adding missing ideas and apendix kl

paper/src/chapters/03-methodology.tex

@@ -223,8 +223,7 @@ The dynamic pricing mechanism elicited immediate behavioral adjustments. Partici
 
 \subsubsection{Design of Training Factorial Study}
 
-The simulator has multiple configurable factors. We design a multi-factor study across five axes derived from the sweep configurations: (1) RL algorithm (\texttt{ppo}, \texttt{a2c}, \texttt{dqn}, \texttt{qtable}; 4 levels), (2) contamination ratio $\alpha$ sampled from $[0.1, 0.6]$ at four representative levels, (3) robustness radius $\epsilon_\alpha \in \{0.0, 0.15, 0.3\}$ (3 levels), (4) COI penalty weight $\lambda_\text{coi}$ at two reference levels, and (5) pricing action granularity (two discretization settings for \texttt{action\_levels}); giving a grid of $4\times4\times3\times2\times2 = 192$ configurations. Statistical power for the behavioral comparisons is determined by a two-sample test over per-session KL divergence scores; a formal power analysis with minimum detectable effect size at $n_H=13$, $n_A=16$ is reported in the results.
-% Power analysis plan: apply a two-sample Mann-Whitney U (or permutation test) on per-session (delta_H - delta_A) divergence scores comparing the human and agent groups. Compute minimum detectable effect size at alpha=0.05, power=0.8, given n_H=13 and n_A=16. Bootstrap confidence intervals on mean KL are a cleaner complement given the non-normality of divergence distributions.
+The simulator has multiple configurable factors. We design a multi-factor study across five axes derived from the sweep configurations: (1) RL algorithm (\texttt{ppo}, \texttt{a2c}, \texttt{dqn}, \texttt{qtable}; 4 levels), (2) contamination ratio $\alpha$ sampled from $[0.1, 0.6]$ at four representative levels, (3) robustness radius $\epsilon_\alpha \in \{0.0, 0.15, 0.3\}$ (3 levels), (4) COI penalty weight $\lambda_\text{coi}$ at two reference levels, and (5) pricing action granularity (two discretization settings for \texttt{action\_levels}); giving a grid of $4\times4\times3\times2\times2 = 192$ configurations. Behavioral distinguishability is assessed with a two-sample Mann--Whitney test on per-session divergence gap scores at cohort sizes $n_H=13$ and $n_A=16$.
 While this scale is generally expensive for reinforcement learning, we execute it on a large TPU cluster to make the sweep tractable.
 
 Our training budget is provisioned through TPU Research Cloud and spans 384 chips across TPU v4, v5e, and v6e generations, with a spot-heavy allocation plus an on-demand reserve. At peak BF16 throughput this corresponds to approximately 160\,PFLOPS of aggregate compute (derivation in Appendix~\ref{app:compute_budget}), which makes repeated seeds, ablations, and sensitivity sweeps feasible within practical wall-clock limits. We allocate v6e capacity to the highest-intensity policy training jobs, use v5e for wider hyperparameter exploration where throughput-per-dollar is favorable, and reserve on-demand v4 capacity for runs that should not be interrupted.
@@ -504,6 +503,7 @@ Practical implementation of browser agents is a strongly evolving field with nea
 
 
 As part of reward engineering, we keep a UX factor ($UX\in[0,1]$) as an auxiliary evaluation axis. In code, the UX index is implemented as a volatility penalty on relative price changes, with an extra upward-volatility component weighted by $0.5$ and scaled by $\eta_{\text{ux}}$ and an information-budget term. We also keep a separate supra-competitive penalty tied to persistent price excess above a competitive anchor, which punishes high-price behavior even when volatility is low.
+We measure volatility as mean absolute relative price movement, $v_t=\frac{1}{N}\sum_{i=1}^N\bigl|(p_{t,i}-p_{t-1,i})/\max(p_{t-1,i},1)\bigr|$.
 
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