arXiv Machine Learning

Regret Bounds for Market Making with Persistent Orders

arXiv Machine Learning
Sep 11

Bilateral Trade Under Heavy-Tailed Valuations: Minimax Regret without a Variance Bound

The paper studies contextual bilateral trade with full feedback, showing that action-independent observations eliminate the usual polynomial adaptation penalty seen in heavy-tailed bandits. It presents fully parameter-free algorithms that achieve oracle minimax regret rates without knowing the moment order or scale, and derives new regret bounds for both parametric and nonparametric settings. The key technical insight is a paired squared‑loss statistic whose noise cancels, enabling model selection and yielding regret rates that interpolate between classical nonparametric and linear extremes.

By Hangyi Zhao
arXiv Machine Learning
Oct 16

Transfer Learning in Bandits from Unknown Adaptive Policies: Problem-Dependent Lower and Upper Bounds

The paper investigates transfer learning in stochastic multi‑armed bandits when historical data come from an unknown adaptive policy. It establishes asymptotic problem‑dependent lower bounds and introduces the KL‑UCB‑Transfer algorithm, which combines online and historical data to achieve logarithmic regret with an improved constant under certain mean‑gap conditions. The study also relaxes the source‑target discrepancy assumption to a one‑sided condition, demonstrating that logarithmic regret can still be achieved under misspecification and identifying regimes of improvement, degradation, or loss of guarantee.

By Adrien Prevost, Timothee Mathieu, Waris Radji, Odalric-Ambrym Maillard