Since the high frequency asset allocation adjustment of traditional portfolio strategies in each investment period results in high transaction costs and poor final returns, a Semi-Exponential Gradient portfolio (SEG) strategy based on machine learning and online learning was proposed. Firstly, the SEG strategy model was established by adjusting the portfolio only in the initial period of each segmentation of the investment period and not trading in the rest of the time, then a objective function was constructed by combining income and loss. Secondly, the closed-form solution of the portfolio iterative updating was solved by using the factor graph algorithm, and the theorem and its proof of the upper bound on the cumulative loss of assets accumulated were given, guaranteeing the return performance of the strategy theoretically. The experiments were performed on several datasets such as the New York Stock Exchange. Experimental results show that the proposed strategy can still maintain a high return even with the existence of transaction costs, confirming the insensitivity of this strategy to transaction costs.

Focused on the issue that noisy data, single period hypothesis and nonstationary prediction are not fully considered in the existing mean reversion strategy, an efficient OnLine Autoregressive moving average Reversion (OLAR) algorithm based on multi-period was proposed. Firstly, a stock price forecasting model was given by using the autoregressive moving average algorithm, and it was converted into an autoregressive model by a reasonable assumption. Then, an objective function was given by combining the loss function and a regular term, and a closed solution was obtained by using the second-order information of the loss function. The portfolio's closed-form update was obtained by using the online Passive Aggressive (PA) algorithm. Theoretical analysis and experimental results show that, compared with Robust Median Reversion (RMR), the accumulated profits of OLAR increase by 455.6%, 221.5%, 11.2% and 50.3% on NYSE (N), NYSE (N), Dow Jones Industrial Average (DJIA) and MSCI datasets respectively. Meanwhile, the results of statistical test show that the superior performance of OLAR is not caused by random factors. In addition, compared with algorithms such as RMR and Online Moving Average Reversion (OLMAR), OLAR achieves the highest annualized percentage yield, Sharpe ratio and Calmar ratio. Finally, the running time of OLAR is almost the same as that of RMR and OLMAR, therefore OLAR is suitable for large-scale real-time applications.