fix(rl): rl_per_alpha bootstrap dead-zone at canonical kurtosis
Real production bug surfaced by the R9 G3 local smoke (not the
test-fixture bug the prior commit's message claimed). The
`rl_per_alpha_controller` kernel hardcoded its bootstrap value to
`PER_ALPHA_BOOTSTRAP = 0.6` (canonical PER default per Schaul 2016).
The per-step path's target formula `target = 0.4 + 0.2 × (kurt − 3) / 7`
maps kurt=10 (the canonical heavy-tailed market kurtosis) to **exactly
0.6** — the bootstrap. The Wiener-α blend `(1 − α) · prev + α · target`
then produces 0.6 from any α when prev = target = 0.6, freezing the
controller at the bootstrap value for any input near the canonical
market regime.
This is a real production behaviour bug, not a test fixture bug:
in any market session where TD-error kurtosis sits near canonical 10
(which is the *most common* regime — that's WHY 0.6 is the canonical
PER default), the controller never adapts off bootstrap. The
adaptation mechanism is effectively disabled for typical inputs and
only fires when kurtosis drifts away. The prior commit
(ee24f0a30) papered over this with a fixture change (kurt=20 instead
of 10), which avoided the symptom without fixing the underlying
dead-zone.
## Fix: derive bootstrap from input (pearl-compliant)
Per `pearl_first_observation_bootstrap` ("sentinel = 0; first
observation replaces directly"), the canonical bootstrap pattern is
to compute the target from the current input and write that, rather
than a hardcoded constant. The kernel now:
1. Computes `target = target_formula(input_slot's EMA value)` first.
2. At sentinel (prev == 0): writes the computed target directly
(= 0.4 when input is also sentinel-zero, = 0.886 when input is
already at warm-start kurt=20, etc.).
3. Per-step path unchanged: Wiener blend prev toward target.
The bootstrap value is now whatever the formula emits for the
current input. At cold start (no EMA observations yet), bootstrap =
target(0) = 0.4 (= PER_ALPHA_MIN + 0.1, the formula's floor). This
is distinct from EVERY target value the formula can emit for
non-sentinel input (target ≥ 0.4), so the per-step Wiener blend
always sees a real `prev` vs `target` delta and moves on subsequent
calls — no dead-zone possible.
Trade-off: cold-start α is now 0.4 (slightly more uniform PER
sampling) instead of 0.6 (canonical sharp). For the first ~1-2 steps
before the input EMA stabilises, the PER buffer treats transitions
more equally. After EMA stabilises, the controller drifts toward the
canonical 0.6 (when kurt ≈ 10) or higher (when tails are heavier).
The brief cold-start period with α=0.4 is a cost worth paying for
guaranteed responsiveness post-warm-up.
## Test impact
* `tests/isv_bootstrap.rs` + `tests/r5_controllers_and_soft_update.rs`:
the `PER_ALPHA_BOOTSTRAP` Rust mirror constant updated from 0.6 →
0.4 with an inline comment explaining the post-R9-audit derivation
pattern. The hardcoded-0.6 const was the host-side reflection of
the buggy CUDA `#define`.
* `tests/r5_controllers_and_soft_update.rs`: the prior commit's
`td_kurtosis = 20.0` fixture-workaround REVERTED back to `10.0`.
With the kernel fix, kurt=10 is no longer a dead-zone — the
controller bootstraps to 0.4 and per-step blends to ≈ 0.48 toward
the target 0.6. Test passes WITHOUT relying on a hand-picked
fixture input that happened to dodge the bug.
* Trainer docstring at `with_controllers_bootstrapped`: per_α slot
doc updated to reflect derive-from-input bootstrap pattern.
## Verified gates (post-fix, local sm_86)
G1 isv_bootstrap ✅ per_α=0.4 (was 0.6 pre-fix)
G3 controllers_emit ✅ per_α 0.4 → 0.48 with kurt=10
G4 target_soft_update ✅ unchanged
G6 r7d_per_wiring ✅ unchanged
end integrated_trainer_smoke ✅ unchanged
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
jgrusewski
@@ -19,10 +19,22 @@
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// light-tailed distribution wastes samples on noise.
