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Meta optimization and its application to portfolio selection

Several data mining algorithms use iterative optimization methods for learning predictive models. It is not easy to determine upfront which optimization method will perform best or converge fast for such tasks. In this paper, we analyze Meta Algorithms (MAs) which work by adaptively combining iterates from a pool of base optimization algorithms. We show that the performance of MAs are competitive with the best convex combination of the iterates from the base algorithms for online as well as batch convex optimization problems. We illustrate the effectiveness of MAs on the problem of portfolio selection in the stock market and use several existing ideas for portfolio selection as base algorithms. Using daily S\&P500 data for the past 21 years and a benchmark NYSE dataset, we show that MAs outperform existing portfolio selection algorithms with provable guarantees by several orders of magnitude, and match the performance of the best heuristics in the pool.