Summary. This teaser post sketches our current ideas for dealing with more complex environments. It will ultimately be replaced by one or more longer posts describing these in more detail. Reach out if you would like to collaborate on these issues.
Multi-dimensional aspirations
For real-world tasks that are specified in terms of more than a single evaluation metric, e.g., how much apples to buy and how much money to spend at most, we can generalize Algorithm 2 as follows from aspiration intervals to convex aspiration sets:
- Assume there are d>1 many evaluation metrics ui, combined into a vector-valued evaluation metric u=(u1,…,ud).
- Preparation: Pick d+1 many linear combinations fj in the space spanned by these metrics so that their convex hull is full-dimensional and contains
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