Question

Pleasure-seeking was the belief of (Roman)

Answer 1

The answer you're looking for could be a HEDONIST or an EPICUREAN.

"Hedonism" is the general philosophical term for someone seeking pleasure -- though how pleasure was defined differed between different persons.

Epicureans were a particular group in Greco-Roman history that had "pleasure-seeking" as a core belief.

Let's clarify what "pleasure seeking" meant in the original theory of the the ancient Greek philosopher Epicurus.  Epicurus (341-270 BC) believed that the universe and all life within it is essentially a random interaction of atomic particles.  So according to Epicurus, human life is what we have while we're living in this form, but there is no afterlife of individual souls.  So he advocated that the best way to live life, while we are alive, was to seek pleasure and avoid pain.  But his definition of "pleasure" was not some wild party, but the most comfortable and fulfilling sort of mental and physical existence.  So he urged living a life of moderation in order to avoid as much pain as possible.  Pursuing highly emotional relationships or stressful responsibilities in society would cause too much mental pain, he thought, so he refrained from such things.  Similarly, eating too much of rich foods can make you sick, or drinking too much leaves you with a hangover -- so the pain isn't worth the initial pleasure you might feel.  Epicurus and his followers lived very simple lives in order to be free of as much mental and physical pain as possible.  

Some have characterized the "Epicurean" way of life as one that says, "Eat, drink and be merry, for tomorrow we die!"  But Epicurus himself would not have pursued a lifestyle that sought excessive pleasure through eating, drinking and partying, because too much pain would come along with it..