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fix: typo

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Daniel Rosel
2026-02-02 12:08:24 +01:00
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paper/src/chapters/03-methodology.tex
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@@ -300,7 +300,7 @@ where $R(p, d)$ is the revenue function and $\lambda$ weighs the penalty for inf
Another proposed formulation of the optimal policy would be to adjust the ambiguity set dyanmically over the live computed divergence where $\epsilon(\Delta_H)$ to adjust the ball around or estimator according to each behavioral signal emited through a given trajctory. We state this as a possibility but do not peruse it due to literature suggesting that wesserstine methods do not require absolute continuity and are better with ``black swans'' \parencite{kuhn_wasserstein_2024}. Another proposed formulation of the optimal policy would be to adjust the ambiguity set dyanmically over the live computed divergence where $\epsilon(\Delta_H)$ to adjust the ball around or estimator according to each behavioral signal emited through a given trajctory. We state this as a possibility but do not peruse it due to literature suggesting that wesserstine methods do not require absolute continuity and are better with ``black swans'' \parencite{kuhn_wasserstein_2024}.
\subsubsection{Actor Implementation} \subsubsection{Actor Implementation}
In our simulation, the "Follower" is implemented as a set of Actors. Each Actor is initialized with a type $\theta$ which samples a specific demand curve $d(p; \theta)$ from the latent distribution. This formalization ensures that our DR-RL agent does not overfit to a single deterministic demand function but learns a policy robust to the distributional uncertainty defined by $\mathcal{U}_\epsilon$. In our simulation, the ``follower'' is implemented as a set of Actors. Each Actor is initialized with a type $\theta$ which samples a specific demand curve $d(p; \theta)$ from the latent distribution. This formalization ensures that our DR-RL agent does not overfit to a single deterministic demand function but learns a policy robust to the distributional uncertainty defined by $\mathcal{U}_\epsilon$.
As part of our reward engineering we think about the UX factor ($UX \in [0,1]$) whic his our proxy for user experience degradation, this is computed as a mixture of contribution from the separability model metric of $\frac{1}{\text{Specificity}}$. As part of our reward engineering we think about the UX factor ($UX \in [0,1]$) whic his our proxy for user experience degradation, this is computed as a mixture of contribution from the separability model metric of $\frac{1}{\text{Specificity}}$.
@@ -320,7 +320,7 @@ We also need to think about a policy like taxation to the agents Strategy-Proof
We now present the complete pricing mechanism that integrates the behavioral separability, contamination estimation, and robust optimization components developed in the preceding sections. Algorithm~\ref{alg:phantom_loop_clean} formalizes the defensive pricing loop as a Stackelberg game where the platform (leader) sets prices and the aggregate demand (follower) responds through observed session trajectories. We now present the complete pricing mechanism that integrates the behavioral separability, contamination estimation, and robust optimization components developed in the preceding sections. Algorithm~\ref{alg:phantom_loop_clean} formalizes the defensive pricing loop as a Stackelberg game where the platform (leader) sets prices and the aggregate demand (follower) responds through observed session trajectories.
\begin{algorithm}[t] \begin{algorithm}[t]
\caption{PHANTOM defensive pricing loop (bachelor-thesis level)} \caption{PHANTOM defensive pricing loop}
\label{alg:phantom_loop_clean} \label{alg:phantom_loop_clean}
\DontPrintSemicolon \DontPrintSemicolon
\SetKwInOut{Input}{Input}\SetKwInOut{Output}{Output} \SetKwInOut{Input}{Input}\SetKwInOut{Output}{Output}