Excess Risk Bounds for Exponentially Concave Losses

Understand

The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings.

• Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, and negative logarithm loss in portfolio management.
• In batch setting, we obtain sharp bounds on the performance of empirical risk minimization performed in a linear hypothesis space and with respect to the exp-concave loss functions.
• We also extend the results to the online setting where the learner receives the training examples in a sequential manner.