Solving convex programs by random walks
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Static optimality and dynamic search-optimality in lists and trees
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Fast Universalization of Investment Strategies with Provably Good Relative Returns
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Efficient algorithms for universal portfolios
The Journal of Machine Learning Research
Online convex optimization in the bandit setting: gradient descent without a gradient
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Online trading algorithms and robust option pricing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
IEEE Transactions on Signal Processing
Online optimization with switching cost
ACM SIGMETRICS Performance Evaluation Review
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A constant rebalanced portfolio is an investment strategy which keeps the same distribution of wealth among a set of stocks from day to day. There has been much work on Cover's Universal algorithm, which is competitive with the best constant rebalanced portfolio determined in hindsight (D. Helmbold et al., 1995; A. Blum and A. Kalai, 1999; T.M. Cover and E. Ordentlich, 1996). While this algorithm has good performance guarantees, all known implementations are exponential in the number of stocks, restricting the number of stocks used in experiments. We present an efficient implementation of the Universal algorithm that is based on non-uniform random walks that are rapidly mixing (D. Applegate and R. Kannanm, 1991). This same implementation also works for non-financial applications of the Universal algorithm, such as data compression (T.M. Cover, 1886) and language modeling (A. Kalai et al., 1999).