What is the epsilon (ε) parameter in differential privacy, and what does it control?

Epsilon is the "privacy budget" — it bounds how much one person's data can change the output; smaller ε means stronger privacy but more noise (less utility).

In differential privacy, ε (epsilon) quantifies the privacy guarantee: it bounds the ratio by which the probability of any output can differ when a single individual is added to or removed from the dataset. Intuitively, it's a privacy budget:

• Small ε → outputs barely change with/without you → strong privacy, but more noise and lower accuracy.
• Large ε → outputs can change more → weaker privacy, but higher utility.

This makes the privacy/utility trade-off explicit and tunable — and because DP is composable, repeated queries spend the budget, so total ε must be tracked across all releases.

Tip: ε turns "how private is it?" from a vague claim into a number you can set, audit, and spend. That quantifiability is DP's superpower.