Belief-state sequential information value

VOIAGE’s experimental belief-state contract values information inside a sequential control problem. Its fixed chronology is control, transition, observation, then Bayesian belief update. The comparator is a matched Bellman problem that receives no observations; it is not a one-step EVPI label or a generic acquisition score.

import json
from pathlib import Path

from voiage import belief_state_information_value

request = json.loads(
    Path(
        "specs/frontier/belief-state-information/v1/fixtures/normative/input.json"
    ).read_text()
)
result = belief_state_information_value(request).to_contract_dict()

assert result["values"]["myopic_information_value"] == 0.0
assert result["values"]["nonmyopic_information_value"] == 6.5
assert result["policy_tree"]["selected_control"] == "probe"

The normative example makes the diagnostic informative only after the probe control. A one-stage calculation cannot benefit from that observation. With a second decision stage, the closed-loop policy accepts the probe and sensing costs, updates its belief, and selects a state-directed control.

The JSON result includes the complete chosen belief/policy tree, all tolerance-tied controls and sensors, conditional sensor values, gross and net value, value by horizon, the posterior-martingale residual, exact bounds, and language dispositions. The exact evaluator reports a conservative recursive evaluator-call estimate covering adaptive, no-information, myopic, conditional-sensing and fully observed regret calculations. It rejects requests above its 50,000-call budget before recursion. Repeated belief states are memoized. The result also embeds the strict input contract and its canonical SHA-256 commitment. Standalone result validation reruns the bounded exact evaluator, so the reported expansion count, horizon values, selected policy and ties, and diagnostic flags remain auditable without trusting the result envelope itself.

dual_control_diagnostic requires both an action-dependent, state-informative observation law and a usable downstream control response. Action-dependent observation frequency without state information, and transition dependence alone, do not trigger it. The diagnostic is deliberately not presented as a uniquely defined additive value component.

Run the same contract from the CLI:

voiage --format json calculate-belief-state-information request.json

This surface is experimental and Python-only. Scientific review, continuous or approximate solvers, Rust/R/Julia parity, stable promotion, and release are separate gates.