Maximizing the length of a success run for many-armed bandits

One of a number of Bernoulli processes is selected at each of a number of stages. A success at stage i is worth α_i and the problem is to maximize the expected payoff before the first failure. Results of Berry and Viscusi (1981) are generalized. In particular, we show that there is always an optimal strategy that uses a single process exclusively and indefinitely whenever the arms are independent and the discount sequence (α₁, α₂,…) is superregular. There is not always a similar reduction in the number of strategies when the discount sequence is not superregular.