2019-06-25-jun19a.md

abstract	section	title	layout	series	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	publisher	container-title	volume	genre	issued	pdf	extras
We consider the problem of unconstrained online convex optimization (OCO) with sub-exponential noise, a strictly more general problem than the standard OCO. In this setting, the learner receives a subgradient of the loss functions corrupted by sub-exponential noise and strives to achieve optimal regret guarantee, without knowledge of the competitor norm, i.e., in a parameter-free way. Recently, Cutkosky and Boahen (COLT 2017) proved that, given unbounded subgradients, it is impossible to guarantee a sublinear regret due to an exponential penalty. This paper shows that it is possible to go around the lower bound by allowing the observed subgradients to be unbounded via stochastic noise. However, the presence of unbounded noise in unconstrained OCO is challenging; existing algorithms do not provide near-optimal regret bounds or fail to have a guarantee. So, we design a novel parameter-free OCO algorithm for Banach space, which we call BANCO, via a reduction to betting on noisy coins. We show that BANCO achieves the optimal regret rate in our problem. Finally, we show the application of our results to obtain a parameter-free locally private stochastic subgradient descent algorithm, and the connection to the law of iterated logarithms.	contributed	Parameter-Free Online Convex Optimization with Sub-Exponential Noise	inproceedings	Proceedings of Machine Learning Research	jun19a	0	Parameter-Free Online Convex Optimization with Sub-Exponential Noise	1802	1823	1802-1823	1802	false	Jun, Kwang-Sung and Orabona, Francesco	given family Kwang-Sung Jun given family Francesco Orabona	2019-06-25		PMLR	Proceedings of the Thirty-Second Conference on Learning Theory	99	inproceedings	date-parts 2019 6 25	http://proceedings.mlr.press/v99/jun19a/jun19a.pdf