24 research outputs found
Defensive online portfolio selection
The class of defensive online portfolio selection algorithms,designed for fi nite investment horizon, is introduced. The Game Constantly Rebalanced Portfolio and the Worst Case Game Constantly Rebalanced Portfolio, are presented and theoretically analyzed. The analysis exploits the rich set of mathematical tools available by means of the connection between Universal Portfolios and the Game- Theoretic framework. The empirical performance of the Worst Case Game Constantly Rebalanced Portfolio algorithm is analyzed through numerical experiments concerning the FTSE 100, Nikkei 225, Nasdaq 100 and S&P500 stock markets for the time interval, from January 2007 to December 2009, which includes the credit crunch crisis from September 2008 to March 2009. The results emphasize the relevance of the proposed online investment algorithm which signi fi cantly outperformed the market index and the minimum variance Sharpe-Markowitz’s portfolio.on-line portfolio selection; universal portfolio; defensive strategy
The on-line shortest path problem under partial monitoring
The on-line shortest path problem is considered under various models of
partial monitoring. Given a weighted directed acyclic graph whose edge weights
can change in an arbitrary (adversarial) way, a decision maker has to choose in
each round of a game a path between two distinguished vertices such that the
loss of the chosen path (defined as the sum of the weights of its composing
edges) be as small as possible. In a setting generalizing the multi-armed
bandit problem, after choosing a path, the decision maker learns only the
weights of those edges that belong to the chosen path. For this problem, an
algorithm is given whose average cumulative loss in n rounds exceeds that of
the best path, matched off-line to the entire sequence of the edge weights, by
a quantity that is proportional to 1/\sqrt{n} and depends only polynomially on
the number of edges of the graph. The algorithm can be implemented with linear
complexity in the number of rounds n and in the number of edges. An extension
to the so-called label efficient setting is also given, in which the decision
maker is informed about the weights of the edges corresponding to the chosen
path at a total of m << n time instances. Another extension is shown where the
decision maker competes against a time-varying path, a generalization of the
problem of tracking the best expert. A version of the multi-armed bandit
setting for shortest path is also discussed where the decision maker learns
only the total weight of the chosen path but not the weights of the individual
edges on the path. Applications to routing in packet switched networks along
with simulation results are also presented.Comment: 35 page
Logistic Regression in Datastreams
Learning from data streams is a well researched task both in theory and practice. As remarked by Clarkson, Hazan and Woodruff, many classification problems cannot be very well solved in a streaming setting. For previous model assumptions, there exist simple, yet highly artificial lower bounds prohibiting space efficient one- pass algorithms. At the same time, several classification algorithms are often successfully used in practice. To overcome this gap, we give a model relaxing the constraints that previously made classification impossible from a theoretical point of view and under these model assumptions provide the first (1 + epsilon) -approximate algorithms for sketching the objective values of logistic regression and perceptron classifiers in data streams
The perceptron algorithm versus winnow: linear versus logarithmic mistake bounds when few input variables are relevant
AbstractWe give an adversary strategy that forces the Perceptron algorithm to make Ω(kN) mistakes in learning monotone disjunctions over N variables with at most k literals. In contrast, Littlestone's algorithm Winnow makes at most O(k log N) mistakes for the same problem. Both algorithms use thresholded linear functions as their hypotheses. However, Winnow does multiplicative updates to its weight vector instead of the additive updates of the Perceptron algorithm. In general, we call an algorithm additive if its weight vector is always a sum of a fixed initial weight vector and some linear combination of already seen instances. Thus, the Perceptron algorithm is an example of an additive algorithm. We show that an adversary can force any additive algorithm to make (N + k −1)2 mistakes in learning a monotone disjunction of at most k literals. Simple experiments show that for k ⪡ N, Winnow clearly outperforms the Perceptron algorithm also on nonadversarial random data