Эксперимент: Inexact High-Order Moreau DC Optimizer (#1247)

{ "worked": true, "confidence": 7, "verdict": "Built an inexact high-order Moreau DC optimizer for a capped-L1-like toy DC objective, including p=2 and p=4 proximal updates with fixed inner iterations and decreasing smoothing. The envelope-gradient identity was numerically verified for both orders, with finite-difference error around 3e-7 and proximal residuals below 8e-6. In the fixed-seed comparison, p=4 reached a lower final objective than raw DC descent (1.8981 vs 1.9394) and had much lower RMS update norm (0.2005 vs 1.0892); p=2 was smoother but ended worse, so the signal is promising but not uniform.", "metrics": { "baseline": "Raw DC gradient descent: final objective 1.9393945, best objective 1.8920250, gradient RMS 1.0892316, spikes >10: 0", "idea": "Inexact p=2: final objective 2.7906681, best objective 1.8815078, gradient RMS 0.8987517; inexact p=4: final objective 1.8980709, best objective 1.8980709, gradient RMS 0.2004824; both had 0 spikes >10" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a 24-dimensional synthetic capped-L1-like DC problem was tested. No CIFAR/MLP experiment, wall-clock or FLOP accounting, hyperparameter sweep, multiple-seed statistical test, or residual-based adaptive inner termination was performed." }