Adaptive Hedge

Most methods for decision-theoretic online learning are based on the Hedge algorithm, which takes a parameter called the learning rate. In most previous analyses the learning rate was carefully tuned to obtain optimal worst-case performance, leading to suboptimal performance on easy instances, for example when there exists an action that is significantly better than all others. We propose a new way of setting the learning rate, which adapts to the difficulty of the learning problem: in the worst case our procedure still guarantees optimal performance, but on easy instances it achieves much smaller regret. In particular, our adaptive method achieves constant regret in a probabilistic setting, when there exists an action that on average obtains strictly smaller loss than all other actions. We also provide a simulation study comparing our approach to existing methods.Comment: This is the full version of the paper with the same name that will appear in Advances in Neural Information Processing Systems 24 (NIPS 2011), 2012. The two papers are identical, except that this version contains an extra section of Additional Materia

Adaptive Control System Having Hedge Unit And Related Apparatus And Methods

The invention includes an adaptive control system used to control a plant. The adaptive control system includes a hedge unit that receives at least one control signal and a plant state signal. The hedge unit generates a hedge signal based on the control signal, the plant state signal, and a hedge model including a first model having one or more characteristics to which the adaptive control system is not to adapt, and a second model not having the characteristic(s) to which the adaptive control system is not to adapt. The hedge signal is used in the adaptive control system to remove the effect of the characteristic from a signal supplied to an adaptation law unit of the adaptive control system so that the adaptive control system does not adapt to the characteristic in controlling the plant.Georgia Tech Research Corporatio

Adaptive control system having hedge unit and related apparatus and methods

The invention includes an adaptive control system used to control a plant. The adaptive control system includes a hedge unit that receives at least one control signal and a plant state signal. The hedge unit generates a hedge signal based on the control signal, the plant state signal, and a hedge model including a first model having one or more characteristics to which the adaptive control system is not to adapt, and a second model not having the characteristic(s) to which the adaptive control system is not to adapt. The hedge signal is used in the adaptive control system to remove the effect of the characteristic from a signal supplied to an adaptation law unit of the adaptive control system so that the adaptive control system does not adapt to the characteristic in controlling the plant

A parameter-free hedging algorithm

We study the problem of decision-theoretic online learning (DTOL). Motivated by practical applications, we focus on DTOL when the number of actions is very large. Previous algorithms for learning in this framework have a tunable learning rate parameter, and a barrier to using online-learning in practical applications is that it is not understood how to set this parameter optimally, particularly when the number of actions is large. In this paper, we offer a clean solution by proposing a novel and completely parameter-free algorithm for DTOL. We introduce a new notion of regret, which is more natural for applications with a large number of actions. We show that our algorithm achieves good performance with respect to this new notion of regret; in addition, it also achieves performance close to that of the best bounds achieved by previous algorithms with optimally-tuned parameters, according to previous notions of regret.Comment: Updated Versio

Adaptive filtering for stochastic risk premia in bond market

We consider the adaptive filtering problem for estimating the randomly changing risk premium and its system parameters for zero-coupon bond models. The term structure model for a zero-coupon bond is formulated including the stochastic risk-premium factor. We specify our observation data from the yield curve and bond data which are used to hedge some option claims. For the xed system parameters, the Kalman filter for the risk-premium and the factor process is constructed first. Secondly, by using the parallel filtering technique and resampling technique commonly used in particle filters, the on-line estimation algorithm for model parameters is constructed. Some simulation studies are nally presented

Hedge fund return predictability; To combine forecasts or combine information?

While the majority of the predictability literature has been devoted to the predictability of traditional asset classes, the literature on the predictability of hedge fund returns is quite scanty. We focus on assessing the out-of-sample predictability of hedge fund strategies by employing an extensive list of predictors. Aiming at reducing uncertainty risk associated with a single predictor model, we first engage into combining the individual forecasts. We consider various combining methods ranging from simple averaging schemes to more sophisticated ones, such as discounting forecast errors, cluster combining and principal components combining. Our second approach combines information of the predictors and applies kitchen sink, bootstrap aggregating (bagging), lasso, ridge and elastic net specifications. Our statistical and economic evaluation findings point to the superiority of simple combination methods. We also provide evidence on the use of hedge fund return forecasts for hedge fund risk measurement and portfolio allocation. Dynamically constructing portfolios based on the combination forecasts of hedge funds returns leads to considerably improved portfolio performance