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The Golden Rule

Instead of finding x to optimize a function,

find a distribution over x that optimizes
an associated expectation value.

(This transforms optimization problems over discrete or hybrid domains to problems over continuous domains.)


  1. Works for arbitrary (mixed) data types x. P(x) is always a vector of real numbers, no matter what data type x is.
  2. Leverages techniques for the optimization of Euclidean vectors — the most powerful optimization techniques we have. ("Gradient descent for symbolic variables.")
  3. P(x) provides sensitivity information (i.e., which components of x are most important).
  4. Can be "seeded" with solutions of other algorithms: peaks of initial P(x).
  5. Can include Bayesian prior knowledge.
  6. Automatically accommodates noisy, poorly modeled problems.

  7. Deep connections with statistical physics and game theory. So...

    • Especially suited for distributed domains.
    • Especially suited for very large problems.
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