Non-stationary Online Regression

Abstract

Online forecasting under changing environment has been a problem of increasing importance in many real-world applications. In this paper, we consider the meta-algorithm presented in Zhang et al. [22] combined with different subroutines. We show that an expected cumulative error of order Õ(n 1/3 C 2/3 n ) can be obtained for non-stationary online linear regression where the total variation of parameter sequence is bounded by C n . Our paper extends the result of online forecasting of one dimensional time-series as proposed in [2] to general d-dimensional non-stationary linear regression. We improve the rate O( √ nC n ) obtained by Zhang et al. [22] and Besbes et al. [3]. We further extend our analysis to non-stationary online kernel regression. Similar to the non-stationary online regression case, we use the meta-procedure of Zhang et al. [22] combined with Kernel-AWV [16] to achieve an expected cumulative controlled by the effective dimension of the RKHS and the total variation of the sequence. To the best of our knowledge, this work is the first extension of non-stationary online regression to non-stationary kernel regression. Lastly, we evaluate our method empirically with several existing benchmarks and also compare it with the theoretical bound obtained in this paper.

Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability

“…In such cases, one can achieve Eqn. (4) with non-trivial Reg Sq (T ) [Raj et al, 2020;Baby and Wang, 2021], which can then be used in Theorem 3.…”