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Meinolf SellmannGuestMike WatsonHost
Vijay MehrotraHostHave you worked on the multi-objective problem since then? And how are you thinking about it? Do you have different weights for the different KPIs? Do you do them in sequence? What's your thought on the current state of the art?

Well, I mean, the traditional is, of course, either aggregate them somehow.

So if you do a linear aggregation of multiple KPIs, but that means you're fixing the exchange rate between them, right? So X units of this is favorable to Y units of that.

I mean, if you run a business, you want your KPIs to run between, you know, in the reasonable range.

And if you have, I mean, think of buying a house, right? There's a typical quintessential multi-objective optimization problem.

If you're really squeezed in space, But your school district is at 10 stars and, you know, you could go to another one that really makes progress and gives you like 50% more square feet.

If it's the other way around, the school district is in shambles, but you have awesome space, right? You will not do the same trade.

So if you either make one the primary and everything else a secondary, then it means that you're willing to accept arbitrary losses in the secondary objective function for epsilon improvements on the first one.

Or you could say, well, you know, if you have these kind of, hey, where is the OK range for an objective function? You could say, well, let's constrain one and optimize for the other.

And that's nonsense because you don't know what threshold that should be until you actually do the search and you see, well, where can you get the biggest bang for the buck? And that's kind of the way how we are going about it, that we're saying, hey, there is a way to get out of the ill-definedness of the problem.

It's ill-defined because obviously anything that is Pareto optimal would be a potential solution.

So you kind of have to get out of there by asking for a little bit more information from the user.

The way how we do it is that we just ask them to give us acceptable ranges.

Or they can be had simply by optimizing for individual objective functions up front and then kind of getting an idea on how well you can get.
Have you worked on the multi-objective problem since then? And how are you thinking about it? Do you have different weights for the different KPIs? Do you do them in sequence? What's your thought on the current state of the art?

Well, I mean, the traditional is, of course, either aggregate them somehow.

So if you do a linear aggregation of multiple KPIs, but that means you're fixing the exchange rate between them, right? So X units of this is favorable to Y units of that.

I mean, if you run a business, you want your KPIs to run between, you know, in the reasonable range.

And if you have, I mean, think of buying a house, right? There's a typical quintessential multi-objective optimization problem.

If you're really squeezed in space, But your school district is at 10 stars and, you know, you could go to another one that really makes progress and gives you like 50% more square feet.

If it's the other way around, the school district is in shambles, but you have awesome space, right? You will not do the same trade.

So if you either make one the primary and everything else a secondary, then it means that you're willing to accept arbitrary losses in the secondary objective function for epsilon improvements on the first one.

Or you could say, well, you know, if you have these kind of, hey, where is the OK range for an objective function? You could say, well, let's constrain one and optimize for the other.

And that's nonsense because you don't know what threshold that should be until you actually do the search and you see, well, where can you get the biggest bang for the buck? And that's kind of the way how we are going about it, that we're saying, hey, there is a way to get out of the ill-definedness of the problem.

It's ill-defined because obviously anything that is Pareto optimal would be a potential solution.

So you kind of have to get out of there by asking for a little bit more information from the user.

The way how we do it is that we just ask them to give us acceptable ranges.

Or they can be had simply by optimizing for individual objective functions up front and then kind of getting an idea on how well you can get.
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