## Line Chart: EGA vs. Environment Step for Different Alpha Values ### Overview The image is a line chart that plots the Expected Goal Achievement (EGA) against the Environment Step for four different values of alpha (α): 7, 8, 9, and 10. The chart shows how the EGA changes over time (environment steps) for each alpha value. The legend is located in the bottom-right corner of the chart. ### Components/Axes * **X-axis:** Environment step, ranging from 0 to 3000 in increments of 1000. * **Y-axis:** EGA (Expected Goal Achievement), ranging from 0.2 to 1.0 in increments of 0.2. * **Legend:** Located in the bottom-right corner, indicating the alpha values: * Dark Blue: αᵢ = 7 * Orange: αᵢ = 8 * Blue: αᵢ = 9 * Teal: αᵢ = 10 ### Detailed Analysis * **αᵢ = 7 (Dark Blue):** The EGA starts at approximately 0.2, increases steadily until around environment step 1500 where it reaches approximately 0.95, and then plateaus at approximately 0.95 for the remainder of the steps. * **αᵢ = 8 (Orange):** The EGA starts at approximately 0.15, increases steadily until around environment step 1500 where it reaches approximately 0.95, and then plateaus at approximately 0.95 for the remainder of the steps. * **αᵢ = 9 (Blue):** The EGA starts at approximately 0.15, increases steadily until around environment step 1500 where it reaches approximately 0.97, and then plateaus at approximately 0.97 for the remainder of the steps. * **αᵢ = 10 (Teal):** The EGA starts at approximately 0.15, increases steadily until around environment step 1500 where it reaches approximately 0.98, and then plateaus at approximately 0.98 for the remainder of the steps. ### Key Observations * All four alpha values show a similar trend: a rapid increase in EGA up to around 1500 environment steps, followed by a plateau. * Higher alpha values (9 and 10) achieve slightly higher EGA plateaus compared to lower alpha values (7 and 8). * The shaded regions around each line indicate the variance or uncertainty in the EGA values. ### Interpretation The chart suggests that increasing the alpha value generally leads to a slightly higher Expected Goal Achievement. However, the difference in EGA between the different alpha values is relatively small, especially after the initial learning phase (up to 1500 environment steps). The plateauing of EGA indicates that after a certain number of environment steps, further training does not significantly improve the agent's performance, regardless of the alpha value. The alpha values of 9 and 10 appear to perform slightly better than 7 and 8.

\n ## Line Chart: EGA vs. Environment Step for Different Alpha Values ### Overview This image presents a line chart illustrating the relationship between EGA (presumably a performance metric) and the number of environment steps, for four different values of αᵢ (alpha i). The chart shows how EGA evolves over time for each alpha value. ### Components/Axes * **X-axis:** "Environment step" ranging from approximately 0 to 3000. * **Y-axis:** "EGA" ranging from approximately 0.0 to 1.0. * **Legend:** Located in the top-right corner, it identifies four lines, each corresponding to a different αᵢ value: * αᵢ = 7 (Black line) * αᵢ = 8 (Gray line) * αᵢ = 9 (Orange line) * αᵢ = 10 (Teal line) * **Grid:** A light gray grid is present, aiding in reading values from the chart. ### Detailed Analysis The chart displays four lines, each representing the change in EGA over environment steps for a specific αᵢ value. * **αᵢ = 7 (Black Line):** The line starts at approximately 0.15 at Environment step 0. It increases steadily until around Environment step 800, where it begins to plateau. It reaches approximately 0.95 at Environment step 1500 and remains relatively stable around 0.97-0.99 for the rest of the range. * **αᵢ = 8 (Gray Line):** This line begins at approximately 0.16 at Environment step 0. It shows a similar trend to αᵢ = 7, but with a slightly slower initial increase. It reaches approximately 0.94 at Environment step 1400 and stabilizes around 0.97-0.99. * **αᵢ = 9 (Orange Line):** Starting at approximately 0.17 at Environment step 0, this line exhibits a faster initial increase compared to αᵢ = 7 and αᵢ = 8. It reaches approximately 0.96 at Environment step 1300 and stabilizes around 0.98-0.99. * **αᵢ = 10 (Teal Line):** This line starts at approximately 0.18 at Environment step 0. It demonstrates the fastest initial increase among all four lines. It reaches approximately 0.97 at Environment step 1200 and stabilizes around 0.98-0.99. All four lines converge towards a similar EGA value (around 0.97-0.99) as the number of environment steps increases. ### Key Observations * The lines show a clear upward trend, indicating that EGA generally increases with the number of environment steps. * Higher αᵢ values lead to faster initial increases in EGA. * The lines converge as the number of environment steps increases, suggesting that the impact of αᵢ diminishes over time. * There is a slight difference in the final EGA values achieved by each αᵢ value, with αᵢ = 9 and αᵢ = 10 achieving slightly higher values than αᵢ = 7 and αᵢ = 8. ### Interpretation The data suggests that the parameter αᵢ plays a role in the initial