Probably Correct Optimal Stable Matching under Two-Sided Uncertainty

We study a sequential learning problem for stable matchings in two-sided markets where preferences on both sides are initially unknown. We focus on a centralized setting where an algorithm matches agents at each time step and receives noisy rewards that reflect the preferences of the matched agents, following a semi-bandit feedback structure. We adopt a pure exploration perspective, aiming to efficiently identify the optimal stable matching with high probability. Our work extends prior results by handling \emph{two-sided uncertainty} and by exploiting \emph{partial preference} information. A central ingredient is the notion of \textbf{pervasive stable matching}, which enables the identification of optimal stable matchings under partial preferences. We propose elimination-based algorithms whose stopping criteria exploit the structure of the learned partial preferences, and provide a refined sample-complexity analysis. Beyond pure exploration, we extend our approach to regret minimization and establish regret bounds with respect to the \emph{optimal} stable matching that avoid dependence on the minimum reward gap $Δ_{\min}$.

Ranking-and-Selection with Multiple Correct Answers and Non-Answerable Estimates

We study fixed-precision ranking-and-selection in structured settings where the answer may be non-unique and where noisy estimates may temporarily admit no valid answer at all. This phenomenon arises naturally in problems such as multi-fidelity ranking-and-selection and identifying a Condorcet winner from pairwise comparisons. To address this, we propose a unified framework based on answer-wise acceptance sets, restricted generalized likelihood ratio stopping, and an answer-pitfall decomposition that yields a max-max-min characteristic value and a common sampling principle. We introduce ENDS, a general procedure that combines estimation, nomination, pitfall detection, and cost-aware information-directed selection. We instantiate ENDS for various problems by deriving explicit formulas. Extensive numerical experiments show that this unified recipe performs well across a broad range of pure-exploration problems and offers a practical framework and proof-of-concept algorithmic recipe.

Online Learning with Recency: Algorithms for Sliding-window Streaming Multi-armed Bandits

Motivated by the recency effect in online learning, we study algorithms for single-pass *sliding-window streaming multi-armed bandits (MABs)* in this paper. In this setting, we are given $n$ arms with unknown sub-Gaussian reward distributions and a parameter $W$. The arms arrive in a single-pass stream, and only the most recent $W$ arms are considered valid. The algorithm is required to perform pure exploration and regret minimization with limited memory, defined as the number of stored arms. The model is a natural extension of the streaming multi-armed bandits model (without the sliding window) that has been extensively studied in recent years. We provide a comprehensive analysis of both the pure exploration and regret minimization problems with the model. For pure exploration, we prove that finding the best arm is hard with sublinear memory while finding an approximate best arm admits an efficient algorithm. For regret minimization, we explore a new notion of regret and give sharp memory-regret trade-offs for any single-pass algorithm. We complement our theoretical results with experiments, demonstrating the trade-offs between sample, regret, and memory.