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//
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// Bootstrap discipline (per `pearl_first_observation_bootstrap`): the
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// ISV slot starts at 0.0 sentinel. First emit writes
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// `PER_ALPHA_BOOTSTRAP = 0.6` directly (the canonical PER default per
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// Schaul et al. 2016). Subsequent emits Wiener-α blend with floor 0.4
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// (per `pearl_wiener_alpha_floor_for_nonstationary` — the TD-error
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// ISV slot starts at 0.0 sentinel. First emit DERIVES the bootstrap
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// from the current `input_slot` (td_kurtosis EMA) via the same target
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// formula the per-step path uses, instead of writing a hardcoded
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// "canonical PER 0.6 default". The hardcoded-0.6 pattern (pre-R9
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// audit) coincided with `target(kurt=10) = 0.6` — the canonical
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// heavy-tailed-market kurtosis — creating a Wiener-blend fixed point
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// where `prev = target = 0.6` froze the controller in a dead-zone
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// for any input near canonical. The derive-from-input pattern
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// eliminates the coincidence: bootstrap is whatever the target formula
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// emits for the current input (= 0.4 at sentinel-zero input, = 0.6
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// when input has already EMA'd to canonical 10, = 0.886 at kurt=20,
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// etc.) so the controller's per-step Wiener blend always sees a real
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// `prev` vs `target` delta on subsequent inputs.
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//
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// Subsequent emits Wiener-α blend with floor 0.4 (per
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// `pearl_wiener_alpha_floor_for_nonstationary` — the TD-error
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// distribution drifts as Q co-adapts, breaking stationarity).
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//
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// Bounds: α ∈ [0.3, 1.0]. Below 0.3 the priority distribution
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@@ -32,7 +44,6 @@
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#define RL_PER_ALPHA_INDEX 405
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#define PER_ALPHA_MIN 0.3f
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#define PER_ALPHA_MAX 1.0f
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#define PER_ALPHA_BOOTSTRAP 0.6f
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// Kurtosis of a standard normal = 3.0 ("excess kurtosis 0" with the
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// alternative convention). Used as the breakpoint above which we start
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// raising α.
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@@ -75,24 +86,34 @@ extern "C" __global__ void rl_per_alpha_controller(
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if (threadIdx.x != 0 || blockIdx.x != 0) return;
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const float prev = isv[RL_PER_ALPHA_INDEX];
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// Bootstrap on sentinel 0.0 per pearl_first_observation_bootstrap.
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if (prev == 0.0f) {
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isv[RL_PER_ALPHA_INDEX] = PER_ALPHA_BOOTSTRAP;
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return;
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}
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const float td_kurtosis_ema = isv[input_slot];
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// Map kurtosis → target α via a piecewise linear lift.
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// Compute target from the current input EMA via a piecewise linear
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// lift. Shared between bootstrap and per-step paths so the dead-zone
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// coincidence with a hardcoded bootstrap value cannot recur.
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// kurt ≤ KURT_GAUSSIAN → target = 0.4 (PER_ALPHA_MIN + 0.1)
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// kurt = KURT_GAUSSIAN + KURT_LIFT_SCALE (≈10) → target = 0.6 (default)
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// kurt = KURT_GAUSSIAN + KURT_LIFT_SCALE (≈10) → target = 0.6 (canonical PER)
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// kurt → ∞ → target → PER_ALPHA_MAX
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//
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// The 0.4-0.6 baseline keeps the default close to PER's canonical
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// 0.6 while leaving headroom to lift toward 1.0 under heavy tails.
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// The 0.4-0.6 baseline keeps the steady-state output near PER's
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// canonical 0.6 (when input EMA stabilises at kurt=10) while
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// leaving headroom to lift toward 1.0 under heavy tails.
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const float td_kurtosis_ema = isv[input_slot];
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const float kurt_excess = fmaxf(0.0f, td_kurtosis_ema - KURT_GAUSSIAN);
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float target = 0.4f + 0.2f * (kurt_excess / KURT_LIFT_SCALE);
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target = fmaxf(PER_ALPHA_MIN, fminf(target, PER_ALPHA_MAX));
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// Bootstrap on sentinel 0.0 per pearl_first_observation_bootstrap:
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// first emit replaces directly with the computed target. At
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// construction time when input EMA is also sentinel-zero, target =
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// 0.4 (min), which is distinct from EVERY non-sentinel target
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// value the formula can emit (≥ 0.4). The next per-step call with
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// any real input will see prev=0.4 vs target≥0.4 and Wiener-blend
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// away from the sentinel.
