| name | finite-reliability-representations |
| description | Finite Reliability Representations (FRR) methodology for noise-calibrated belief-space covers in decision-making systems. Provides certified suboptimality bounds based on sensing, process, and actuation noise. Use when designing reliable decision systems, POMDP policies, or safety-critical control. |
| version | 1.0.0 |
| author | Hermes Agent |
| license | MIT |
| source | arXiv:2607.04019 |
| tags | ["systems-engineering","reliability","POMDP","belief-space","noise-calibration","decision-making","control-theory"] |
| activation | reliability representations, belief space covers, noise-calibrated decision making, POMDP reliability, certified suboptimality, belief complexity, reliability entropy |
Finite Reliability Representations (FRR)
Source: arXiv:2607.04019 - "Finite Reliability Representations: Noise-Calibrated Belief-Space Covers for Reliable Decision-Making"
Core Theory
Physical sensing and actuation noise floors should inform how much belief resolution a decision-making system can reliably use. FRR covers belief spaces by reliability cells: regions within which the optimal action-value function Q*(b,u) varies by at most a tolerance ε, uniformly over actions.
Key Insight
Noisy Bayesian updates should not be treated as globally contractive on arbitrary beliefs. Separate three objects:
- Fixed-observation filter map
- Predictive observation law
- Controlled belief-transition kernel
Methodology
Step 1: Construct Reliability Cells
For a given tolerance ε:
- Partition the belief space into cells where Q*(b,u) varies by ≤ ε
- Use reachable-set Lipschitz modulus for belief-transition kernel
- Cells are NOT equivalence classes (approximate decision-closeness is not transitive)
Step 2: Certification Conditions
For nonlinear continuous-state systems:
- FRR obtained under reachable-set Lipschitz modulus for belief-transition kernel
For finite-state POMDPs:
- Prediction is linear
- Bayesian correction is normalized positive linear map
- Sensor noise enters through observation-distribution distinguishability
- Actuation uncertainty enters through action-execution channel
Step 3: Cell-Constant Policy
Under action-value Lipschitz condition:
- Construct policy constant on each reliability cell
- Suboptimality bound: 2ε/(1-γ) where γ is discount factor
Step 4: Reliability Entropy
H = log(N_min) where N_min = minimal number of reliability cells
- Measures certified decision-relevant belief complexity
- Distinguishes representation sufficiency from fundamental performance floors
Application Domains
- Finite POMDPs - Exact construction on belief simplex
- Linear-Gaussian filters - Analytic certification
- Locally linearized nonlinear filters - Empirical certification
- Particle-filter implementations - Empirical certification of reliability cells
