2022-06-28-gupta22b.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Faster online calibration without randomization: interval forecasts and the power of two choices	We study the problem of making calibrated probabilistic forecasts for a binary sequence generated by an adversarial nature. Following the seminal paper of Foster and Vohra (1998), nature is often modeled as an adaptive adversary who sees all activity of the forecaster except the randomization that the forecaster may deploy. A number of papers have proposed randomized forecasting strategies that achieve an $\epsilon$-calibration error rate of $O(1/\sqrt{T})$, which we prove is tight in general. On the other hand, it is well known that it is not possible to be calibrated without randomization, or if nature also sees the forecaster’s randomization; in both cases the calibration error could be $\Omega(1)$. Inspired by the equally seminal works on the power of two choices and imprecise probability theory, we study a small variant of the standard online calibration problem. The adversary gives the forecaster the option of making two nearby probabilistic forecasts, or equivalently an interval forecast of small width, and the endpoint closest to the revealed outcome is used to judge calibration. This power of two choices, or imprecise forecast, accords the forecaster with significant power—we show that a faster $\epsilon$-calibration rate of $O(1/T)$ can be achieved even without deploying any randomization.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	gupta22b	0	Faster online calibration without randomization: interval forecasts and the power of two choices	4283	4309	4283-4309	4283	false	Gupta, Chirag and Ramdas, Aaditya	given family Chirag Gupta given family Aaditya Ramdas	2022-06-28		Proceedings of Thirty Fifth Conference on Learning Theory	178	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v178/gupta22b/gupta22b.pdf