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I'm not sure that "Bayesian genetic algorithms" is a real term or even a concept in research. For a while now, I've preferred genetic algorithms as my go-to heuristic optimization technique, as they're relatively easy to implement, can produce an output relatively quickly, and generally get good (or not bad) decision recommendations. Concurrently, I've been using Probabilistic programming to estimate things like per channel marketing budget allocation, inferring parameters such as time-to-effect and saturation.

Previously, I would use MLE results and linear programming to arrive at optimal decisions; however, I've found that this neglects the variance component of these parameter estimates. But by using GAs in conjunction with a "stochastic reward function" (a function defined by parameter estimates sampled from the posterior chain) I'm able to account for this variance; I've been generally pleased by the results.

When using genetic algorithms with MLE estimates, the algorithm will generally converge and stay put, as consecutive steps away from a local optimal will be necessary to reach another local (or the global) optima. However, a stochastic reward function, (in my experience) keeps the algorithm "jumping" throughout iterations. Somewhat like MCMC sampling, after a warm-up period, the rewards found in each iteration seem to bounce around a certain value. And this would give us a probabilistic estimate of the maximum expected reward.

Is anyone else doing this? Or something similar?

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I had some trouble understanding your question, to be honest, but...

  • Yes, Bayesian genetic algorithms are a thing. Take a look at Ter Braak's (2006) work on Differential Evolution Markov Chains. This is a Bayesian sampler that uses a genetic algorithm to efficiently propose parameter values to evaluate on high-dimensional problems.
  • It really isn't clear that the distribution of samples in the approach you describe should match the posterior distribution, so I wouldn't put too much trust in this method without further verification.
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  • $\begingroup$ Hi, maybe this will add some clarification: Constraints are sometimes deterministic and in such a situation, linear programming (simplex algo) offers a clean way to optimize decisions. You can use MLE point estimates as deterministic constraints in linear programming. However, when constraints are sampled from a distribution, linear programming is no longer appropriate. I used a genetic algorithm, which iteratively evolves whereby the constraints, which the solutions are subject to, are randomly drawn from the posterior chain. Notionally, this helps estimate the variance around the optima. $\endgroup$
    – jbuddy_13
    Mar 9, 2021 at 18:59
  • $\begingroup$ Cool. I have no idea if that would work or not, but then I'm not an expert on MCMC samplers, so I wouldn't know. $\endgroup$
    – Eoin
    Mar 9, 2021 at 19:36
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What you describe sounds like EDAs: https://en.m.wikipedia.org/wiki/Estimation_of_distribution_algorithm

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