We also algorithm family, propose as a conjecture that they reach the minimum average items and analyze their complexity. In the second model, we analyze a specific the algorithms that minimize the average number of queries required to cluster the independently following a fixed distribution. In the first model, we characterize they form is drawn uniformly, the other one where each item chooses its class items, we consider two random models for the classes: one where the set partition classes (which can be labeled cheaply at the very end of the process). Given the cheap task of answering pairwise queries, and the computer groups the items into for training data gathering where the human experts perform the comparatively to see whether they belong to the same class. Thus motivated, we propose a setting determining the correct labels is much more expensive than comparing two items most practical cases rely on humans-in-the-loop to label the data. The process of has a high impact on the performance of the learned function.

Random walk (RW)-based algorithms have long been popular in distributed systems due to low overheads and scalability, with recent growing applications in decentralized learning. However, their reliance on local interactions makes them inherently vulnerable to malicious behavior. In this work, we investigate an adversarial threat that we term the ``Pac-Man'' attack, in which a malicious node probabilistically terminates any RW that visits it. This stealthy behavior gradually eliminates active RWs from the network, effectively halting the learning process without triggering failure alarms. To counter this threat, we propose the Average Crossing (AC) algorithm--a fully decentralized mechanism for duplicating RWs to prevent RW extinction in the presence of Pac-Man. Our theoretical analysis establishes that (i) the RW population remains almost surely bounded under AC and (ii) RW-based stochastic gradient descent remains convergent under AC, even in the presence of Pac-Man, with a quantifiable deviation from the true optimum. Our extensive empirical results on both synthetic and real-world datasets corroborate our theoretical findings. Furthermore, they uncover a phase transition in the extinction probability as a function of the duplication threshold. We offer theoretical insights by analyzing a simplified variant of the AC, which sheds light on the observed phase transition.

The objective is to identify the best arm with a given level of certainty while minimizing the sampling budget.

We consider the stochastic contextual bandit problem in the P AC setting.

We study the Stochastic Multi-armed Bandit problem under bounded arm-memory.