FA-12021 / Optimization solver contracts / Open access

Trust region accepts steps with a nondecreasing model · case 01

Trust region accepts steps with a nondecreasing model.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Acceptance tests actual improvement without predicted reduction.

VERIFIED REPAIR

Require positive predicted reduction and ratio at least eta.

Unsuccessful approach: Taking absolute predicted reduction masks a model that forecasts an increase.

Case contract

Accept iff predicted>0 and actual/predicted>=eta, for 0<eta<1; reductions use old-new convention.

Why this case matters

This deterministic solver-step model isolates an algorithmic invariant used by iterative optimization implementations.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(actual, predicted, eta):
    return actual > 0
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('model increase', solve(N, -N, 0.5), False)
check('poor agreement', solve(N, 10*N, 0.5), False)
check('threshold', solve(N, 2*N, 0.5), True)
check('good agreement', solve(2*N, N, 0.5), True)
check('flat model', solve(N, 0, 0.5), False)
check('actual increase', solve(-N, N, 0.5), False)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
model increase	`True`	`False`	Failed
poor agreement	`True`	`False`	Failed
threshold	`True`	`True`	Passed
good agreement	`True`	`True`	Passed
flat model	`True`	`False`	Failed
actual increase	`False`	`False`	Passed

SHA-256 / d475b94f1cea49cf1dd54899665ebb6b10f7877768b4230fc83f1d4385901aa8

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(actual, predicted, eta):
    return predicted != 0 and actual/abs(predicted) >= eta
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('model increase', solve(N, -N, 0.5), False)
check('poor agreement', solve(N, 10*N, 0.5), False)
check('threshold', solve(N, 2*N, 0.5), True)
check('good agreement', solve(2*N, N, 0.5), True)
check('flat model', solve(N, 0, 0.5), False)
check('actual increase', solve(-N, N, 0.5), False)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
model increase	`True`	`False`	Failed
poor agreement	`False`	`False`	Passed
threshold	`True`	`True`	Passed
good agreement	`True`	`True`	Passed
flat model	`False`	`False`	Passed
actual increase	`False`	`False`	Passed

SHA-256 / 0f56f86ffec3b72df42aa9cdd618d6479d62e392327e28aa71efe019b97e6c57

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(actual, predicted, eta):
    return predicted > 0 and actual/predicted >= eta
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('model increase', solve(N, -N, 0.5), False)
check('poor agreement', solve(N, 10*N, 0.5), False)
check('threshold', solve(N, 2*N, 0.5), True)
check('good agreement', solve(2*N, N, 0.5), True)
check('flat model', solve(N, 0, 0.5), False)
check('actual increase', solve(-N, N, 0.5), False)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
model increase	`False`	`False`	Passed
poor agreement	`False`	`False`	Passed
threshold	`True`	`True`	Passed
good agreement	`True`	`True`	Passed
flat model	`False`	`False`	Passed
actual increase	`False`	`False`	Passed

SHA-256 / f35f9f2470fb05db35b9e1253c238c6c9c5ddf30f7f8d4daeebf8b579e1354f0

Verification & scope

Controlled finite inputs and explicit one-step contracts; this is not a production solver or a numerical stability benchmark. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:38:53.038173+00:00.

Case digest / c94a9365a8d12a3ed84a8763d9b1b3d5158b106869157ff353b35e862a2e8ab5