Types of Environments — Discrete vs Continuous — Beginner-Friendly Notes

1. Definitions (three things checked: states, actions, percepts)

• Discrete: there is a finite, countable set of states, actions, and percepts. You can list them.
• Continuous: values are real-numbered, smooth, infinitely many possibilities.

If you can count it on fingers → discrete. If you need a ruler/dial → continuous.

2. Examples

Environment	Discrete/Continuous	Why?
Chess	Discrete (states, actions)	64 squares, finite moves
Vacuum (grid world)	Discrete	Cells A/B, actions left/right/suck
Taxi driving (steering angle, speed)	Continuous (states + actions)	Steering 12.37°, speed 42.8 km/h
Image classification with pixels 0-255	Discrete (percepts)	Finite pixel values, but image space is huge
Robot joint angles, sensor voltages	Continuous	Real-valued sensors/actuators
Crossword	Discrete	Letters A-Z

Mixed case (important): Self-driving = discrete decisions (turn left/right) but continuous underlying state (exact position, velocity). Exams call it continuous if any core part is continuous.

3. Why It Matters

• Discrete: can use search / logic — enumerate possibilities (Module 2, 3).
• Continuous: needs calculus, probability, function approximation, neural nets — cannot enumerate, must approximate (Module 4, 5).
• Many real tasks are discretised to make them manageable (e.g., grid map for navigation) — accuracy vs computation tradeoff.

4. Quick Trap

"Large = continuous" is wrong. Chess has ~10^120 states (huge) but still discrete. Continuous means infinitely divisible, not just big.

5. One-Line Summary to Write in Exam

A discrete environment has a finite set of distinct states and actions that can be enumerated for search, while a continuous environment varies over real values and requires approximation and calculus-based methods.

6. Quick Self-Check

1. Is poker discrete or continuous?
2. Why is a thermostat with temperature reading 22.15°C continuous?
3. How would you make a continuous navigation task discrete?