I have the following contrived scenario... I've participated on various auction platforms where I bid on widgets. Assume that win/loss outcomes on individual platforms are well-separated such that for each platform k there exists a positive value x_k where P(win|bid>x_k) = 1 and P(win|bid<=x_k) = 0. There is a new platform k' where I can bid on widgets. I want to determine x_k as quickly as possible.
I can overcome the cold start problem to finding x_k' by modeling a win probability curve P(win|bid==x) derived from my performance on the other platforms. Such a model would help determine where to make my first bid. Based on the win/loss outcome from that first bid, how should I bid in successive auctions on platform k'?
In a way, this feels like it becomes a binary search problem after the cold start but that becomes impractical when you consider that I would not want to overbid some value z such that z >> x_k'. Doing so would lead me to go broke in a real-world example. Is there a way to continue to use the win probability curve from the historical performance as a soft prior combined with the hyper-relevant early outcomes on this new platform to find x_k' in a way that is both "fast" and financially prudent?
