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As we saw in our plot, stochastic gradient
tends to oscillate around the optimum.

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And so you should never trust the last
parameter it finds, unfortunately.

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Gradient will eventually
stabilize on the optimal solution.

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So even though it takes
a hundred times longer or

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more, like was shown in this example, so

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if you look at the x-axis a hundred times
more time to converge, you get there.

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And you feel really good
when you get there.

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Stochastic gradient, when you think
it converged, is really that it's

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oscillating around the optimum, and
that can lead to bad practical behavior.

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So for example here,
I'm just giving you some numbers,

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say w at iteration 1000 might look really,
really bad.

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But maybe W at iteration 1005 looks
really, really good and needs some kind of

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approach to minimize the risk of picking
a really bad one or a really good one.

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And there is a very simple technique
which works really well in practice, and

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theoretically is what you should do.

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So all the theorems require
something like this.

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And what it says is.

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When you are outputting w hat,
your final self-coefficient,

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you don't use the last value, w(t),

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capital T, you use the average of
all the values that you've computed.

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All the coefficients you
computed along the way.

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So, what I'm showing here is what your
algorithm should output as it's fitting

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the solution to make some
predictions in the real world.

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>> [MUSIC]