What would be a good machine learning model to predict the next vending machine location? I want to build a machine learning model to choose a location for the next vending machine in Boston. I want to divide the map into small neighborhood, and I came up with features that are related to the geospatial locations and user information.
One paradox that concerns me is that: we'll use past vending machines' features (X) and sales (y) to train the model; in that case, the model that predict the next vending machine will likely choose some place very close to the old vending machine locations. But at the same time, we wouldn't want to build a vending machine in exactly the same location as an older one.
Additionally, vending machines are usually built one by one as time goes by; the model used to choose the 10th vending machine in the city, and the 1300th vending machine could be very different. This almost made me think this is a time-series problem. How to build a model that can take these problems into consideration? Any insight on features, logistics, or models are all deeply appreciated!

I would try to create some explanatory variables for each geographic location, such as the income distribution at this location, traffic, amount of pedestrians, and similar features. Then I would use the data from existing vending machines to train a model that predicts your response variable from those explanatory variables, e.g. the profit made by a vending machine.
If that works, you can predict for each spot in the city the amount of money made by a vending machine placed there. Then you select the places where this prediction returns particularly favorable values and where you don't already have a vending machine.
You might also do an experiment and place some new vending machines next to already existing ones, use (some function of) the distances to other vending machines as an additional explanatory variable, and thus learn how the "vending machine density" of a location affects the sales of a new vending machine.
I don't really see a time series property here. I would guess that the sales numbers of a vending machine are only affected by the explanatory features referred to above. If the sales numbers of a vending machine depend on those of previously installed vending machines then, I would suspect, only via those features.
