We consider strategies which use a collection of popular technical indicators as input and seek a profitable trading rule defined in terms of them. We consider two popular computational learning approaches, reinforcement learning and genetic programming, and compare them to a pair of simpler methods: the exact solution of an appropriate Markov decision problem, and a simple heuristic. We find that although all methods are able to generate significant in-sample and out-of-sample profits when transaction costs are zero, the genetic algorithm approach is superior for non-zero transaction costs, although none of the methods produce significant profits at realistic transaction costs. We also find that there is a substantial danger of overfitting if in-sample learning is not constrained.