Trying to learn winners

Let's digress to a protfolio selection algorithm. The most direcxt approach to expert learning and portfolio selection is a "reward based weighted average prediction" algorithm which adaptively computes a weighted average of experts by gradually increasing (by multiplicative or additive factors) the relative weights of the more successful experts.

consider the exponential gradient algorithm by Helmboldt et al:

b_{t+1}(j) = b_t(j) . exp{\eta x_t(j) / b_t.x_t} / \Sum [b_t(j) . exp{\eta x_t(j) / b_t.x_t}]

where \eta is a leraning parameter which is proportional to x_min, root(log m) and inversely propotional to root(n).

setting \eta to 0 for instance is nothing but the uniform cbal and hence is not universal.
combining a small learing rate with a "reasonably balanced" market we expect the performance of EG to be similar to that of the uniform CBAL and this is confirmed by experiments.