Bandits with an Edge [article]

Dotan Di Castro, Claudio Gentile, Shie Mannor
2011 arXiv   pre-print
We consider a bandit problem over a graph where the rewards are not directly observed. Instead, the decision maker can compare two nodes and receive (stochastic) information pertaining to the difference in their value. The graph structure describes the set of possible comparisons. Consequently, comparing between two nodes that are relatively far requires estimating the difference between every pair of nodes on the path between them. We analyze this problem from the perspective of sample
more » ... ty: How many queries are needed to find an approximately optimal node with probability more than 1-δ in the PAC setup? We show that the topology of the graph plays a crucial in defining the sample complexity: graphs with a low diameter have a much better sample complexity.
arXiv:1109.2296v1 fatcat:rqaxdtmarzgvfpux2w3ze7yzdi