learning or performance rate, with higher values leading to faster progress. However, the convergence of the lines indicates that the long-term performance is less sensitive to the initial αᵢ value. This could imply that the system reaches a saturation point where further increases in αᵢ do not significantly improve EGA. The EGA metric likely represents some form of accumulated reward or performance score within the environment. The environment steps represent the progression of the agent's interaction with the environment. The chart demonstrates how different learning rates (controlled by αᵢ) affect the speed at which the agent learns and optimizes its performance. The convergence suggests that the environment presents a limited learning opportunity, and the agent eventually reaches a point of diminishing returns regardless of the initial learning rate.

## Line Chart: EGA vs. Environment Step for Different α_i Values ### Overview The image displays a line chart plotting the metric "EGA" against "Environment step" for four different values of a parameter labeled α_i. The chart shows a learning or performance curve where EGA increases rapidly with environment steps before plateauing. All four lines follow a very similar trajectory, with minor differences in their final plateau values. ### Components/Axes * **X-Axis (Horizontal):** * **Label:** "Environment step" * **Scale:** Linear scale from 0 to 3000. * **Major Tick Marks:** 0, 1000, 2000, 3000. * **Y-Axis (Vertical):** * **Label:** "EGA" * **Scale:** Linear scale from 0.2 to 1.0. * **Major Tick Marks:** 0.2, 0.4, 0.6, 0.8, 1.0. * **Legend:** * **Position:** Bottom-right corner of the plot area. * **Content:** Four entries, each associating a line color with a value of α_i. * Dark Blue Line: α_i = 7 * Orange Line: α_i = 8 * Blue Line: α_i = 9 * Green Line: α_i = 10 * **Data Series:** Four colored lines, each with a shaded band of the same color surrounding it, likely representing variance or confidence intervals. ### Detailed Analysis **Trend Verification:** All four data series exhibit the same fundamental trend: a steep, roughly linear increase from the start (step 0) until approximately step 1500, followed by a sharp transition to a flat plateau for the remainder of the steps (up to 3000). **Data Point Extraction (Approximate):** * **Starting Point (Step 0):** All lines begin at an EGA value of approximately **0.15**. * **Growth Phase (Steps 0-1500):** The lines are tightly clustered, making individual values difficult to distinguish. They cross key EGA thresholds at approximate environment steps: * EGA = 0.4: ~Step 500 * EGA = 0.6: ~Step 800 * EGA = 0.8: ~Step 1100 * **Plateau Phase (Steps 1500-3000):** The lines diverge slightly at their final, stable values. * **α_i = 7 (Dark Blue):** Plateaus at the lowest value, approximately **EGA = 0.92**. * **α_i = 8 (Orange), α_i = 9 (Blue), α_i = 10 (Green):** These three lines plateau at a very similar, higher value, approximately **EGA = 0.97**. The green line (α_i=10) may be infinitesimally higher than the orange and blue lines, but the difference is within the visual uncertainty of the plot. ### Key Observations 1. **High Similarity in Learning Dynamics:** The primary observation is the remarkable similarity in the learning trajectory for all four α_i values during the growth phase (0-1500 steps). The lines overlap significantly, suggesting the parameter α_i has minimal impact on the *rate* of EGA improvement during this phase. 2. **Parameter Impact on Final Performance:** The main differentiating effect of α_i appears in the final plateau value. The lowest tested value (α_i=7) results in a slightly lower asymptotic performance compared to the higher values (8, 9, 10), which cluster together. 3. **Clear Phase Transition:** There is a distinct "knee" in the curve around step 1500, marking a rapid shift from active learning/improvement to a stable, converged state. 4. **Low Variance:** The shaded error bands around each line are relatively narrow, indicating consistent performance across multiple runs or low variance in the measurement of EGA for each condition. ### Interpretation This chart likely illustrates the performance of a learning agent (e.g., in reinforcement learning) where "EGA" is a success metric (e.g., Expected Goal Achievement, Episode Gain Average) and "Environment step" represents training time or interaction count. The parameter α_i could be a hyperparameter like a learning rate, exploration factor, or network capacity. The data suggests that within the tested range (7-10), α_i is not a critical factor for the *speed* of learning, as all agents learn at nearly the same rate. However, it does influence the *final quality* of the learned policy or solution. A value of α_i=7 leads to a sub-optimal plateau, while values of 8 and above allow the agent to reach a higher, near-maximal performance ceiling (close to 1.0). The clustering of α_i=8,9,10 indicates a saturation point; increasing α_i beyond 8 yields diminishing returns for final performance. The sharp transition to a plateau suggests the task has a clear maximum achievable score, which the agents with α_i ≥ 8 successfully reach and maintain.

