commit 3b66da8d75aef92493c251a3b2e8039c86ad91fb
parent 93246df3eb4bd63c4e970fe43fdfe1b0b439d2fd
Author: Jared Tobin <jared@jtobin.io>
Date: Fri, 3 Jul 2026 14:13:05 -0230
docs: rationale for the Newton accumulator-seed deviation from WSR
Diffstat:
1 file changed, 15 insertions(+), 0 deletions(-)
diff --git a/lib/Numeric/Eproc/Common.hs b/lib/Numeric/Eproc/Common.hs
@@ -73,6 +73,21 @@ import GHC.Float (log1p)
-- rate @2 \/ (2 - log 3)@. Achieves logarithmic regret against
-- the best constant bet in hindsight and is in practice the
-- strongest of the three bettors under most signal regimes.
+--
+-- One deliberate deviation from WSR: Algorithm 2 seeds the
+-- squared-gradient accumulator at @1@, which presumes
+-- observations scaled to @[0, 1]@. On raw-scale data that
+-- constant is dimensionally wrong -- negligible when
+-- @z^2 >> 1@, paralysing when @z^2 << 1@ -- so the accumulator
+-- here is instead seeded near zero, making the update
+-- scale-adaptive. The trade is bold early play: the first
+-- nonzero observation typically drives the bet straight to
+-- the @lambda_max@ ceiling, annealing back toward the Kelly
+-- point as gradients accumulate. Validity is unaffected --
+-- predictability and clipping are all it needs -- and regret
+-- stays logarithmic with a somewhat larger constant. The
+-- visible effect is higher-variance early wealth: a supremum
+-- modestly above its floor is expected even under @H_0@.
data Bettor =
Fixed {-# UNPACK #-} !Double
| Adaptive
