Module 1: Agent Fundamentals
Cost, Latency & Error Risk Trade-offs
Understanding compounding probabilities in multi-step agent trajectories and how to manage runaway token consumption.
The math of autonomous systems dictates that reliability decays exponentially as trajectory steps increase. Understanding this equation is essential for production deployment.
The Exponential Decay Rule
If each individual tool-calling decision has a $95\%$ probability of success ($p = 0.95$), the overall trajectory reliability drops sharply over multiple steps:
\[P(\text{Success}) = p^n\]| Number of Steps ($n$) | Per-Step Reliability ($p=0.95$) | Per-Step Reliability ($p=0.99$) |
|---|---|---|
| 1 step | 95.0% | 99.0% |
| 3 steps | 85.7% | 97.0% |
| 5 steps | 77.4% | 95.1% |
| 10 steps | 59.8% | 90.4% |
| 20 steps | 35.8% | 81.8% |
[!WARNING] Without deterministic validation checkpoints, an agent running 10 steps at 95% accuracy will fail 4 times out of 10.
Controlling Token Drift
Agents tend to expand their context window on every tool execution. Follow these strategies:
- Tool Output Truncation: Never return unfiltered API payloads to the model prompt. Filter to only the fields needed for the decision.
- Hard Loop Ceilings: Cap iterations strictly at 5–8 turns. If the goal isn’t achieved, fail gracefully with an error explanation.
- Budget Guards: Enforce maximum token ceilings per session.
Continue to Module 2: The Agent Control Loop.
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