Relaxed objectives?

[FrigoCoder]

Hi!

Have you thought about the possibility of relaxed constraints on objectives? And how would they affect the Jacobian Descent algorithm and the aggregators?

For example gradients that point away from counterexamples such as synthetic data? And relaxed conflicts where the main objective has to be strict, but the others are flexible enough they do not need to be fulfilled in case of conflicts?

Br,
Frigo

[ValerianRey]

Hi, thanks for your interest! I'm not sure that I fully understand your questions, but I'll try to answer as much as I can.

Have you thought about the possibility of relaxed constraints on objectives? And how would they affect the Jacobian Descent algorithm and the aggregators?

If I understand correctly, your question is about relaxing the constraints that the aggregation of the Jacobian matrix has to respect: for example making it possible for the aggregation to have a negative inner product with some of the secondary objectives' gradients.

We haven't tried this, but it should be possible by creating a custom aggregator. This could make the aggregation faster than it currently is, at the cost of making updates that would possibly degrade some secondary objectives. However, in most practical cases, the aggregation is not the bottleneck of Jacobian descent: we can easily aggregate a matrix of 32 rows (i.e. the 32 gradients of 32 objectives) with UPGrad without really noticing the time taken for aggregation. What takes extra time and memory is to compute this matrix rather than a single gradient. So I'm not sure how that would be practically useful.

For example gradients that point away from counterexamples such as synthetic data?

Sorry, I don't really understand this part, could you clarify it a bit?