  In online portfolio optimization the investor makes decisions based on new,
continuously incoming information on financial assets (typically their prices).
In our study we consider a learning algorithm, namely the Kiefer--Wolfowitz
version of the Stochastic Gradient method, that converges to the log-optimal
solution in the threshold-type, buy-and-sell strategy class.
  The systematic study of this method is novel in the field of portfolio
optimization; we aim to establish the theory and practice of Stochastic
Gradient algorithm used on parametrized trading strategies.
  We demonstrate on a wide variety of stock price dynamics (e.g. with
stochastic volatility and long-memory) that there is an optimal threshold type
strategy which can be learned. Subsequently, we numerically show the
convergence of the algorithm. Furthermore, we deal with the typically
problematic question of how to choose the hyperparameters (the parameters of
the algorithm and not the dynamics of the prices) without knowing anything
about the price other than a small sample.