## Line Graph: EGA Convergence Across Environment Steps ### Overview The image depicts a line graph illustrating the convergence of Expected Goal Achievement (EGA) values across different environment steps for four distinct α (alpha) parameter settings. The graph shows four colored lines representing α values of 7, 8, 9, and 10, with shaded regions indicating uncertainty bounds. All lines plateau at high EGA values after approximately 1,500 environment steps. ### Components/Axes - **Y-axis (EGA)**: Ranges from 0.0 to 1.0 in increments of 0.2. Represents the Expected Goal Achievement metric. - **X-axis (Environment step)**: Ranges from 0 to 3,000 in increments of 1,000. Represents sequential training steps in an environment. - **Legend**: Located in the bottom-right corner, mapping colors to α values: - Black: α = 7 - Orange: α = 8 - Blue: α = 9 - Green: α = 10 - **Shaded Regions**: Gray bands around each line indicate uncertainty estimates, with width decreasing as environment steps increase. ### Detailed Analysis 1. **α = 7 (Black Line)**: - Starts at ~0.15 EGA at 0 steps. - Gradually increases to ~0.95 EGA by 2,000 steps. - Plateaus with minimal fluctuation beyond 2,000 steps. - Uncertainty band widest at early steps (~0.1–0.2 range), narrowing to ±0.02 by 3,000 steps. 2. **α = 8 (Orange Line)**: - Begins slightly higher (~0.18 EGA) than α = 7. - Reaches ~0.97 EGA by 2,000 steps. - Maintains a stable plateau with uncertainty band narrowing to ±0.015 by 3,000 steps. 3. **α = 9 (Blue Line)**: - Initial EGA ~0.22 at 0 steps. - Accelerates to ~0.98 EGA by 1,500 steps. - Uncertainty band reduces to ±0.01 by 3,000 steps. 4. **α = 10 (Green Line)**: - Highest starting EGA (~0.25). - Rapidly converges to 1.0 EGA by 1,200 steps. - Uncertainty band collapses to ±0.005 by 3,000 steps. ### Key Observations - **Convergence Pattern**: All α values exhibit rapid EGA growth in early steps, with diminishing returns after ~1,500 steps. - **α Sensitivity**: Higher α values achieve higher plateau EGA (α = 10 reaches 1.0 vs. α = 7 at 0.95). - **Uncertainty Trends**: Confidence intervals shrink significantly with more environment steps, suggesting improved model stability. - **Line Proximity**: Lines for α = 8–10 overlap closely after 2,000 steps, indicating similar performance at high α thresholds. ### Interpretation The graph demonstrates that increasing α accelerates EGA convergence and achieves higher maximum values. The shaded uncertainty regions imply that early training is less reliable, with models stabilizing after ~1,500 steps. The near-identical performance of α = 8–10 at 3,000 steps suggests diminishing returns for α > 9. This could indicate an optimal α range for balancing computational cost and performance. The rapid rise in EGA for α = 10 (green line) implies that higher α values may prioritize goal achievement at the expense of other factors (e.g., exploration efficiency), warranting further investigation into trade-offs.