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fluctuate around +0.65. No algorithm sees a future outcome.","readout":"Lower is better. Each point is average squared prediction error so far, averaged over 40 independent streams. Shading is ±1.96 standard errors across streams.","note":"Both learners start at zero. The frozen predictor stays at zero. This is predict-then-update evaluation, not in-sample fit."},{"id":"drift","name":"Abrupt concept drift","title":"Learn from a changing stream","unit":"Running mean squared error ↓","parameter":"Observed 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AdaGrad is not a drift detector; compare the whole trajectory."},{"id":"experts","name":"Switching experts · Hedge","title":"When yesterday’s expert loses its edge","unit":"Cumulative regret vs best fixed expert 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experts reveal all their binary losses each round. The strongest expert changes halfway through.","readout":"Regret uses the best single expert for the prefix in hindsight, not a clairvoyant switching expert. Hedge loss is expected mixture loss, not a sampled expert's loss.","note":"Hedge updates exponential weights only after seeing the current losses. Full-information feedback makes this a different problem from Bandits. Negative realized regret is possible."}],"config":{"runs":40,"horizon":400,"seed":20260927,"hedgeSeed":30260927,"ogdEta":0.3,"adagradEta":0.3,"hedgeEta":0.15},"method":["Scalar predictions are projected to [−1, 1]. OGD uses 0.3/√t; AdaGrad uses 0.3 divided by the square root of accumulated squared gradients. Loss is measured before either update.","40 paired synthetic streams, 400 outcomes each. Stable and drift cases use the same noise seeds. Curves report running mean squared error; the separate expert case reports cumulative regret, not MSE.","Hedge uses η=0.15 and three full-information binary-loss experts. Intervals are pointwise normal approximations across seeds; they are not simultaneous confidence bands."],"limits":["This scalar teaching experiment is not a benchmark of River or scikit-multiflow, nor a proof of a regret bound.","Hyperparameters are illustrative, not tuned on held-out data. Running averages can hide short-lived failures after drift."],"references":[["Duchi et al. · Adaptive Subgradient Methods","https://jmlr.org/papers/v12/duchi11a.html"],["Hazan · Online Convex Optimization","https://arxiv.org/abs/1909.05207"]],"provenance":{"python":"3.13.0","numpy":"2.4.6","sourceSha256":{"showcase_benchmark.py":"0283d1ef2257aa3634b18960f59f9ea085936f91839c4d4f751c795145b0c9b9"}}}