Not really. You're making the choice to explore or exploit at each branch. It's closer to an A-star search, where the weights and heuristics are uncovered over time.
Also, the typical framing of the problem is the same "kind" of choice being repeatedly executed (e.g., betting on a coin-flip of unknown bias, or balancing the gain of consumer purchasing information vs exploiting known information when setting items into aisle end-caps in a grocery store). That has a lot more structure than arbitrary graphs, enough so to make it worthy of its own dedicated study (especially given the real-world applicability).
Also, the typical framing of the problem is the same "kind" of choice being repeatedly executed (e.g., betting on a coin-flip of unknown bias, or balancing the gain of consumer purchasing information vs exploiting known information when setting items into aisle end-caps in a grocery store). That has a lot more structure than arbitrary graphs, enough so to make it worthy of its own dedicated study (especially given the real-world applicability).