Greedy k-means++ is a generalization of k-means++ where, in each iteration, a new seed is greedily chosen among multiple ℓ 2points sampled, as opposed to a single seed being sampled in k-means++. While empirical studies consistently show the superior performance of greedy k-means++, making it a preferred method in practice, a discrepancy exists between theory and practice. No theoretical justification currently explains this improved performance. Indeed, the prevailing theory suggests that greedy k-means++ exhibits worse performance than k-means++ in worst-case scenarios. This paper presents an analysis demonstrating the outperformance of the greedy algorithm compared to k-means++ for a natural class of well-separated instances with exponentially decaying distributions, such as Gaussian, specifically when ℓ = lnk +Θ(1), a common parameter setting in practical applications.

Neural Information Processing Systems http://nips.cc/

We consider nonconvex stochastic optimization problems in the asynchronous centralized distributed setup where the communication times from workers to a server can not be ignored, and the computation and communication times are potentially different for all workers.

(Theorem 4). We also consider Assumption 3. Note that this assumption does not restrict the class of considered Iterative algorithms are traditionally evaluated based on their gradient complexity .

Neural Information Processing Systems http://nips.cc/

In this paper, we study stochastic structured bandits for minimizing regret.