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Why is a continuous action space harder than a discrete one?

  • A.Continuous spaces always contain far more states than discrete ones
  • B.Sensors cannot measure the outcome of a continuous action
  • C.The best action cannot be found by enumerating the possibilities
  • D.Continuous actions take longer for the actuators to execute

Answer: C

With infinitely many options, the agent must optimise over the space rather than compare a list, which brings in gradients, sampling and parametrised policies. Robot control and vehicle steering are the usual examples. Execution time, state count and measurement are separate concerns. Whether a decision can be made by enumeration or requires optimisation is one of the sharpest practical divisions in agent design and it determines the whole class of algorithm used.

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