Hence, the following research questions arise: What is the optimal regret lower bound in contextual MNL bandits?

These are achieved by guiding the randomized greedy algorithm with a fast local search algorithm. Further, we develop deterministic versions of these algorithms, maintaining the same ratio and asymptotic time complexity.

Such embeddings induce the so-called maximum mean discrepancy (MMD; [Smola et al., 2007, Gretton et al., 2012]), which quantifies the discrepancy Many estimators for HSIC exist. The classical ones rely on U-statistics or V -statistics [Gretton et al., 2005, Quadrianto et al., 2009, Pfister et al., 2018] and are known to converge at a rate of Lower bounds for the related MMD are known [Tolstikhin et al., 2016], but the existing analysis considers radial kernels and relies on independent Gaussian distributions.

An obstacle in applying supervised paradigms to such problems is the need for costly target solutions often produced with exact solvers.

Three sampling techniques are presented for comparative investigations.

An efficient two-staged approach is designed for exploring CSPG, with fast approaching and cross-partition expansion.

We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds.

We propose adaptive, line search-free second-order methods with optimal rate of convergence for solving convex-concave min-max problems.