## Line Chart: 8x8 Gridworld: Success vs Optimal Rate ### Overview The image is a line chart comparing the success rate and optimal rate of two methods, "Best Baseline" and "L-ICL," across varying numbers of training examples in an 8x8 Gridworld environment. The chart displays the performance of each method, along with shaded regions indicating variability or confidence intervals. ### Components/Axes * **Title:** 8x8 Gridworld: Success vs Optimal Rate * **X-axis:** Training Examples, with markers at 0, 30, 60, 90, 120, 150, 180, 210, and 240. * **Y-axis:** Rate (%), with markers at 0, 10, 20, 30, 40, 50, 60, 70, 80, and 90. * **Legend:** Located at the bottom of the chart. * Best Baseline Success (Self-Consistency) - Dashed Blue Line * Best Baseline Optimal (Self-Consistency) - Dashed Orange Line * L-ICL Success - Solid Blue Line * L-ICL Optimal - Solid Orange Line ### Detailed Analysis * **Best Baseline Success (Self-Consistency):** Represented by a dashed blue line. The line is approximately flat at a rate of 45%. * **Best Baseline Optimal (Self-Consistency):** Represented by a dashed orange line. The line is approximately flat at a rate of 45%. * **L-ICL Success:** Represented by a solid blue line. * Starts at approximately 10% at 0 Training Examples. * Rises sharply to approximately 46% at 30 Training Examples. * Increases to approximately 63% at 60 Training Examples. * Decreases slightly to approximately 59% at 90 Training Examples. * Increases to approximately 63% at 120 Training Examples. * Increases to approximately 69% at 150 Training Examples. * Increases to approximately 77% at 180 Training Examples. * Decreases slightly to approximately 73% at 210 Training Examples. * Increases to approximately 74% at 240 Training Examples. * **L-ICL Optimal:** Represented by a solid orange line. * Starts at approximately 10% at 0 Training Examples. * Rises sharply to approximately 46% at 30 Training Examples. * Decreases slightly to approximately 51% at 60 Training Examples. * Increases to approximately 63% at 90 Training Examples. * Increases to approximately 65% at 120 Training Examples. * Increases to approximately 69% at 150 Training Examples. * Decreases to approximately 67% at 180 Training Examples. * Increases to approximately 78% at 210 Training Examples. * Decreases slightly to approximately 71% at 240 Training Examples. ### Key Observations * The "Best Baseline" methods (both Success and Optimal) remain relatively constant across all training examples, hovering around 45%. * The "L-ICL" methods (both Success and Optimal) show a significant increase in rate as the number of training examples increases, particularly in the early stages. * The "L-ICL Success" rate is generally higher than the "L-ICL Optimal" rate, especially after 60 training examples. * Both "L-ICL" lines show some fluctuation, but generally trend upwards. ### Interpretation The data suggests that the "L-ICL" methods are more effective than the "Best Baseline" methods in the 8x8 Gridworld environment, as they achieve higher success and optimal rates with increasing training examples. The "Best Baseline" methods appear to have a fixed performance level, regardless of the number of training examples. The fluctuations in the "L-ICL" lines could be due to the learning process, where the model adjusts its strategy based on the training data. The shaded regions around the lines likely represent the variance in the results across multiple runs or experiments, indicating the reliability of the observed trends.

## Line Chart: 8x8 Gridworld: Success vs Optimal Rate ### Overview This line chart compares the success rate and optimal rate in an 8x8 Gridworld environment as a function of the number of training examples. The chart displays two main lines representing the success and optimal rates, along with shaded areas indicating the lower and upper confidence intervals (L-ICL). Two dashed lines represent the baseline success and optimal rates. ### Components/Axes * **Title:** 8x8 Gridworld: Success vs Optimal Rate * **X-axis:** Training Examples (Scale: 0 to 240, increments of 30) * **Y-axis:** Rate (%) (Scale: 0 to 90, increments of 10) * **Legend:** Located at the bottom-center of the chart. * Best Baseline Success (Self-Consistency) - Dashed Orange Line * Best Baseline Optimal (Self-Consistency) - Dashed Blue Line * L-ICL Success - Blue Line with Shaded Area * L-ICL Optimal - Orange Line with Shaded Area ### Detailed Analysis The chart shows the following trends and data points: * **Best Baseline Success (Self-Consistency):** This is a horizontal dashed orange line. It remains relatively constant at approximately 44% throughout the range of training examples. * **Best Baseline Optimal (Self-Consistency):** This is a horizontal dashed blue line. It remains relatively constant at approximately 42% throughout the range of training examples. * **L-ICL Success (Blue Line):** This line starts at approximately 44% at 0 training examples. It decreases to around 30% at 30 training examples, then increases, reaching a peak of approximately 75% at 150 training examples. It then fluctuates, ending at approximately 72% at 240 training examples. * **L-ICL Optimal (Orange Line):** This line starts at approximately 42% at 0 training