## 3 Preliminary Study
Similarly, if the game designer considers an adjustment to be difficult, some players may find it not very challenging. Considering all aforementioned concerns, we employed GPR, which can quickly and effectively adapt to players for rapid player modeling. In addition, we designed a new goal for our DDA mechanism that balances designer preferences and player performance. Furthermore, we selected a relatively objective in-game variable, the game clear time, to evaluate player performance. In Section 4.3, we detail the current metric for evaluating player performance. By assessing player performance, which can be influenced by changes in their gaming device or environment and result in different perceptions of audio loudness, we can demonstrate that our DDA can still quickly adapt to each player. Algorithm 1 describes the entire DDA process, referred to as GPR-DDA, and Equation (1) illustrates how we balance designer preference and player performance. ```
0:\(\mathit{PT}\)
0:\(\mathit{AS}\)\(\mathit{T}_{\mathit{Best}}\), \(\mathit{T}_{\mathit{Worst}}=\mathit{max}(\mathit{PT}),\mathit{min}(\mathit{PT})\)\(\mathit{PC}=\{\}\)\(\mathit{G}_{\mathit{Final}}=1/2(\mathit{T}_{\mathit{Best}}+\mathit{T}_{ \mathit{Worst}})\)\(\mathit{AS}=\mathit{PT}^{-1}(\mathit{G}_{\mathit{Final}})\)\(\mathit{P}=\mathit{Game}(\mathit{AS})\)\(\mathit{MP}=|\mathit{P}-\mathit{G}_{\mathit{Final}}|\)\(\mathit{i}=1\) Initialize \(\mathit{f}_{\mathit{cur}}\) while\(\mathit{i}\leq\mathit{MaxIterations}\) and \(\mathit{MP}\geq\mathit{Threshold}\)do  Append \((\mathit{AS},\mathit{P})\) to \(\mathit{PC}\)  Fit \(\mathit{f}_{\mathit{cur}}\) with \(\mathit{PC}\) \(\mathit{C}_{\mathit{Best}},\mathit{C}_{\mathit{Worst}}=\mathit{max}(\mathit{f}_ {\mathit{cur}}),\mathit{min}(\mathit{f}_{\mathit{cur}})\)\(\mathit{G}_{\mathit{Final}}=\mathit{GPR}\) Goal Recommendation\((\mathit{C}_{\mathit{Best}},\mathit{C}_{\mathit{Worst}},\mathit{T}_{\mathit{Best}},\mathit{T}_{ \mathit{Worst}})\)\(\mathit{AS}=\mathit{f}_{\mathit{cur}}^{-1}(\mathit{G}_{\mathit{Final}})\)\(\mathit{P}=\mathit{Game}(\mathit{AS})\)\(\mathit{MP}=|\mathit{P}-\mathit{G}_{\mathit{Final}}|\) endwhile
```  
**Algorithm 1** : GPR-DDA  
This algorithm shows that, given a goal called \(G_{\mathit{Final}}\), we use GPR to determine an audio setting that would make the current player's performance close to \(G_{\mathit{Final}}\). In this study, the term \"goal\" refers to the degree of challenge in the \(\mathit{Game}\). \(\mathit{PT}\) is a line representing a designer's preferences, mapping audio cue settings to players' performance. This line can be obtained by using prior data to calculate the average performance of test players. \(\mathit{PC}\) represents the current player's data set, consisting of audio setting \(i\) and the player's performance at this setting. \(\mathit{f}_{\mathit{cur}}\) is a GPR model that returns the current player's predicted performance, \(\mathit{P}\), for a given audio setting, \(\mathit{AS}\). In this algorithm, \(\mathit{C}\) represents the respective performance of the current player and \(\mathit{T}\) represents the respective performance of prior data derived beforehand for each game level, either objectively from test players or subjectively from game designers. The subscripts \(\mathit{Best}\) and \(\mathit{Worst}\), respectively, stand for their best and worst performance among all levels, based on both the actual performance at each seen level and the predicted performance by GPR for each unseen level. \(\mathit{MP}\) is the value used to validate our model's performance, where a value closer to zero indicates a better prediction. The \(\mathit{GPR}\)_Goal Recommendation_, which determines \(G_{\mathit{Final}}\), is the method we used for balancing player performance and designer preference. This algorithm is called the goal recommendation algorithm (Equation (1)). By choosing the enemy audio cue volume setting based on this algorithm in each round, DDA is realized, aligning players' performance with their recommended goals.