# Эксперимент: Adaptive Proximal Quasi-Newton Training (#939)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a deterministic proximal quasi-Newton-style optimizer and verified the quadratic stability mechanism. The predicted stability boundary was eta_c=0.08889, while the observed binary-search boundary was 0.08915 (0.3% error); the predicted contraction factor 0.97556 matched 0.97343 observed. Adaptive enlargement produced 157 accepted and 23 rejected trials and reached the same sparse-regression objective as fixed proximal gradient, although its late stepsizes sometimes exceeded eta_c, so the claimed conservative settling behavior was not fully demonstrated.",
  "metrics": {
    "baseline": "Sparse regression: SGD final composite objective 0.0855266, 24 nonzeros.",
    "idea": "Sparse regression: adaptive proximal method final composite objective 0.0823621, 5 nonzeros; 194 accepted and 56 rejected trials. Fixed proximal baseline also reached 0.0823621 with 5 nonzeros. Quadratic eta boundary: predicted 0.0888889 vs observed 0.0891509; contraction factor predicted 0.975556 vs observed 0.973429."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "This was a toy diagonal quadratic and small full-batch sparse linear regression, not an MLP or image benchmark. The implementation uses diagonal secant curvature rather than limited-memory dense quasi-Newton pairs, does not measure wall-clock/FLOP speedup, and the adaptive stepsize was not consistently below the theoretical boundary near convergence."
}