Interesting post. "All models are wrong, some models are useful" - Box. This one seems useful and is simple to explain. It started me thinking about the distr

Interesting post. "All models are wrong, some models are useful" - Box. This one seems useful and is simple to explain. It started me thinking about the distribution of customers who convert, viewed as a function of ad spend. I am not sure there is any reason this distribution need have a particularly simple shape, or even be continuous. E.g. maybe some customers can be addressed and convert at a modest ad spend, while if you double the ad spend you don't get any more conversions, then if you double ad spend again maybe suddenly you're out bidding a competitor and the number of conversions shoots up, perhaps giving you a better overall net profit than if you stopped earlier with a modest budget. This might mean that the curve we're trying to maximise (net profit) has more than one local maxima, or might not even be continuous. There's probably also an explore/exploit tradeoff here as well: how much of the total budget should you spend sampling to try out different ad spends across the whole range of plausible values (from 0 up to the long term value of a conversion, I guess) to get enough data to start optimising.