# K 29

K29 is an algorithm given by Defensive Forecasting tecnique to make forecasts of the events correspondingly to the purpose of competitive on-line prediction. The following algorithm was firsly named K29*, but now it is known as K29. If the forecaster follows this algortihm, he will compete with all functions on from the Reproducing Kernel Hilbert Space corresponding to the taken kernel.

**K29 algorithm**:

Parameter: forecast-continuous kernel K on

FOR :

Read

Set for .

If , output . Otherwise, output any root

Read

END.

Such forecasts have the property calibration-cum-resolution. It is not proven, when if the function has the same sign in 0 and 1, it has no roots. But in practice it usually holds, and the root is unique.

### Bibliography

- On-line regression competitive with reproducing kernel Hilbert spaces (extended abstract). In:
*Theory and Applications of Models of Computation. Proceedings of the Third Annual Conference on Computation and Logic*(ed by J-Y Cai, S B Cooper and A Li),*Lecture Notes in Computer Science*, vol 3959, pp 452–463. Berlin: Springer, 2006. - Non-asymptotic calibration and resolution.
*Theoretical Computer Science*(Special Issue devoted to ALT 2005)**387**, 77–89 (2007).