Wei_Dai comments on Worse Than Random - Less Wrong

25 Post author: Eliezer_Yudkowsky 11 November 2008 07:01PM

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Comment author: Eliezer_Yudkowsky 12 November 2008 03:27:22AM 1 point [-]

To be precise, in every case where the environment only cares about your actions and not what algorithm you use to produce them, any algorithm that can be improved by randomization can always be improved further by derandomization.

Comment author: Wei_Dai 24 January 2010 01:45:30AM *  8 points [-]

It seems that randomization can serve as a general substitute for memory. It's not a perfect substitute, but whenever you don't want to, or can't, remember something for some reason, randomization might help.

Besides the example of The Absent-Minded Driver, I've realized there are other examples in cryptography:

  • nonces - Many encryption schemes require a unique nonce to be generated for each message to be encrypted. You can either pick random nonces, or keep a counter. But keeping a counter might be too troublesome, and you might be running in a virtual machine that can be rolled back from time to time, so it's usually better to use a random nonce, even though you'll need a longer nonce than if you used a counter (to keep the probability of collision sufficiently small).
  • distributed key search - You can either have a central server that hands out regions of the key space to search, or each participant can search a random region. The latter is less efficient in computing time, but more efficient in communications cost.

I might do a post on this, if I could figure out a way to think about why randomization substitutes for memory.

Comment author: pengvado 24 January 2010 04:27:33AM *  5 points [-]

if I could figure out a way to think about why randomization substitutes for memory.

Let A and B be actions leading to deterministic outcomes, and let C be some lottery between A and B. A rational agent will never prefer both C>A and C>B.

When you repeat the scenario without memory, the lottery is no longer exactly over choices the agent could deterministically make: the randomness is re-rolled in places where the agent doesn't get another decision. Despite what the options are labeled, you're really choosing between 2xA, 2xB, and a lottery over {2xA, 2xB, A+B}. Since the lottery contains an outcome that isn't available to the deterministic decision, it may be preferred.

I think this is equivalent to the role played by observational evidence in UDT1: Observations allow a constant strategy to take different actions in different places, whereas without any observations to distinguish agent instances you have to pick one action to optimize both situations. Of course good evidence is reliably correlated with the environment whereas randomness doesn't tell you which is which, but it's better than nothing.

Comment author: Tyrrell_McAllister 29 January 2010 09:50:14PM 0 points [-]

I might do a post on this, if I could figure out a way to think about why randomization substitutes for memory.

I had some comments in this thread that outline the way that I think about this.

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