Learning theory definitely seems most relevant. Methodologically I think any domain where you are designing and analyzing algorithms, especially working with fuzzy definitions or formalizing intuitive problems, is also useful practice though much less bang for your buck (especially if just learning about it rather than doing research in it). That theme cuts a bunch across domains, though I think cryptography, online algorithms, and algorithmic game theory are particularly good.
Learning theory definitely seems most relevant. Methodologically I think any domain where you are designing and analyzing algorithms, especially working with fuzzy definitions or formalizing intuitive problems, is also useful practice though much less bang for your buck (especially if just learning about it rather than doing research in it). That theme cuts a bunch across domains, though I think cryptography, online algorithms, and algorithmic game theory are particularly good.