The four-armed Avalokitesvara is known as the Bodhisattva of Infinite Mercy.
Compare this specific representation of Avalokitesvara with another 17th/18th century tibetan gilt-bronze figure of Sadaksari (although much more smaller), illustrated in Buddhist Images in Gilt Metal, The Chang Foundation, Taipei 1993, pl.34. From the same collection see also the 17th/18th century Chinese figure of Buddha Sakyamuni (Op. Cit, pl.14) which face and tiara are almost identical to those of the present lot.
See also another massive figure of Avalokitesvara Sadaksari from the Kangxi period, illustrated in Buddhist Statues of Tibet - The Complete Collection of Treasures of the Palace Museum, Hong Kong 2003, p.237, pl.226.