Trajectory success from per-step reliability
NumericalFoundation⏱ 15 minAgentscompoundinghorizon
Problem
- An agent takes 15 steps, each succeeding independently with probability 0.97. Compute the trajectory success rate.
- What per-step reliability is needed for 95% success over 15 steps?
- If the horizon can be cut to 5 steps at the same per-step reliability of 0.97, what is the new success rate, and how does that compare with the improvement in part 2?
Compute the requested quantities and say what they mean. A number without an interpretation is not an answer.
Solution
Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.
Related problems
All problems| Solved | Problem | Field | Type | Difficulty | Time |
|---|---|---|---|---|---|
| The reliability wall | Agents | Numerical | 15 min | ||
| Detect-and-retry arithmetic | Agents | Proof | 30 min | ||
| Majority voting via Hoeffding | Agents | Proof | 30 min | ||
| What correlation does to voting | Agents | Proof | 30 min | ||
| Simulate an agent pipeline end to end run | Agents | Coding | 1 day |