Losev was born in Novocherkassk, the administrative center of the Don Host Oblast, the far western Russian territory held by the Don Cossacks on the banks of the Don River. He was named after his maternal grandfather, Aleksei Polyakov; a priest in the Russian Orthodox Church. Losev's paternal great-grandfather was also named Aleksei, and was awarded for heroism during the Napoleonic Wars, while fighting in a Cossack Brigade. Losev's father was Fyodor Petrovich Losev, a violinist and conductor by avocation and a teacher of mathematics and physics by trade. Attracted to a bohemian lifestyle, Losev's father left the family in the hands of his wife, Natal'ya Alekseevna Loseva (née Polyakova), who raised Losev as an only child at her father's house.