examples. It decreases sharply to around 25% at 30 training examples, then increases, reaching a peak of approximately 72% at 150 training examples. It then fluctuates, ending at approximately 70% at 240 training examples. * **L-ICL Success Shaded Area:** The shaded area around the blue line represents the lower and upper confidence intervals. The width of the shaded area varies, indicating the uncertainty in the success rate. * **L-ICL Optimal Shaded Area:** The shaded area around the orange line represents the lower and upper confidence intervals. The width of the shaded area varies, indicating the uncertainty in the optimal rate. Here's a more detailed breakdown of approximate values at specific training example points: | Training Examples | L-ICL Success (%) | L-ICL Optimal (%) | |---|---|---| | 0 | 44 | 42 | | 30 | 30 | 25 | | 60 | 58 | 52 | | 90 | 62 | 58 | | 120 | 68 | 64 | | 150 | 75 | 72 | | 180 | 70 | 66 | | 210 | 73 | 68 | | 240 | 72 | 70 | ### Key Observations * Both the success and optimal rates initially decrease with a small number of training examples (0-30). * Both rates increase significantly between 30 and 150 training examples, suggesting a learning phase. * After 150 training examples, the rates fluctuate but generally remain high. * The success rate (blue line) is consistently slightly higher than the optimal rate (orange line) after approximately 60 training examples. * The confidence intervals (shaded areas) are wider at the beginning and end of the training period, indicating greater uncertainty. ### Interpretation The data suggests that the agent's performance (both success and optimal rates) in the 8x8 Gridworld environment improves with more training examples. The initial decrease in performance may be due to the agent exploring the environment and learning the basic dynamics. The subsequent increase indicates that the agent is learning to navigate and achieve its goals more effectively. The fact that the success rate is consistently higher than the optimal rate after a certain point suggests that the agent is not only finding optimal solutions but also succeeding in other, potentially suboptimal, ways. The confidence intervals provide a measure of the reliability of the results, indicating that the performance is more consistent with a larger number of training examples. The baseline rates are relatively low, indicating that the self-consistency method provides a significant improvement in performance. The fluctuations in the rates after 150 training examples could be due to the complexity of the environment or the stochastic nature of the learning process.

## Line Chart: 8×8 Gridworld: Success vs Optimal Rate ### Overview The image displays a line chart comparing the performance of two methods ("L-ICL Success" and "L-ICL Optimal") against two baseline benchmarks over an increasing number of training examples. The chart tracks two metrics—Success Rate and Optimal Rate—measured as percentages. The data shows a general upward trend for the L-ICL methods, with performance surpassing the static baselines after approximately 30 training examples. ### Components/Axes * **Title:** "8×8 Gridworld: Success vs Optimal Rate" (Top-left corner). * **Y-Axis:** Labeled "Rate (%)". Scale ranges from 0 to 90, with major tick marks at intervals of 10 (0, 10, 20, ..., 90). * **X-Axis:** Labeled "Training Examples". Scale ranges from 0 to 240, with major tick marks at intervals of 30 (0, 30, 60, ..., 240). * **Legend:** Positioned at the bottom center of the chart. It contains four entries: 1. `--` **Best Baseline Success (Self-Consistency)**: A dashed blue line. 2. `--` **Best Baseline Optimal (Self-Consistency)**: A dashed orange line. 3. `●-` **L-ICL Success**: A solid blue line with circular markers. 4. `●-` **L-ICL Optimal**: A solid orange line with circular markers. * **Data Series & Confidence Intervals:** Each solid line (L-ICL) is accompanied by a shaded region of the same color, representing a confidence interval or variance band around the mean performance. ### Detailed Analysis **Trend Verification & Data Points (Approximate):** * **L-ICL Success (Blue Line with Markers):** * **Trend:** Shows a steep initial increase, followed by a generally upward but fluctuating trend. It consistently remains above the L-ICL Optimal line. * **Key Points:** * At 0 examples: ~12% * At 30 examples: ~46% * At 60 examples: ~63% * At 120 examples: ~64% * At 150 examples: ~69% * At 165 examples (peak): ~77% * At 180 examples: ~71% * At 210 examples: ~78% * At 240 examples: ~74% * **L-ICL Optimal (Orange Line with Markers):** * **Trend:** Follows a very similar trajectory to the Success line but is consistently a few percentage points lower. Also shows an initial steep rise and subsequent fluctuations. * **Key Points:** * At 0 examples: ~12% * At 30 examples: ~43% * At 60 examples: ~51% * At 120 examples: ~59% * At 150 examples: ~64% * At 165 examples (peak): ~76% * At 180 examples: ~67% * At 210 examples: ~75% * At 240 examples: ~71% * **Best Baseline Success (Dashed Blue Line):** * **Trend:** Horizontal, constant line. * **Value:** Approximately 45% across all training examples. * **Best Baseline Optimal (Dashed Orange Line):** * **Trend:** Horizontal, constant line. * **Value:** Approximately 43% across all training examples. **Confidence Intervals (Shaded Regions):** * The shaded bands for both L-ICL lines are narrow at low training example counts (0-30) and widen significantly as the number of examples increases, particularly beyond 90 examples. This indicates greater variance or uncertainty in performance with more training data. * The blue shaded region (Success) is generally wider than the orange one (Optimal) at higher example counts. ### Key Observations 1. **Performance Crossover:** Both L-ICL methods surpass their respective baselines after approximately 30 training examples. 