## Chart: Training Accuracy ### Overview The image is a line graph comparing the training accuracy of two algorithms, GRPO (w/o PRM) and AIRL-S (w. PRM), over a number of steps. The graph shows the accuracy of each algorithm as a function of the training step, with shaded regions indicating the variance or standard deviation around the mean accuracy. ### Components/Axes * **Title:** Training Accuracy * **X-axis:** Step, with markers at 0, 50, 100, 150, and 200. * **Y-axis:** Accuracy, with markers at 0.32, 0.34, 0.36, 0.38, 0.40, and 0.42. * **Legend:** Located at the bottom of the chart. * Blue line: GRPO (w/o PRM) * Red line: AIRL-S (w. PRM) ### Detailed Analysis * **GRPO (w/o PRM) - Blue Line:** * Trend: The blue line generally slopes upward, indicating an increase in accuracy as the number of steps increases. The line exhibits fluctuations. * Data Points: * At step 0, accuracy is approximately 0.32. * At step 50, accuracy is approximately 0.36. * At step 100, accuracy is approximately 0.37. * At step 150, accuracy is approximately 0.37. * At step 200, accuracy is approximately 0.38. * **AIRL-S (w. PRM) - Red Line:** * Trend: The red line generally slopes upward, indicating an increase in accuracy as the number of steps increases. The line exhibits fluctuations. * Data Points: * At step 0, accuracy is approximately 0.32. * At step 50, accuracy is approximately 0.38. * At step 100, accuracy is approximately 0.40. * At step 150, accuracy is approximately 0.41. * At step 200, accuracy is approximately 0.42. ### Key Observations * Both algorithms show an increase in accuracy as the number of training steps increases. * AIRL-S (w. PRM) consistently outperforms GRPO (w/o PRM) in terms of training accuracy. * The shaded regions around each line indicate the variance in the accuracy, with AIRL-S (w. PRM) showing less variance than GRPO (w/o PRM). ### Interpretation The data suggests that AIRL-S (w. PRM) is a more effective algorithm for this particular training task, as it achieves higher accuracy and exhibits less variance compared to GRPO (w/o PRM). The inclusion of PRM (presumably a specific technique or module) in AIRL-S appears to contribute to its superior performance. The increasing accuracy of both algorithms over time indicates that they are learning and improving their performance as they are exposed to more training data. The fluctuations in the lines suggest that the learning process is not perfectly smooth and may be affected by noise or other factors.

\n ## Line Chart: Training Accuracy ### Overview This line chart displays the training accuracy of two different models, GRPO (without PRM) and AIRL-S (with PRM), over a series of training steps. The chart shows the mean accuracy for each model, along with a shaded region representing the standard deviation around the mean. ### Components/Axes * **Title:** "Training Accuracy" - positioned at the top-center of the chart. * **X-axis:** "Step" - ranging from approximately 0 to 220, with tick marks at intervals of 50. * **Y-axis:** "Accuracy" - ranging from approximately 0.32 to 0.42, with tick marks at intervals of 0.02. * **Legend:** Located in the bottom-center of the chart. * **Blue Line:** "GRPO (w/o PRM)" * **Red Line:** "AIRL-S (w. PRM)" * **Shaded Regions:** Light blue around the blue line, and light red around the red line, representing the standard deviation. ### Detailed Analysis **AIRL-S (w. PRM) - Red Line:** The red line representing AIRL-S shows an upward trend throughout the training process. * At Step 0, the accuracy is approximately 0.33. * At Step 50, the accuracy is approximately 0.39. * At Step 100, the accuracy is approximately 0.40. * At Step 150, the accuracy is approximately 0.41. * At Step 200, the accuracy is approximately 0.41. * At Step 220, the accuracy is approximately 0.41. The shaded region around the red line indicates a relatively consistent standard deviation, ranging from approximately 0.01 to 0.02. **GRPO (w/o PRM) - Blue Line:** The blue line representing GRPO shows a more fluctuating trend, with periods of increase and decrease. * At Step 0, the accuracy is approximately 0.33. * At Step 50, the accuracy is approximately 0.36. * At Step 100, the accuracy is approximately 0.37. * At Step 150, the accuracy is approximately 0.37. * At Step 200, the accuracy is approximately 0.38. * At Step 220, the accuracy is approximately 0.38. The shaded region around the blue line indicates a larger and more variable standard deviation, ranging from approximately 0.01 to 0.03. ### Key Observations * AIRL-S consistently outperforms GRPO in terms of training accuracy. * The standard deviation of AIRL-S is smaller than that of GRPO, indicating more stable training. * GRPO exhibits more volatility in its training accuracy, suggesting it may be more sensitive to variations in the training data or hyperparameters. * Both models appear to converge towards a stable accuracy level after approximately 150 steps. ### Interpretation The data suggests that incorporating PRM (as in AIRL-S) leads to improved and more stable training accuracy compared to not using PRM (as in GRPO). The consistent upward trend and smaller standard deviation of AIRL-S indicate that it learns more effectively and is less prone to overfitting or instability during training. The fluctuating behavior of GRPO suggests that it may require more careful tuning or regularization to achieve comparable performance. The convergence of both models after 150 steps implies that the training process is reaching a point of diminishing returns, and further training may not yield significant improvements in accuracy. The difference in performance between the two models highlights the importance of the PRM component in achieving optimal results.

