Online sparse linear regression is the task of applying linear regression analysis to examples arriving sequentially subject to a resource constraint that a limited number of features of examples can be observed. Despite its importance in many practical applications, it has been recently shown that there is no polynomial-time sublinear-regret algorithm unless NP$\subseteq$BPP, and only an exponential-time sublinear-regret algorithm has been found. In this paper, we introduce mild assumptions to solve the problem.

Online sparse linear regression is the task of applying linear regression analysis to examples arriving sequentially subject to a resource constraint that a limited number of features of examples can be observed. Despite its importance in many practical applications, it has been recently shown that there is no polynomial-time sublinear-regret algorithm unless NP BPP, and only an exponential-time sublinear-regret algorithm has been found. In this paper, we introduce mild assumptions to solve the problem.

The paper considers the online sparse regression problem introduced by Kale (COLT'14), in which the online algorithm can only observe a subset of k features of each data point and has to sequentially predict a label based only on this limited observation (it can thus only use a sparse predictor for each prediction). Without further assumptions, this problem has been recently shown to be computationally hard by Foster et al (ALT'16). To circumvent this hardness, the authors assume a stochastic i.i.d. The results are not particularly exciting, but they do give a nice counter to the recent computational impossibility of Foster et al, in a setting where the data is i.i.d. and well-specified by a k-sparse vector. One of the main things I was missing in the paper is a proper discussion relating its setup, assumptions and results to the literature on sparse recovery / compressed sensing / sparse linear regression.

Online sparse linear regression is the task of applying linear regression analysis to examples arriving sequentially subject to a resource constraint that a limited number of features of examples can be observed. Despite its importance in many practical applications, it has been recently shown that there is no polynomialtime sublinear-regret algorithm unless NP BPP, and only an exponential-time sublinear-regret algorithm has been found. In this paper, we introduce mild assumptions to solve the problem.

Online sparse linear regression is the task of applying linear regression analysis to examples arriving sequentially subject to a resource constraint that a limited number of features of examples can be observed. Despite its importance in many practical applications, it has been recently shown that there is no polynomial-time sublinear-regret algorithm unless NP$\subseteq$BPP, and only an exponential-time sublinear-regret algorithm has been found. In this paper, we introduce mild assumptions to solve the problem. In addition, thorough experiments with publicly available data demonstrate that our algorithms outperform other known algorithms. Papers published at the Neural Information Processing Systems Conference.

Online sparse linear regression is the task of applying linear regression analysis to examples arriving sequentially subject to a resource constraint that a limited number of features of examples can be observed. Despite its importance in many practical applications, it has been recently shown that there is no polynomial-time sublinear-regret algorithm unless NP$\subseteq$BPP, and only an exponential-time sublinear-regret algorithm has been found. In this paper, we introduce mild assumptions to solve the problem. Under these assumptions, we present polynomial-time sublinear-regret algorithms for the online sparse linear regression. In addition, thorough experiments with publicly available data demonstrate that our algorithms outperform other known algorithms.