diff --git a/crates/ml-alpha/cuda/compute_advantage_return.cu b/crates/ml-alpha/cuda/compute_advantage_return.cu
index 9369556f7..fbc58ca26 100644
--- a/crates/ml-alpha/cuda/compute_advantage_return.cu
+++ b/crates/ml-alpha/cuda/compute_advantage_return.cu
@@ -1,19 +1,26 @@
-// compute_advantage_return.cu — KL-regularized advantage computation.
+// compute_advantage_return.cu — KL-regularized advantage with split
+// static/dynamic components for on-policy/off-policy consistency.
 //
-// Combines environment reward with an RLHF-style KL penalty that feeds
-// through the STANDARD advantage pipeline (no separate gradient term).
+// The KL penalty has two parts:
+//   -β × (log π_θ(a|s) - log π_ref(a))
+// = -β × log π_θ(a|s) + β × log π_ref(a)
 //
-// r_modified = r_env - β_kl × (log π_θ(a|s) - log π_ref(a))
+// Static part: β × log π_ref(a) — depends only on which action was
+//   taken, not on the current policy. Written to rewards_d so PER
+//   captures it. Q's Bellman targets see this consistently across
+//   replays, giving Q a stable Hold preference.
 //
-// On non-done steps (r_env=0): the KL penalty is the ONLY reward signal.
-// It rewards actions that stay near the reference (Hold-heavy) and
-// penalizes actions that drift away. On done-steps: the trade PnL
-// dominates the KL penalty.
+// Dynamic part: -β × log π_θ(a|s) — depends on the CURRENT policy.
+//   Only added to the on-policy advantage (not stored in PER).
+//   Provides the adaptive signal that pushes π back toward the
+//   reference when it drifts.
 //
-// This avoids the structural imbalance of a separate KL gradient
-// (which fired 100% of steps vs PPO's 6%, overwhelming PPO at any β).
-// As a reward signal, KL feeds through PPO's own importance ratio
-// mechanism with matched per-step coverage.
+// This split ensures Q and π optimize the SAME objective:
+//   Q learns: E[r_env + β·log π_ref(a) + γV(s')]  (stable across replays)
+//   π maximizes: E[A] where A = (r + β·log π_ref - β·log π_θ) + γV(s') - V(s)
+//   The β·log π_ref terms cancel between reward and KL, leaving:
+//   π effectively maximizes: E[r_env - β·log π_θ + γV(s') - V(s)]
+//   = standard entropy-regularized objective (SAC-like)
 
 #define RL_GAMMA_INDEX          400
 #define RL_KL_REF_BETA_INDEX    578
@@ -22,7 +29,7 @@
 
 extern "C" __global__ void compute_advantage_return(
     const float* __restrict__ isv,           // ISV bus
-    float*       __restrict__ rewards,       // [b_size] IN/OUT (augmented in place)
+    float*       __restrict__ rewards,       // [b_size] IN/OUT
     const float* __restrict__ dones,         // [b_size] 0.0 / 1.0
     const float* __restrict__ v_t,           // [b_size] V(s_t)
     const float* __restrict__ v_tp1,         // [b_size] V(s_{t+1})
@@ -41,32 +48,26 @@ extern "C" __global__ void compute_advantage_return(
     const float done   = dones[b];
     const float vt     = v_t[b];
     const float vtp1   = v_tp1[b];
+    const int a        = actions[b];
 
-    // RLHF-style KL penalty: -β × (log π_θ(a|s) - log π_ref(a))
-    // = -β × log(π_θ / π_ref)
-    //
-    // When π_θ(a) > π_ref(a) (over-represented action): penalty < 0
-    // When π_θ(a) < π_ref(a) (under-represented action): penalty > 0 (bonus)
-    //
-    // For Hold: π_ref = 0.5. If π_θ(Hold) dropped to 0.1:
-    //   penalty = -β × (log(0.1) - log(0.5)) = -β × (-1.61) = +1.61β (bonus!)
-    // For BuyL1: π_ref = 0.05. If π_θ(Buy) rose to 0.3:
-    //   penalty = -β × (log(0.3) - log(0.05)) = -β × (1.79) = -1.79β (penalty)
-    const int a = actions[b];
+    // Static log π_ref — consistent across replays.
     const float log_pi_ref = (a == HOLD_ACTION)
         ? -0.6931472f    // log(0.5)
         : -2.9957323f;   // log(0.05)
-    const float kl_penalty = -beta * (log_pi_old[b] - log_pi_ref);
 
-    const float r = r_env + kl_penalty;
-    rewards[b] = r;  // write back so PER push captures augmented reward
+    // Reward with static KL component only (stored in PER for Q).
+    const float r = r_env + beta * log_pi_ref;
+    rewards[b] = r;
 
     const float ret = r + gamma * (1.0f - done) * vtp1;
     returns[b] = ret;
 
-    // All steps get advantages — KL penalty provides signal on non-done
-    // steps, trade PnL provides signal on done steps. No done-gating
-    // needed because the KL reward prevents the noise problem (non-done
-    // advantages are small but directional, not zero/noise).
-    advantages[b] = ret - vt;
+    // Advantage with BOTH static (in ret) and dynamic KL components.
+    // Dynamic: -β × log π_θ(a|s) adds entropy-regularized signal.
+    // When π_θ(a) is low (unlikely action taken): -β × negative = positive
+    //   → reinforce exploring unlikely actions
+    // When π_θ(a) is high (likely action taken): -β × ~0 = small
+    //   → don't reinforce further concentration
+    const float dynamic_kl = -beta * log_pi_old[b];
+    advantages[b] = ret - vt + dynamic_kl;
 }