From: ted.dunning@gmail.com   
      
   On Mar 15, 3:37 am, jones...@emporia.edu wrote:   
   > In conventional capitalist economics one assumes value   
   > monism and a scalar utility   
      
   I really don't think that the convenience of having a scalar objective   
   function is philosophically related to capitalism.  The reason for   
   optimizing a scalar-valued objective is that it is a much simpler   
   problem to state.  Real numbers form a total order which lets the   
   definition of "optimum" make sense.   
      
   If the parameters are real valued then you also get things like   
   gradients and Hessians to work with.   
      
   > It may be, however, that value monism is wrong and we   
   > can not reduce all rewards to a single scalar   
      
   As you note, this idea is hardly new.   
      
   But you should observe that most approaches to multiple objective   
   optimization start with some way of defining an order function on R^n,   
   if only so that you can say what "optimum" means.  In many approaches,   
   this is done by defining some heuristic way of reducing the multiple   
   cost functions to a single value.   
      
   > Initial results suggest that use of a vector utility   
   > may make the system less likely of get stuck in local   
   > maxima.  If the system can not improve L, for example,   
   > it may be able to increase N.  After evolving for a while   
   > one may then find L and N can both improve.   
      
   This statement is way too over-arching.   
      
   First, there are many methods that avoid the problem of local minima   
   using scalar objectives.  These include simulated annealing various   
   evolutionary algorithms.  There are also a number of methods in many   
   settings that avoid the need for optimization, per se.  For instance,   
   maximum likelihood methods are often better replaced by sampling   
   techniques which evaluate posterior likelihoods directly.  Thus,   
   scalar objective functions with local minima are not a hopeless   
   problem.   
      
   Secondly, it has been known for some time that the introduction of   
   auxiliary variables can make many problems much easier.  Latent   
   variable techniques are an impressive example of exactly this.  For   
   instance, in regression problems where you are trying to estimate a   
   few parameters, it can be helpful to introduce two latent variables   
   per observed data point.  Thus, this idea that increasing the   
   dimensionality of the problem is useful is hardly novel.   
      
   Most importantly, though, all of this has nothing to do with   
   capitalism or alternatives.   
      
   But you may also have something interesting.   
      
   Can you say more about your specific examples and methods?   
      
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