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Regret is a common criteria to optimize in online learning. I'm wondering if anyone knows of other alternative criteria to optimize that have been proposed or explored in an online learning problem. References and links to papers, blogs, etc. are encouraged.

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It occurred to me after reconsidering this again after some months that the regret can be defined as a different of a (time-averaged) loss and an expected loss. Using this intuition the loss function can be anything.

In particular if you only can about point estimates, consider a linear loss function. If you care about variances consider a quadratic or other loss function similarly chosen to handle variance estimates. For other scenarios similar comments apply.

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