English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Adaptivity to the difficulties of a problem is a key property in sequentialdecision-making problems to broaden the applicability of algorithms.Follow-the-Regularized-Leader (FTRL) has recently emerged as one of the mostpromising approaches for obtaining various types of adaptivity in banditproblems. Aiming to further generalize this adaptivity, we develop a genericadaptive learning rate, called Stability-Penalty-Adaptive (SPA) learning ratefor FTRL. This learning rate yields a regret bound jointly depending onstability and penalty of the algorithm, into which the regret of FTRL istypically decomposed. With this result, we establish several algorithms withthree types of adaptivity: sparsity, game-dependency, and Best-of-Both-Worlds(BOBW). Sparsity frequently appears in real-world problems. However, existingsparse multi-armed bandit algorithms with $k$-arms assume that the sparsitylevel $s \leq k$ is known in advance, which is often not the case in real-worldscenarios. To address this problem, with the help of the new learning rateframework, we establish $s$-agnostic algorithms with regret bounds of$\tilde{O}(\sqrt{sT})$ in the adversarial regime for $T$ rounds, which matchesthe existing lower bound up to a logarithmic factor. Meanwhile, BOBW algorithmsaim to achieve a near-optimal regret in both the stochastic and adversarialregimes. Leveraging the new adaptive learning rate framework and a novelanalysis to bound the variation in FTRL output in response to changes in aregularizer, we establish the first BOBW algorithm with a sparsity-dependentbound. Additionally, we explore partial monitoring and demonstrate that theproposed learning rate framework allows us to achieve a game-dependent boundand the BOBW simultaneously.

Stability-penalty-adaptive Follow-the-regularized-leader: Sparsity, Game-dependency, and Best-of-both-worlds