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Article Dans Une Revue Journal of Machine Learning Research Année : 2016

Gains and losses are fundamentally different in regret minimization: the sparse case

Résumé

We demonstrate that, in the classical non-stochastic regret minimization problem with d decisions, gains and losses to be respectively maximized or minimized are fundamentally different. Indeed, by considering the additional sparsity assumption (at each stage, at most s decisions incur a nonzero outcome), we derive optimal regret bounds of different orders. Specifically, with gains, we obtain an optimal regret guarantee after T stages of order root T logs, so the classical dependency in the dimension is replaced by the sparsity size. With losses, we provide matching upper and lower bounds of order root Ts log(d)/d, which is decreasing in d. Eventually, we also study the bandit setting, and obtain an upper bound of order root Ts log(d/s) when outcomes are losses. This bound is proven to be optimal up to the logarithmic factor root log(d/s).
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Dates et versions

hal-02630070 , version 1 (27-05-2020)

Identifiants

  • HAL Id : hal-02630070 , version 1
  • PRODINRA : 481340
  • WOS : 000391916200001

Citer

Joon Kwon, Vianney Perchet. Gains and losses are fundamentally different in regret minimization: the sparse case. Journal of Machine Learning Research, 2016, 17 (227), pp.1-32. ⟨hal-02630070⟩
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