Is Empower considered optional addition cost?

No — Empower's cost is not an optional additional cost.

Empower is an Activated Ability keyword (Rule 827.1). Its cost is the base cost of that ability — the part before the ":" — not an additional cost of playing a card. "Optional additional cost" is a specific category that requires both "as an additional cost" and "may" (Rule 356.2.b.1), like Accelerate or Repeat.

Practical upshot: Ezreal, Prodigy's discount ("optional additional costs you pay cost [1] or [A] less") does not reduce Empower costs — same reason it doesn't touch Equip costs (Rule 204.1.b; FAQ #234). You pay the full Empower cost listed on the card.