## Abstract

In this paper we consider learning in passive setting but with a slight modification. We assume that the target expected loss, also referred to as target risk, is provided in advance for learner as prior knowledge. Unlike most studies in the learning theory that only incorporate the prior knowledge into the generalization bounds, we are able to explicitly utilize the target risk in the learning process. Our analysis reveals a surprising result on the sample complexity of learning: by exploiting the target risk in the learning algorithm, we show that when the loss function is both strongly convex and smooth, the sample complexity reduces to O(log (1/ε)), an exponential improvement compared to the sample complexity O(1/ε) for learning with strongly convex loss functions. Furthermore, our proof is constructive and is based on a computationally efficient stochastic optimization algorithm for such settings which demonstrate that the proposed algorithm is practically useful.

Original language | English (US) |
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Pages (from-to) | 252-269 |

Number of pages | 18 |

Journal | Journal of Machine Learning Research |

Volume | 30 |

State | Published - Jan 1 2013 |

Event | 26th Conference on Learning Theory, COLT 2013 - Princeton, NJ, United States Duration: Jun 12 2013 → Jun 14 2013 |

## All Science Journal Classification (ASJC) codes

- Software
- Control and Systems Engineering
- Statistics and Probability
- Artificial Intelligence