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Poster

Efficient Sublinear-Regret Algorithms for Online Sparse Linear Regression with Limited Observation

Shinji Ito · Daisuke Hatano · Hanna Sumita · Akihiro Yabe · Takuro Fukunaga · Naonori Kakimura · Ken-Ichi Kawarabayashi

Pacific Ballroom #35

Keywords: [ Computational Complexity ] [ Hardness of Learning and Approximations ] [ Regression ] [ Sparsity and Compressed Sensing ] [ Convex Optimization ] [ Online Learning ] [ Bandit Algorithms ]

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Abstract: 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.

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