Lecture 7

Question 1

What kind of distribution do real valued EDAs require?

Answer 1

practically useful, such as normal distribution

Question 2

What is ML? (in EDA)

Answer 2

Maximum Likelihood

Question 3

What is the limitation of ML?

Answer 3

Can only model linear-like dependencies.

Question 4

What is the difference between ES and normal based EDA?

Answer 4

ES uses normal distributions for self adaption of models. The model updates implicitly through selection and random mutation

normal based EDA Explicitly couples population to model-update rules by performing estimation on the direction of improvements.

Question 5

When can the direct use of ML-normal in a EDA have a positive result

Answer 5

• The Function is unimodal (one peak)
• The function is centered at origin
• Easy to converge towards minimum

Question 6

What is the big downside of using direct ML-normal in EDA

Answer 6

• Structure of solution is very complicated and hardly matches normal distribution
• Improving directions are ignored in MLE
• The EDA does not observe the direction of the population
• Hence, no exploration ouside of the data range, so real optimum can easily be missed.

Question 7

What would we expect to observe over multiple generations of Direct ML normal on EDA?

Answer 7

The algorithm tries to find a distribution that best fits the observed data, rather than the best solution in solution space. (skewed initial data stays skewed)

Question 8

Explain the premature convergence problem

Answer 8

In direct ML-normal on real valued EDA, the variance of the normal distribution estimation will convergence to 0 very fast before the search space has been explored.

Question 9

Why is Gradient Hybridization not a great solution for real values EDAs?

Answer 9

It requires gradient information, which is not always possible in complex problems, and not always reliable.

Question 10

What are the three ingredients for Adaptive ML estimation?

Answer 10

• Adaptive Variance Scaling (AVS)
• Standard Deviation Ratio (SDR)
• Anticipated Mean Shift (AMS)

Question 11

What is AVS?

Answer 11

Adaptive Variance Scaling

Question 12

What is SDR?

Answer 12

Standard Deviation Ratio

Question 13

What is AMS?

Answer 13

Anticipated Mean Shift

Question 14

In SDR-AVS, what is the NIC counter?

Answer 14

When there are multiple local optima in your problem, it will take SDR-AVS too long to converge to one of them. It limits the adaption of variance in the estimation distribution.

Question 15

Explain what the distribution muliplier does for SDR-AVS.

Answer 15

It will enlarge the variance of which new samples are taken

Question 16

What are the two reasons that no improvement was found in the SDR-AVS?

Answer 16

Either the vairance is too large and ED took samples of worse solutions.
Or the distribution covers multiple local optima, in which randomly sampled solutions between these optima can worsen the average.

Question 17

What is the shortcomming of SDR-AVS?

Answer 17

It solves searching in 1D space, but not in 2D space.

Question 18

What is the idea of AMS?

Answer 18

Anticipate where the mean will be shifiting, then alter part of generated solutions using that shfit.
Predictions on slope will be better. But we require balanced selection to re-align covariance matrix.

Question 19

How is the shift in AMS calculated?

Answer 19

𝝁𝑆ℎ𝑖𝑓𝑡(𝑡) =𝝁(𝑡) −𝝁(𝑡 − 1),
(𝝁 should be MEAN 𝝁)
such that 𝒙 ← 𝒙 + 𝛿 * 𝝁𝑆ℎ𝑖𝑓𝑡(𝑡).

Where t is the generation number and factor 𝛿 the impact of the shift.

Question 20

What behaviour does AMS have on a peak?

Answer 20

No change, as
𝝁(𝑡) ≈ 𝝁(𝑡 − 1)

Question 21

Why is AMS still not a optimal approach for real-valued EDA?

Answer 21

Because choosing the right parameters is really finicky and still requires a lot of attention.

Question 22

What does AMaLGaM spell?

Answer 22

Adapted Maximum-Likelihood Gaussian Model

Question 23

What is the idea of AMaLGaM?

Answer 23

It uses the variance approach from SDR-AVS to widen the search space. And it uses the mean-shift from AMS in order to faster move solutions down slopes.