## Line Chart: Sokoban Gridworld: Adjusted Trap Rate ### Overview The image is a line chart comparing the adjusted trap rate (%) in a Sokoban Gridworld environment with and without a grid, as a function of the number of training examples. The chart displays two lines, one representing "Without Grid" (orange) and the other representing "With Grid" (blue). Shaded regions around each line indicate the uncertainty or variability in the data. ### Components/Axes * **Title:** Sokoban Gridworld: Adjusted Trap Rate * **X-axis:** Training Examples, with markers at 0, 30, 60, 90, 120, 150, 180, 210, and 240. * **Y-axis:** Adjusted Trap Rate (%), with markers at 0, 10, 20, 30, 40, 50, 60, 70, and 80. * **Legend:** Located at the bottom of the chart. * Orange line: Without Grid * Blue line: With Grid ### Detailed Analysis **Without Grid (Orange Line):** * **Trend:** The line starts high, drops sharply, then increases, and then decreases again, showing a fluctuating pattern. * **Data Points:** * 0 Training Examples: Approximately 68% * 30 Training Examples: Approximately 0% * 60 Training Examples: Approximately 11% * 90 Training Examples: Approximately 25% * 120 Training Examples: Approximately 23% * 150 Training Examples: Approximately 8% * 180 Training Examples: Approximately 23% * 210 Training Examples: Approximately 21% * 240 Training Examples: Approximately 19% **With Grid (Blue Line):** * **Trend:** The line starts high, drops, then increases, and then decreases again, showing a fluctuating pattern. * **Data Points:** * 0 Training Examples: Approximately 50% * 30 Training Examples: Approximately 38% * 60 Training Examples: Approximately 14% * 90 Training Examples: Approximately 35% * 120 Training Examples: Approximately 18% * 150 Training Examples: Approximately 15% * 180 Training Examples: Approximately 26% * 210 Training Examples: Approximately 15% * 240 Training Examples: Approximately 9% ### Key Observations * Initially, the "Without Grid" trap rate is higher than the "With Grid" trap rate. * Both lines show a significant drop in the trap rate between 0 and 60 training examples. * Both lines fluctuate, indicating that the adjusted trap rate varies with the number of training examples. * The shaded regions around the lines suggest variability in the trap rate for both conditions. ### Interpretation The chart compares the adjusted trap rate in a Sokoban Gridworld environment with and without a grid. The data suggests that initially, the absence of a grid leads to a higher trap rate. However, as the number of training examples increases, both conditions exhibit fluctuating trap rates. The variability indicated by the shaded regions suggests that the performance is not consistent and may depend on other factors not explicitly represented in the chart. The "With Grid" line generally shows a lower trap rate after the initial drop, suggesting that the grid provides some benefit in reducing the likelihood of traps.

\n ## Line Chart: Sokoban Gridworld Adjusted Trap Rate ### Overview This line chart displays the adjusted trap rate (%) for two conditions – "With Grid" and "Without Grid" – as a function of the number of training examples. The chart shows the performance of a Sokoban Gridworld system as it is trained with increasing amounts of data. Shaded areas around each line represent uncertainty or variance in the data. ### Components/Axes * **Title:** Sokoban Gridworld: Adjusted Trap Rate * **X-axis:** Training Examples (ranging from 0 to 240, with markers at 30, 60, 90, 120, 150, 180, 210, and 240) * **Y-axis:** Adjusted Trap Rate (%) (ranging from 0 to 80, with markers at 0, 10, 20, 30, 40, 50, 60, 70, and 80) * **Legend:** * "Without Grid" – Orange line * "With Grid" – Blue line * **Shaded Areas:** Light orange and light blue areas surrounding the respective lines, indicating variance. ### Detailed Analysis The chart presents two lines representing the adjusted trap rate for "With Grid" and "Without Grid" conditions across varying training examples. **"Without Grid" (Orange Line):** The line starts at approximately 48% at 0 training examples. It then sharply declines to around 10% at 30 training examples. It fluctuates between approximately 10% and 30% for the remainder of the training examples, with a peak around 32% at 90 training examples, a dip to approximately 11% at 150 training examples, and ending at approximately 17% at 240 training examples. **"With Grid" (Blue Line):** The line begins at approximately 50% at 0 training examples. It rapidly decreases to around 5% at 30 training examples. It then rises to approximately 33% at 90 training examples, falls to around 10% at 150 training examples, rises again to approximately 25% at 180 training examples, and finally declines to approximately 10% at 240 training examples. The shaded areas around each line indicate the variance in the data. The "Without Grid" shaded area is generally wider than the "With Grid" shaded area, suggesting greater variability in the "Without Grid" condition. ### Key Observations * Both conditions exhibit a significant