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And so that’s one case where you can compute the augmax and we can compute that expectation without needing to sample an average over some sample. Another very common case actually it turns out is if you have a stochastic simulator, but if your similar happens to take on a very specific form of ST+1=F(s)T,AT+?T where this is galsie noise. The [inaudible] is a very common way to build simulators where you model the next state as a function of the current state and action plus some noise and so once specific example would be that sort of mini dynamical system that we talked about with linear function of the current state and action plus galsie noise. In this case, you can approximate augment over A, well.
In that case you take that expectation that you’re trying to approximate. The expected value of V* of S prime, we can approximate that with V* of the expected value of S prime, and this is approximation. Expected value of a function is usually not equal to the value of an expectation but it is often a reasonable approximation and so that would be another way to approximate that expectation and so you choose the actions according to watch we do the same formula as I wrote just now. And so this would be a way of approximating this augmax, ignoring the noise in the simulator essentially. And this often works pretty well as well just because many simulators turn out to be the form of some linear or some nonlinear function plus zero mean galsie noise, so and just that ignore the zero mean galsie noise, so that you can compute this quickly.
And just to complete about this, what that is, right, that V* F of SA, this you down rate as data transfers Fi of S prime where S prime=F of SA. Great, so this V* you would compute using the parameters data that you just learned using the fitted value iteration algorithm. Questions about this?
Student: [Inaudible] case, for real-time application is it possible to use that [inaudible], for example for [inaudible].
Instructor (Andrew Ng) :Yes, in real-time applications is it possible to sample case phases use [inaudible] expectation. Computers today actually amazingly fast. I’m actually often surprised by how much you can do in real time so the helicopter we actually flying a helicopter using an algorithm different than this? I can’t say. But my intuition is that you could actually do this with a helicopter. A helicopter would control at somewhere between 10hz and 50hz. You need to do this 10 times a second to 50 times a second, and that’s actually plenty of time to sample 1,000 states and compute this expectation.
They’re real difficult, helicopters because helicopters are mission critical, and you do something it’s like fast. You can do serious damage and so maybe not for good reasons. We’ve actually tended to avoid tossing coins when we’re in the air, so the ideal of letting our actions be some up with some random process is slightly scary and just tend not to do that. I should say that’s prob’ly not a great reason because you average a large number of things here very well fine but just as a maybe overly conservative design choice, we actually don’t, tend not to find anything randomized on which is prob’ly being over conservative. It’s the choice we made ‘cause other things are slightly safer. I think you can actually often do this.
So long as I see a model can be evaluated fast enough where you can sample 100 state transitions or 1,000 state transitions, and then do that at 10hz. They haven’t said that. This is often attained which is why we often use the other approximations that don’t require your drawing a large sample. Anything else? No, okay, cool. So now you know one algorithm [inaudible] reinforcement learning on continuous state spaces. Then we’ll pick up with some more ideas on some even more powerful algorithms, the solving MDPs of continuous state spaces. Thanks. Let’s close for today.
[End of Audio]
Duration: 77 minutes
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