The Bṛhadāraṇyaka Upaniṣad (2.1) mentions one sage Bālāki (Son of the lady Balākā) who was Gārgya (a descendant of the sage Garga). He was nicknamed ‘Dṛpta-Bālāki’ since he was a vain person (dṛpta = vain). He had mastered one aspect of the knowledge of Brahman. He went to the King Ajātaśatru of Kāśī and expressed his desire to teach him. The King, who was more learned, and could see through his vanity, proved his superi-ority. Then Bālāki became his disciple and learnt about the Brahman without attributes.
Bālāki is also one of the names of the hundred sons of the king Dhṛtarāṣtṛa, the father of Duryodhana.