. After the group learning, among the 129 agents examined, 96% are able to achieve a learning speed-up, and 72% are able to learn over 100 times faster. Also, around 41% of those agents have achieved a higher accumulated reward score by learning in less than 5% of the time steps required by a single agent when learning on its own.