decrease in adjusted trap rate with increasing training examples. * The "With Grid" condition initially shows a lower trap rate than the "Without Grid" condition, but the lines cross around 60 training examples. * The "With Grid" condition demonstrates more fluctuation in trap rate as training progresses, with a notable peak around 90 training examples. * The "Without Grid" condition shows a more stable, though still fluctuating, trap rate after the initial decline. * The shaded areas suggest that the "Without Grid" condition has more variance in its trap rate than the "With Grid" condition. ### Interpretation The data suggests that both the presence and absence of a grid in the Sokoban Gridworld environment lead to improved performance (lower trap rate) with increased training. Initially, the grid seems to provide a more significant advantage, but as training progresses, the "Without Grid" condition catches up. The fluctuations in the "With Grid" condition might indicate that the grid introduces complexities that require more training to overcome, or that the grid's benefits are more sensitive to the specific training examples. The wider variance in the "Without Grid" condition suggests that the system's performance is more unpredictable in that environment. The initial high trap rates for both conditions indicate that the system starts with a poor understanding of the environment, and learning is crucial for improving performance. The convergence of the lines towards the end of the training period suggests that both conditions are approaching a similar level of performance, although the "Without Grid" condition still exhibits more variability.

## Line Chart: Sokoban Gridworld: Adjusted Trap Rate ### Overview This is a line chart comparing the performance of two methods ("Without Grid" and "With Grid") in a Sokoban Gridworld environment over the course of training. The performance metric is the "Adjusted Trap Rate," expressed as a percentage. The chart includes shaded regions representing confidence intervals or variability around each data point. ### Components/Axes * **Title:** "Sokoban Gridworld: Adjusted Trap Rate" (Top-left, dark blue text). * **Y-Axis:** Labeled "Adjusted Trap Rate (%)". Scale runs from 0 to 80 in increments of 10. * **X-Axis:** Labeled "Training Examples". Scale runs from 0 to 240 in increments of 30. * **Legend:** Located at the bottom center of the chart. * Orange line with circular markers: "Without Grid" * Blue line with circular markers: "With Grid" * **Data Series:** Two lines with associated shaded confidence bands. * **Orange Line ("Without Grid"):** Starts high, drops sharply, then fluctuates. * **Blue Line ("With Grid"):** Starts lower than orange, shows a more gradual overall decline with fluctuations. ### Detailed Analysis **Data Series: "Without Grid" (Orange Line)** * **Trend:** The line exhibits high volatility. It begins with the highest trap rate, plummets to near zero, then experiences a series of rises and falls, ending with a gradual decline. * **Data Points (Approximate):** * 0 Training Examples: ~67% (Highest point on the chart) * 30 Training Examples: ~0% (Lowest point on the chart) * 60 Training Examples: ~11% * 90 Training Examples: ~25% (Local peak) * 120 Training Examples: ~23% * 150 Training Examples: ~9% (Local trough) * 180 Training Examples: ~22% (Local peak) * 210 Training Examples: ~21% * 240 Training Examples: ~19% * **Confidence Interval:** The shaded orange band is widest at 0 examples, narrows significantly at 30, and remains moderately wide through the rest of the series, indicating substantial variability in performance. **Data Series: "With Grid" (Blue Line)** * **Trend:** The line shows a more consistent, though still fluctuating, downward trend. It starts lower than the "Without Grid" method and generally maintains a lower trap rate after the initial training phase, except for two notable spikes. * **Data Points (Approximate):** * 0 Training Examples: ~50% * 30 Training Examples: ~32% * 60 Training Examples: ~14% * 90 Training Examples: ~35% (Significant local peak, surpassing the "Without Grid" rate at this point) * 120 Training Examples: ~18% * 150 Training Examples: ~15% * 180 Training Examples: ~26% (Another local peak, again surpassing the "Without Grid" rate) * 210 Training Examples: ~16% * 240 Training Examples: ~9% (Lowest point for this series) * **Confidence Interval:** The shaded blue band is fairly consistent in width, with slight widening around the peaks at 90 and 180 examples. ### Key Observations 1. **Initial Performance Disparity:** At the start of training (0 examples), the "Without Grid" method has a significantly higher trap rate (~67%) compared to the "With Grid" method (~50%). 2. **Dramatic Early Drop:** The "Without Grid" method shows an extreme, near-total drop in trap rate to ~0% by 30 examples, which is the most dramatic single change in the chart. 3. **Crossover Points:** The two lines cross multiple times. Notably, the "With Grid" method has a higher trap rate at 90 and 180 training examples, creating two distinct peaks where it underperforms the "Without Grid" method. 