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

We study the problem of making calibrated probabilistic forecasts for abinary sequence generated by an adversarial nature. Following the seminal paperof Foster and Vohra (1998), nature is often modeled as an adaptive adversarywho sees all activity of the forecaster except the randomization that theforecaster may deploy. A number of papers have proposed randomized forecastingstrategies that achieve an $\epsilon$-calibration error rate of$O(1/\sqrt{T})$, which we prove is tight in general. On the other hand, it iswell known that it is not possible to be calibrated without randomization, orif nature also sees the forecaster's randomization; in both cases thecalibration error could be $\Omega(1)$. Inspired by the equally seminal workson the "power of two choices" and imprecise probability theory, we study asmall variant of the standard online calibration problem. The adversary givesthe forecaster the option of making two nearby probabilistic forecasts, orequivalently an interval forecast of small width, and the endpoint closest tothe revealed outcome is used to judge calibration. This power of two choices,or imprecise forecast, accords the forecaster with significant power -- we showthat a faster $\epsilon$-calibration rate of $O(1/T)$ can be achieved evenwithout deploying any randomization.

Faster online calibration without randomization: interval forecasts and the power of two choices