On Thu, Mar 6, 2014 at 12:21 AM, Laurens Van Houtven <_...@lvh.cc> wrote:
> > Yep. A big part of the issue is that the *real* function that maps grant > fraction to probability of coming is of course unknowable. A linear > approximation is an excellent start. Once I have some test data I'll be > able to tell for sure, but I imagine a closer approximation might look more > like x**2 than x over [0, 1] (e.g. when I give someone 50% of their grant, > the odds they'll come are closer to 25% than to 50%). Are Choco/Loco > limited to linear programming? > No, it doesn't have to be linear. Let's say the probability p = (allocated/requested)^2 for a given person. So we're trying to maximize the sum of score*p. Let's reorganize score*p to isolate the variable we're solving for from the known quantities: score*p = score*(allocated/requested)^2 = allocated * allocated * (score/(requested^2)) The score and the requested amount are known in advance for a given person, so in the sample code I provided, the precomputed "grant-value" would no longer be based on score/requested, but score/(requested^2). Then when solving for the allocations, you instead maximize: (apply $+ (map $* (map $* allocation-vars allocation-vars) grant-values)) Those are the only changes you need to make for it to be based on quadratic versus linear. Here is the revised code, also incorporating the dynamic scaling suggestion I put in the comments of the other gist: https://gist.github.com/Engelberg/9385992 It definitely makes a difference for the toy example given in the problem. In both versions, it allocates $120 to Alex (guaranteeing the highest scored person). In the linear version, it gives the $80 to David (choosing the 4/5 probability of getting a 4 [an expected value of 16/5], over a certainty of getting a 3, since 16/5>3) In the non-linear version, it gives the $80 to Mark (guaranteeing a person worth 3, rather than a 16/25 probability of getting a 4). -- You received this message because you are subscribed to the Google Groups "Clojure" group. To post to this group, send email to clojure@googlegroups.com Note that posts from new members are moderated - please be patient with your first post. To unsubscribe from this group, send email to clojure+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/clojure?hl=en --- You received this message because you are subscribed to the Google Groups "Clojure" group. To unsubscribe from this group and stop receiving emails from it, send an email to clojure+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/groups/opt_out.