4. **Final Convergence:** By the end of the observed training (240 examples), both methods show low trap rates, with "With Grid" (~9%) performing better than "Without Grid" (~19%). 5. **Volatility:** Both methods display non-monotonic learning curves, with performance (trap rate) worsening at several points (e.g., 90 and 180 examples) before improving again. ### Interpretation The data suggests that the inclusion of a "Grid" structure in the Sokoban learning environment has a complex, non-linear impact on the agent's tendency to fall into traps. * **Stabilizing vs. Guiding Effect:** The "With Grid" method starts with a lower trap rate and ends with the lowest overall rate, suggesting the grid provides useful structural information that aids long-term learning. However, its performance is not consistently superior, as evidenced by the spikes at 90 and 180 examples. This could indicate phases where the agent is exploring new strategies facilitated by the grid, temporarily increasing risk. * **The "Without Grid" Volatility:** The "Without Grid" method's extreme volatility—especially the crash to near 0% at 30 examples followed by a rebound—might indicate a form of rapid, brittle overfitting to early training examples. The agent may learn a very specific, narrow policy that avoids traps in the initial scenarios but fails to generalize, leading to increased trap rates as training progresses and new scenarios are introduced. * **Underlying Learning Dynamics:** The synchronized peaks at 90 and 180 examples for both methods are striking. This correlation suggests these points in training correspond to the introduction of particularly challenging levels or a shift in the training distribution that causes both agents to struggle, regardless of the grid's presence. The grid appears to mitigate the severity of these struggles somewhat (the blue peaks are lower than the surrounding orange values at those points). * **Conclusion:** The "With Grid" approach appears more robust and leads to better final performance. The "Without Grid" approach shows potential for rapid initial improvement but is unstable and less reliable over the full course of training. The chart highlights that learning in this environment is not a smooth process and is subject to significant setbacks, possibly due to curriculum changes or the inherent complexity of the Sokoban puzzle dynamics.

## Line Chart: Sokoban Gridworld Adjusted Trap Rate ### Overview The chart compares the adjusted trap rate (%) for two Sokoban Gridworld configurations ("Without Grid" and "With Grid") across varying numbers of training examples (0–240). Both lines show a general downward trend, with the "With Grid" configuration consistently outperforming the "Without Grid" variant, particularly at lower training example counts. ### Components/Axes - **X-axis**: Training Examples (0, 30, 60, 90, 120, 150, 180, 210, 240) - **Y-axis**: Adjusted Trap Rate (%) (0–80) - **Legend**: Located at the bottom center, with orange representing "Without Grid" and blue representing "With Grid." - **Shaded Regions**: Gray bands around each line indicate variability/confidence intervals. ### Detailed Analysis 1. **"Without Grid" (Orange Line)** - Starts at **~65%** trap rate at 0 training examples. - Drops sharply to **~0%** at 30 examples. - Fluctuates between **~10%–25%** for 60–240 examples, with minor peaks at 90 (~20%) and 180 (~22%) examples. - Variability decreases over time, with the shaded region narrowing after 120 examples. 2. **"With Grid" (Blue Line)** - Begins at **~50%** trap rate at 0 examples. - Declines to **~10%** at 60 examples. - Peaks at **~35%** at 90 examples, then dips to **~15%** at 120 examples. - Rises again to **~25%** at 180 examples before declining to **~10%** at 240 examples. - Variability is higher than "Without Grid," especially at 90 and 180 examples. ### Key Observations - The "With Grid" configuration achieves **~50% higher trap rate** than "Without Grid" at 0 training examples. - Both methods converge to **~10–20%** trap rate by 240 examples, suggesting diminishing returns with increased training. - The "Without Grid" line exhibits a steeper initial decline, while "With Grid" shows more pronounced fluctuations. - Shaded regions indicate that variability in trap rate decreases for "Without Grid" but remains inconsistent for "With Grid." ### Interpretation The data suggests that incorporating a grid improves trap rate efficiency in Sokoban Gridworld, particularly during early training phases. The grid likely provides structural guidance, reducing exploration errors. However, both configurations eventually plateau, implying that additional training examples yield minimal improvements. The higher variability in the "With Grid" line may reflect sensitivity to grid configuration choices or dynamic adjustments during training. The convergence at higher training counts highlights the importance of balancing grid complexity with training data volume for optimal performance.