Regret bounds for online portfolio selection with a cardinality constraint

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

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

Online portfolio selection is a sequential decision-making problem in which a learner repetitively selects a portfolio over a set of assets, aiming to maximize long-term return. In this paper, we study the problem with the cardinality constraint that the number of assets in a portfolio is restricted to be at most k, and consider two scenarios: (i) in the full-feedback setting, the learner can observe price relatives (rates of return to cost) for all assets, and (ii) in the bandit-feedback setting, the learner can observe price relatives only for invested assets. We propose efficient algorithms for these scenarios, which achieve sublinear regrets. We also provide regret (statistical) lower bounds for both scenarios which nearly match the upper bounds when k is a constant. In addition, we give a computational lower bound, which implies that no algorithm maintains both computational efficiency, as well as a small regret upper bound.

Original languageEnglish
Pages (from-to)10588-10597
Number of pages10
JournalAdvances in Neural Information Processing Systems
Volume2018-December
Publication statusPublished - 2018 Jan 1
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: 2018 Dec 22018 Dec 8

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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  • Cite this

    Ito, S., Hatano, D., Sumita, H., Yabe, A., Fukunaga, T., Kakimura, N., & Kawarabayashi, K. I. (2018). Regret bounds for online portfolio selection with a cardinality constraint. Advances in Neural Information Processing Systems, 2018-December, 10588-10597.