Stochastic gradient descent (SGD) and exponentiatedgradient (EG) update methods are widely used in signal processing and machine learning. This study introduces a novel family of generalized exponentiatedgradient up...
详细信息
Stochastic gradient descent (SGD) and exponentiatedgradient (EG) update methods are widely used in signal processing and machine learning. This study introduces a novel family of generalized exponentiatedgradient updates (EGAB) derived from the alpha-beta (AB) divergence regularization. The EGAB framework provides enhanced flexibility for processing data with varying distributions, thanks to the tunable hyperparameters of the AB divergence. We explore the applicability of these updates in online portfolio selection (OLPS) for financial markets with the goal of developing algorithms that achieve high risk-adjusted returns, even under relatively high transaction costs. The proposed EGAB algorithms are developed using constrained gradient optimization with regularization terms, demonstrating their versatility in OLPS by unifying the directional search of various algorithms and enabling interpolation between them. Our analysis and extensive computer simulations reveal that EGAB updates outperform existing OLPS algorithms, delivering good results on several performance metrics, such as cumulative return, average excess return, Sharpe ratio, and Calmar ratio, especially when transaction costs are significant. In conclusion, this study introduces a new family of exponentiatedgradient updates and demonstrates their flexibility and effectiveness through extensive simulations across a wide range of real-world financial datasets.
We investigate the problem of estimating the proportion vector which maximizes the likelihood of a given sample for a mixture of given densities. We adapt a framework developed for supervised learning and give simple ...
详细信息
We investigate the problem of estimating the proportion vector which maximizes the likelihood of a given sample for a mixture of given densities. We adapt a framework developed for supervised learning and give simple derivations for many of the standard iterative algorithms like gradient projection and EM. In this framework the distance between the new and old proportion vectors is used as a penalty term. The square distance leads to the gradient projection update, and the relative entropy to a new update which we call the exponentiatedgradient update (EG(eta)). Curiously, when a second order Taylor expansion of the relative entropy is used, we arrive at an update EMeta which, for eta = 1, gives the usual EM update. Experimentally both the EMeta-update and the EG(eta)-update for eta > 1 outperform the EM algorithm and its variants. We also prove a polynomial bound on the rate of convergence of the EG(eta) algorithm.
暂无评论