Reviews: Efficient Online Portfolio with Logarithmic Regret

This paper introduces a new algorithm (BARRONS) for the online portfolio optimization problem. This is in contrast to the Cover's universal portfolio algorithm, online newton step, and exponentiated gradient, which each achieve at most two of these three goals. The algorithm itself is an application of the online mirror descent framework, using the less-classical log-barrier regularizer. The paper provides good intuition for how the algorithm is able to avoid dependence on the gradient norm: the gradient norm is only big if a previously poorly-performing stock starts to perform well. As a result the learner has a kind of "surplus" of regret that it can fall back on while adapting to the new stock.