It’s a common conundrum: should I stay put or go in search of greener pastures? The question comes up in career choices, animal foraging, and investment strategies. In Physical Review Letters, researchers have formulated a general model for comparing the exploitation of a known resource vs the exploration for potentially more advantageous resources. The model allows the calculation of an optimal migration rate that maximizes profit or growth.
Previous work has tackled the exploration-exploitation tradeoff. A famous example is the multiarm bandit, in which a gambler has to decide whether to stay at one “lucky” slot machine (i.e., a one-arm bandit) or to venture out and take a chance with other machines. Scientists have solved this problem for specific cases, but a general solution framework has yet to be devised. Thomas Gueudré and his colleagues from the École Normale Supérieure in Paris, France, have now created a model that encompasses the general features of exploration vs exploitation.
The authors start by assuming a network of nodes, where each node has a random amount of a certain resource (e.g., food, money). The resource at a node changes in time, such that a “lucky” or “unlucky” node stays that way for a certain characteristic time. Based on this, the researchers show that the migration rate between nodes can be chosen so as to maximize the rate of return. In other words, the best strategy is to find a middle ground between migrating too slowly (staying put) and too quickly (constantly wandering). The team applied their equations to similar problems in materials sciences, like the migration of magnetic vortices between pinning sites inside a superconductor. The results show that there exists an optimal migration, or hopping, rate (tunable through an external magnetic field, for example) that can maximize the critical current of the superconductor. – Michael Schirber