Dynamic Learning Rate Adjustment Algorithm

Developing an investment portfolio for the stock market that will yield positive returns is the primary goal of investors worldwide. A variety of models and algorithms have been developed to decide upon a distribution which maximizes gains in the market, a few examples being the Geometric Brownian Motion model and the universal portfolio. One particular algorithm, known as online gradient descent, can be used for portfolio management with reasonable success. Its performance depends heavily, however, on the choice of the learning rate η, and it is difficult to know a priori which values will yield the best results. In our project, we explored various means of adjusting η based on different attributes of the stock market in an attempt to determine a more systematic approach to dynamically learn profitable values of η. One especially promising algorithm involved an implementation of multiplicative weights, where each expert is represented by a gradient descent algorithm with a unique value for η. To determine the profitability of our algorithms, we tested them on a variety of long-term daily-resolution stock data sets from many different markets.