2. **Metric Hierarchy:** The "Success" rate is consistently higher than the "Optimal" rate for the L-ICL method, which is logically consistent if "Optimal" represents a stricter performance criterion. 3. **Plateau and Fluctuation:** After the initial rapid learning phase (0-60 examples), performance gains slow and exhibit noticeable fluctuations (e.g., dips at 180 examples), though the overall trend remains positive. 4. **Peak Performance:** Both L-ICL metrics appear to peak around 165-210 training examples before a slight decline at 240. 5. **Baseline Comparison:** The static baselines (Self-Consistency) are outperformed by the L-ICL approach with sufficient data, suggesting the latter is a more effective learning method in this context. ### Interpretation The chart demonstrates the learning curve of an "L-ICL" (likely "Learning from In-Context Learning") approach on an 8x8 Gridworld task. The key takeaway is that L-ICL is data-efficient, quickly exceeding strong baseline performance with only ~30 examples. The continued, albeit noisy, improvement up to ~210 examples suggests the method benefits from more data, though returns diminish and variance increases. The consistent gap between "Success" and "Optimal" rates implies that while the agent often succeeds in reaching a goal (Success), it less frequently finds the most efficient or correct path (Optimal). The widening confidence intervals could indicate that with more diverse training examples, the model's performance becomes less predictable—some runs excel while others struggle, increasing the variance. This chart would be critical for a researcher to determine the optimal amount of training data to collect and to understand the reliability (via confidence intervals) of the L-ICL method at different data scales.

## Line Chart: 8x8 Gridworld: Success vs Optimal Rate ### Overview The chart compares the performance of two methods ("Best Baseline" and "L-ICL") across two metrics ("Success" and "Optimal Rate") as training examples increase from 0 to 240. Performance is measured as a percentage rate, with shaded regions indicating confidence intervals. ### Components/Axes - **X-axis**: Training Examples (0–240, increments of 30) - **Y-axis**: Rate (%) (0–90, increments of 10) - **Legend**: - Dashed Blue: Best Baseline Success - Dashed Orange: Best Baseline Optimal - Solid Blue: L-ICL Success - Solid Orange: L-ICL Optimal - **Shaded Regions**: Confidence intervals (wider for L-ICL lines) ### Detailed Analysis 1. **Best Baseline Success (Dashed Blue)**: - Starts at ~10% at 0 training examples. - Peaks at ~60% at 60 examples. - Fluctuates between ~50–70% up to 240 examples. - Confidence interval widens slightly after 60 examples. 2. **Best Baseline Optimal (Dashed Orange)**: - Starts at ~5% at 0 training examples. - Peaks at ~55% at 60 examples. - Fluctuates between ~40–65% up to 240 examples. - Confidence interval remains narrow throughout. 3. **L-ICL Success (Solid Blue)**: - Starts at ~10% at 0 training examples. - Peaks at ~75% at 160 examples. - Dips to ~70% at 240 examples. - Confidence interval widens significantly after 60 examples. 4. **L-ICL Optimal (Solid Orange)**: - Starts at ~5% at 0 training examples. - Peaks at ~70% at 160 examples. - Dips to ~70% at 240 examples. - Confidence interval widens significantly after 60 examples. ### Key Observations - **Performance Trends**: - L-ICL methods outperform Best Baseline in both metrics after ~90 training examples. - L-ICL Success achieves the highest peak (~75%) but shows higher variability. - L-ICL Optimal maintains a narrower confidence interval despite lower peak performance (~70%). - **Crossovers**: - L-ICL Success surpasses Best Baseline Success after ~90 examples. - L-ICL Optimal overtakes Best Baseline Optimal after ~60 examples. - **Confidence Intervals**: - L-ICL methods exhibit greater uncertainty (wider shaded regions) compared to Best Baseline. ### Interpretation The data suggests that L-ICL methods are more effective in the 8x8 Gridworld task as training examples increase, particularly for the "Success" metric. However, their higher confidence intervals indicate less consistency compared to Best Baseline. The "Optimal" metric shows L-ICL methods achieving comparable performance to Best Baseline with fewer training examples but maintaining narrower confidence intervals. This could imply that L-ICL methods are more efficient but less robust to variability in training data. The divergence in performance between "Success" and "Optimal" rates highlights a potential trade-off between achieving high success rates and maintaining optimal behavior in the Gridworld environment.