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Poster
Adaptive Online Estimation of Piecewise Polynomial Trends
Dheeraj Baby · Yu-Xiang Wang

Tue Dec 08 09:00 PM -- 11:00 PM (PST) @ Poster Session 2 #641
in Poster Session 3 »
We consider the framework of non-stationary stochastic optimization [Besbes et.al. 2015] with squared error losses and noisy gradient feedback where the dynamic regret of an online learner against a time varying comparator sequence is studied. Motivated from the theory of non-parametric regression, we introduce a \emph{new variational constraint} that enforces the comparator sequence to belong to a discrete $k^{th}$ order Total Variation ball of radius $C_n$. This variational constraint models comparators that have piecewise polynomial structure which has many relevant practical applications [Tibshirani2015]. By establishing connections to the theory of wavelet based non-parametric regression, we design a \emph{polynomial time} algorithm that achieves the nearly \emph{optimal dynamic regret} of $\tilde{O}(n^{\frac{1}{2k+3}}C_n^{\frac{2}{2k+3}})$. The proposed policy is \emph{adaptive to the unknown radius} $C_n$. Further, we show that the same policy is minimax optimal for several other non-parametric families of interest.

Author Information

Dheeraj Baby (UC Santa Barbara)
Yu-Xiang Wang (UC Santa Barbara)

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