From: olethrosdc@oohay.com   
      
   In expectation-maximisation algorithms, the maximisation normally takes a   
   single step. However, in some cases this is not possible. An example is   
   when gradient descent methods are used for the maximisation step. Since   
   the gradient descent is not guaranteed to reach the maximum, is the   
   stability of the EM algorithm guaranteed in this case?   
      
   I am asking this because I perceive some similarity between the EM with GD   
   for the M step and with gradient-descent methods for reinforcement   
   learning. In fact, RL learning with DP targets using GD (which is an   
   off-policy method) seems to be the same type of algorithm as EM with GD   
   for the M step. RL off-policy learning with gradient-descent has been   
   proven to diverge (i.e. convergence was disproved with simple   
   counterexamples).   
      
   So, what I am asking is: Do similar counterexamples that show divergence   
   exist for EM with GD? If yes, then intuitively, the instability should be   
   greatest when we perform stochastic GD, after each data point. Things   
   should be better if we use batch learning after each E step and perhaps   
   very good stability could be achieved if we have many GD iterations after   
   each E step in order to arpproach the maximum as much as possible.   
      
   Any ideas, papers, experience with EM+GD out there?   
      
   --   
   Christos Dimitrakakis   
   IDIAP (http://www.idiap.ch/~dimitrak/main.html)   
      
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