Prediction With Expert Advice

Prediction with expert advice is a subfield of competitive on-line prediction in which the strategies in the benchmark class are free agents. When understood in a wide sense (as in Cesa-Bianchi and Lugosi 2006), prediction with expert advice is synonymous with competitive on-line prediction.

When strategies are free agents, or experts, the protocol of a game of prediction with expert advice is

Players: Experts, Forecaster, Reality
Protocol:

Initialize ⚠ $L_{0} = 0, L_{0} (k) = 0, k = 1, 2, \dot{s}$

FOR ⚠ $t = 1, 2, \dot{s}$ :

Experts announce ⚠ $γ^{k} \in Γ, k = 1, 2, \dot{s}$

Forecaster announces ⚠ $γ \in Γ$

Reality announces ⚠ $ω \in Ω$

Update cumulative loss ⚠ $L_{t} = L_{t - 1} + λ (ω, γ)$ , ⚠ $L_{t} (k) = L_{t - 1} (k) + λ (ω, γ_{k}), k = 1, 2, \dot{s}$

END

These are some open problems:

Find the n-experts separation curve.

Bibliography

Nicolo Cesa-Bianchi and Gabor Lugosi. Prediction, Learning, and Games. Cambridge: Cambridge University Press, 2006.