Multi-Armed Bandits with Betting

In this paper we consider an extension where the gambler has, at each round, K coins available for play, and the slot machines accept bets. If the player bets m coins on a machine, then the machine will return m times the payoff of that round. It is important to note that betting m coins on a machine results in obtaining a single sample from the rewards distribution of that machine (multiplied by m), not m independent samples. At each round, the gambler must divide all of his or hersK coins among the machines in such a way as to maximize the total expected payoff.