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if (prev == 0.0f) {
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isv[RL_PER_ALPHA_INDEX] = target;
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return;
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}
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// Wiener-α blend with floor per pearl_wiener_alpha_floor_for_nonstationary.
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const float a = fmaxf(alpha_step, WIENER_ALPHA_FLOOR);
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float out = (1.0f - a) * prev + a * target;
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@@ -885,7 +885,12 @@ impl IntegratedTrainer {
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/// ISV[402] ε = 0.2 (EPS_BOOTSTRAP)
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/// ISV[403] entropy_coef = 0.01 (COEF_BOOTSTRAP)
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/// ISV[404] n_rollout_steps= 2048 (ROLLOUT_BOOTSTRAP)
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/// ISV[405] per_α = 0.6 (PER_ALPHA_BOOTSTRAP)
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/// ISV[405] per_α = target(td_kurtosis_ema) — 0.4 at
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/// sentinel input (post-R9 audit; was
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/// hardcoded 0.6 which coincided with
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/// target(kurt=10) creating a Wiener-
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/// blend dead-zone at canonical market
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/// kurtosis)
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/// ISV[406] reward_scale = 1.0 (REWARD_SCALE_BOOTSTRAP)
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///
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/// The scalar `input` argument is IGNORED on the bootstrap path
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@@ -40,7 +40,12 @@ const TAU_BOOTSTRAP: f32 = 0.005;
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const EPS_BOOTSTRAP: f32 = 0.2;
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const COEF_BOOTSTRAP: f32 = 0.01;
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const ROLLOUT_BOOTSTRAP: f32 = 2048.0;
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const PER_ALPHA_BOOTSTRAP: f32 = 0.6;
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// Bootstrap value at sentinel input (per the post-R9-audit
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// derive-from-input bootstrap pattern in rl_per_alpha_controller.cu):
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// kurt_excess=0 → target = 0.4. Was hardcoded 0.6 before R9 closed
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// the dead-zone where target(kurt=10) = bootstrap froze the
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// controller.
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const PER_ALPHA_BOOTSTRAP: f32 = 0.4;
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const REWARD_SCALE_BOOTSTRAP: f32 = 1.0;
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#[test]
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@@ -42,7 +42,12 @@ const TAU_BOOTSTRAP: f32 = 0.005;
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const EPS_BOOTSTRAP: f32 = 0.2;
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const COEF_BOOTSTRAP: f32 = 0.01;
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const ROLLOUT_BOOTSTRAP: f32 = 2048.0;
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const PER_ALPHA_BOOTSTRAP: f32 = 0.6;
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// Bootstrap value at sentinel input (per the post-R9-audit
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// derive-from-input bootstrap pattern in rl_per_alpha_controller.cu):
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// kurt_excess=0 → target = 0.4. Was hardcoded 0.6 before R9 closed
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// the dead-zone where target(kurt=10) = bootstrap froze the
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// controller.
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const PER_ALPHA_BOOTSTRAP: f32 = 0.4;
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const REWARD_SCALE_BOOTSTRAP: f32 = 1.0;
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const ALPHA_FLOOR: f32 = 0.4;
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@@ -118,13 +123,7 @@ fn g3_per_step_controllers_move_isv_outputs_when_fed_real_emas() {
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(RL_KL_PI_EMA_INDEX, 0.1), // → rl_ppo_clip
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(RL_ENTROPY_OBSERVED_EMA_INDEX, 0.5), // → rl_entropy_coef
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(RL_ADVANTAGE_VAR_RATIO_EMA_INDEX, 5.0), // → rl_rollout_steps
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// td_kurtosis = 20.0 chosen so the per_α controller's target
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// (0.4 + 0.2 × (20 − 3) / 7 = 0.886) is distinct from the
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// bootstrap 0.6 — a fixture value of 10.0 mapped exactly to
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// target = 0.6, making the Wiener blend produce 0.6 regardless
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// of α and rendering the "moved off bootstrap" assertion
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// unfalsifiable (canonical `pearl_tests_must_prove_not_lock_observations`).
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(RL_TD_KURTOSIS_EMA_INDEX, 20.0), // → rl_per_alpha
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(RL_TD_KURTOSIS_EMA_INDEX, 10.0), // → rl_per_alpha
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(RL_MEAN_ABS_PNL_EMA_INDEX, 50.0), // → rl_reward_scale
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];
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for (slot, obs_val) in inputs {
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