cygaril

Formalizations for the competition were done by hand.

Proofs are here: https://storage.googleapis.com/deepmind-media/DeepMind.com/B...

Come up with many possible answers, formalize them all, and then try to prove or disprove each of them.

One possible cost measure is thr number of evaluations of the probability function.

I've done that many times and never used exact equality comparisons.

If you do exact comparisons for any non-trivial cases, you'll find different compilers, optimization settings, runtimes, and processors give different results.

Only if each value is equally likely. If you see $1,000 but figure the envelope-filler is a lot more likely to have been willing to put $1,500 in than $3,000 then you should stick.

You're assuming here that there are discrete stages that do different things. I think a better way to conceptualise these deepnets is that they're doing exactly what you want - each layer is "correcting" the mistakes of the previous layer.

Standard RL algorithms will converge to optimal play versus a fixed opponent, but will not find an optimal policy via self play.

One intuitive way to see this is that a sequence of improving pure policies A < B < C < etc. will converge to optimal play in a perfect information game like chess, but not necessarily in an imperfect information game like rock/paper/scissors where Rock < Paper < Scissors < Rock, etc

Seems to have missed the existence of jax.jit, which basically constructs an XLA program (call it a graph if you like) from your Python function which can then be optimized.

Or our entire evolutionary history of data.

I think you were right the first time.

Because you might think that people having employment is a good thing, worth encouraging through the tax / benefit system.

Also, tax credits can be (and are) paid weekly.

The proposed approach amounts to subsidizing human labour over automation. That night be a legitimate public policy aim.

I agree that rejection is always tough. I spent a year manoeuvring to be made redundant from a job I wanted to leave (e.g. told my boss I wanted to go, made sure everything I did was covered by other people). And still, when they did finally let me go, the rejection did hurt quite a bit.

You don't necessarily need the distribution under the alternative to determine the values for which the likelihood ratio will be highest. In your example, the tails will be the areas of maximum likelihood for any (symmetric) alternative.

A more general method is to use the likelihood ratio, ie the ratio of the likelihood of an outcome under the alternative hypothesis to its likelihood under the null hypothesis. And then pick the outcomes which for which this ratio is highest as the ones which will cause you to reject the null hypothesis. Equivalently, the p-value is the probability under the null hypothesis that the likelihood ratio would be at least this large.

This works in the discrete case too, and gives p=1/32 in the original coin flip case.

From The Guardian:

Student housing doesn’t officially classify as housing. It falls into the murky category of “sui generis” (Latin for “of its own kind”). As it falls outside a specific use class, it doesn’t have to adhere to the usual standards associated with dwellings (class C3). Local authorities differ in the their approaches, but student accommodation is usually either treated as a hotel (C1) or residential institution (C2), the same category as care homes, hospitals and boarding schools. Due to their limited occupation, these building types are immune from many of the codes that govern residential dwellings – from space standards to daylight and acoustics.

Daylight is the relevant thing here. This building would be too dark inside to meet housing standards, but it's okay for student accommodation.

[0] https://www.theguardian.com/artanddesign/2013/aug/29/carbunc...

Being only five hundred lines doesn't disqualify it from being a library.

But being impossible to safely integrate into other projects because of illegal names and polluting the global namespace does.

This is at best a rough proof of concept which could at some point be turned into a library.

Building regulations for student accommodation are less stringent than for regular housing, so possibly these designs wouldn't be allowed otherwise.

Yes, me too - I had two weeks of constant headaches and both physical and mental exhaustion. I still went to work, but I got basically nothing done for the whole fortnight.

Still, I'm glad I did it - it was definitely an unhealthy addiction for me. I'm now 15 or so years mostly caffeine-free.

Two players having the same hand is no issue - just split the pot. This already happens when neither player can improve on the five community cards.

Adding five of a kind also seems like a pretty easy adjustment.

The most obvious difference is the possibility of cards matching both suit and rank. So if you have HA HK and the flop is HA HJ S2 you have both top pair and also a very strong flush draw (although HA HA would be better), a combo which is impossible on that board with a single deck.

Online game clients which attempt to verify that a human is playing rather than a bot.

Branded medicines are more effective and result in fewer reported side effects, despite being pharmacologically identical.

Many citations available, eg https://www.ncbi.nlm.nih.gov/m/pubmed/23115341/?i=2&from=/26...

There are lots of other examples, depending on what you consider to be autonomous robotics - grass mowers, delivery drones, autonomous trains, elevators, vending machines.

Do you have an application in mind which is easier than autonomous cars but where there is no current product?

A bank needs to be able to recheck every client's status any time the rules change (which happens on a weekly basis). If they don't hold adequate information about their clients, that would mean suspending their accounts until a new verifiable claim was provided.

Getting involved is risky - even if you are right (and I think you are), the price could still increase by a large amount for a long time before sense reasserts itself.

As Keynes apparently did not say: "The market can stay irrational a lot longer than you can stay solvent."

If you hit your trading / credit limits you could lose a lot of money despite being right in the long run.

And as Keynes definitely did say, "In the long run, we are all dead."

Assuming the definition of ~ is meant to be the same on Q and W (I think there's a typo), then it's no longer transitive and therefore no longer an equivalence relation: (0, 0) ~ (1, 2) and (0, 0) ~ (2, 3) but not (1, 2) ~ (2, 3).

Including the effect of the choices people make is much more informative for deciding on public policy or personal food shopping choices. Imposing calorie restrictions in the experiment that wouldn't be there in real life would make the results much less applicable.