\n ## Line Chart: Training Accuracy Comparison ### Overview The image displays a line chart titled "Training Accuracy," comparing the performance of two machine learning training methods over 200+ steps. The chart plots accuracy values on the y-axis against training steps on the x-axis. Each method is represented by a solid line (mean performance) and a semi-transparent shaded region (likely representing variance or confidence intervals). ### Components/Axes * **Chart Title:** "Training Accuracy" (centered at the top). * **Y-Axis:** * **Label:** "Accuracy" (rotated vertically on the left side). * **Scale:** Linear scale ranging from 0.32 to 0.42. * **Tick Marks:** Major ticks at 0.32, 0.34, 0.36, 0.38, 0.40, 0.42. * **X-Axis:** * **Label:** "Step" (centered at the bottom). * **Scale:** Linear scale from 0 to just beyond 200. * **Tick Marks:** Major ticks at 0, 50, 100, 150, 200. * **Legend:** Located in the bottom-right quadrant of the chart area. * **Blue Line:** Labeled "GRPO (w/o PRM)". * **Red Line:** Labeled "AIRL-S (w. PRM)". * **Data Series:** 1. **Blue Line (GRPO w/o PRM):** A solid blue line with a light blue shaded region around it. 2. **Red Line (AIRL-S w. PRM):** A solid red line with a light red shaded region around it. ### Detailed Analysis **Trend Verification & Data Points:** * **GRPO (w/o PRM) - Blue Line:** * **Visual Trend:** The line shows a rapid initial increase from step 0 to approximately step 50, after which the rate of improvement slows significantly, entering a noisy plateau phase from step 100 onward. * **Approximate Data Points:** * Step 0: ~0.32 * Step 50: ~0.36 * Step 100: ~0.37 * Step 150: ~0.375 * Step 200: ~0.38 * **Uncertainty (Shaded Region):** The blue shaded region is relatively narrow initially but widens considerably after step 50, indicating increased variance in performance. The width suggests the accuracy for this method fluctuates within a band of approximately ±0.01 to ±0.015 around the mean line during the plateau phase. * **AIRL-S (w. PRM) - Red Line:** * **Visual Trend:** The line exhibits a strong, sustained upward trend throughout the entire training period shown. The slope is steepest initially and remains positive, though slightly less steep, after step 100. It consistently stays above the blue line after the first ~20 steps. * **Approximate Data Points:** * Step 0: ~0.32 (similar starting point to blue line) * Step 50: ~0.385 * Step 100: ~0.405 * Step 150: ~0.415 * Step 200: ~0.42 * **Uncertainty (Shaded Region):** The red shaded region is also present and appears to widen as training progresses, similar to the blue region. Its width suggests a variance of approximately ±0.01 to ±0.02 around the mean red line, particularly in the later steps. **Spatial Grounding:** The legend is positioned in the bottom-right, clearly associating the blue color with "GRPO (w/o PRM)" and the red color with "AIRL-S (w. PRM)". The lines and their corresponding shaded regions maintain these color assignments throughout the chart. ### Key Observations 1. **Performance Gap:** A clear and growing performance gap emerges early in training. By step 50, AIRL-S (w. PRM) is already about 0.025 accuracy points higher than GRPO (w/o PRM). This gap widens to approximately 0.04 points by step 200. 2. **Learning Dynamics:** GRPO (w/o PRM) appears to converge or plateau around an accuracy of 0.37-0.38 after step 100. In contrast, AIRL-S (w. PRM) shows no clear signs of plateauing within the 200-step window and continues to improve. 3. **Initial Conditions:** Both methods start at nearly the identical accuracy level (~0.32) at step 0. 4. **Noise/Variance:** Both training processes exhibit significant step-to-step noise, as evidenced by the jaggedness of the mean lines and the width of the shaded confidence bands. The variance appears comparable between the two methods. ### Interpretation The chart presents a comparative analysis of two training algorithms, likely in the domain of reinforcement learning or iterative model optimization, given the "Step" axis and the acronyms (GRPO, AIRL-S, PRM). * **What the data suggests:** The method "AIRL-S (w. PRM)" demonstrates superior learning efficiency and final performance compared to "GRPO (w/o PRM)" on this specific task, as measured by training accuracy. The inclusion of "PRM" (the specific component is not defined in the chart) appears to be a critical factor enabling sustained learning and higher asymptotic performance. * **Relationship between elements:** The direct comparison on the same axes controls for task and evaluation metrics, isolating the effect of the algorithmic difference (AIRL-S vs. GRPO) and the presence/absence of PRM. The shared starting point reinforces that the divergence is due to the training process, not initial model states. * **Notable patterns/anomalies:** The most significant pattern is the divergence in learning trajectories. The plateau of the blue line suggests it may have reached a local optimum or a limit imposed by its algorithmic structure. The continued rise of the red line indicates that AIRL-S with PRM either has a better optimization landscape, avoids premature convergence, or incorporates a mechanism (possibly the PRM) that facilitates ongoing improvement. The high variance in both signals is typical of many stochastic training processes but does not obscure the clear trend difference.

## Line Graph: Training Accuracy ### Overview The image depicts a line graph comparing the training accuracy of two models over 200 training steps. The blue line represents "GRPO (w/o PRM)" and the red line represents "AIRL-S (w. PRM)." Both lines show increasing trends, but the red line consistently outperforms the blue line, with shaded regions indicating variability in accuracy. ### Components/Axes - **X-axis (Step)**: Ranges from 0 to 200 in increments of 50. - **Y-axis (Accuracy)**: Ranges from 0.32 to 0.42 in increments of 0.02. - **Legend**: Located at the bottom-right corner. - Blue line: "GRPO (w/o PRM)" - Red line: "AIRL-S (w. PRM)" - **Shaded Regions**: Gray areas around each line represent variability (likely confidence intervals or standard error). ### Detailed Analysis 1. **GRPO (w/o PRM) [Blue Line]**: - Starts at ~0.32 accuracy at step 0. - Gradually increases to ~0.38 by step 200. - Exhibits moderate fluctuations (e.g., dips to ~0.34 at step 50, peaks at ~0.37 at step 150). - Shaded region spans ~0.32–0.38, indicating variability. 2. **AIRL-S (w. PRM) [Red Line]**: - Starts at ~0.34 accuracy at step 0. - Increases steadily to ~0.42 by step 200. - Shows sharper peaks (e.g., ~0.41 at step 100, ~0.42 at step 200). - Shaded region spans ~0.34–0.42, with higher variability in later steps. ### Key Observations - The red line (AIRL-S with PRM) consistently outperforms the blue line (GRPO without PRM) across all steps. - Both models show upward trends, but AIRL-S with PRM achieves higher final accuracy (~0.42 vs. ~0.38). - Variability (shaded regions) increases for both models as training progresses, suggesting diminishing stability in later steps. ### Interpretation The data suggests that incorporating PRM (Proximal Regularization Method) in the AIRL-S model significantly improves training accuracy compared to the GRPO model without PRM. The steeper and more stable ascent of the red line indicates that PRM may enhance model convergence or reduce overfitting during training. The increasing variability in later steps for both models could reflect challenges in maintaining accuracy as training complexity grows. This highlights the potential value of PRM in optimizing training dynamics for reinforcement learning tasks.