## Line Chart: Accuracy vs. Steps for Different Algorithms ### Overview The image is a line chart comparing the accuracy of three different algorithms (PPO with λ=0.95, PPO with λ=1.0, and GRPO) over a range of steps. The chart displays accuracy on the y-axis and steps on the x-axis. ### Components/Axes * **X-axis:** "Steps", ranging from 0 to 2500, with gridlines at intervals of 500. * **Y-axis:** "Accuracy", ranging from 0.42 to 0.56, with gridlines at intervals of 0.02. * **Legend:** Located in the bottom-right corner, it identifies the three algorithms: * Dark Blue: PPO (λ=0.95) * Light Blue: PPO (λ=1.0) * Green: GRPO ### Detailed Analysis * **PPO (λ=0.95) - Dark Blue Line:** * Trend: Generally increasing, but plateaus and slightly decreases towards the end. * Data Points: * At 250 steps, Accuracy ≈ 0.45 * At 500 steps, Accuracy ≈ 0.47 * At 750 steps, Accuracy ≈ 0.475 * At 1000 steps, Accuracy ≈ 0.48 * At 1250 steps, Accuracy ≈ 0.485 * At 1500 steps, Accuracy ≈ 0.49 * At 1750 steps, Accuracy ≈ 0.495 * At 2000 steps, Accuracy ≈ 0.50 * At 2250 steps, Accuracy ≈ 0.498 * At 2500 steps, Accuracy ≈ 0.502 * **PPO (λ=1.0) - Light Blue Line:** * Trend: Increasing, but plateaus towards the end. * Data Points: * At 250 steps, Accuracy ≈ 0.465 * At 500 steps, Accuracy ≈ 0.49 * At 750 steps, Accuracy ≈ 0.50 * At 1000 steps, Accuracy ≈ 0.515 * At 1250 steps, Accuracy ≈ 0.52 * At 1500 steps, Accuracy ≈ 0.535 * At 1750 steps, Accuracy ≈ 0.535 * At 2000 steps, Accuracy ≈ 0.535 * At 2250 steps, Accuracy ≈ 0.54 * At 2500 steps, Accuracy ≈ 0.535 * **GRPO - Green Line:** * Trend: Increasing rapidly initially, then plateaus, and increases again slightly at the end. * Data Points: * At 250 steps, Accuracy ≈ 0.44 * At 500 steps, Accuracy ≈ 0.495 * At 750 steps, Accuracy ≈ 0.51 * At 1000 steps, Accuracy ≈ 0.53 * At 1250 steps, Accuracy ≈ 0.53 * At 1500 steps, Accuracy ≈ 0.53 * At 1750 steps, Accuracy ≈ 0.545 * At 2000 steps, Accuracy ≈ 0.54 * At 2250 steps, Accuracy ≈ 0.545 * At 2500 steps, Accuracy ≈ 0.55 ### Key Observations * GRPO achieves the highest accuracy overall. * PPO (λ=1.0) performs better than PPO (λ=0.95). * All algorithms show diminishing returns in accuracy as the number of steps increases. ### Interpretation The chart demonstrates the performance of different reinforcement learning algorithms in terms of accuracy over a number of steps. GRPO appears to be the most effective algorithm among the three, achieving the highest accuracy. The PPO algorithm's performance is influenced by the lambda parameter, with λ=1.0 resulting in better accuracy than λ=0.95. The plateauing of the accuracy curves suggests that further training steps may not significantly improve the performance of these algorithms.

## Line Chart: Accuracy vs. Steps for Different PPO and GRPO Algorithms ### Overview This image presents a line chart comparing the accuracy of three different algorithms – PPO (Proximal Policy Optimization) with λ=0.95, PPO with λ=1.0, and GRPO (Generalized Reward-based Policy Optimization) – over a series of steps. The chart visualizes how the accuracy of each algorithm changes as the number of steps increases. ### Components/Axes * **X-axis:** "Steps" ranging from 0 to 2500, with markers at 0, 500, 1000, 1500, 2000, and 2500. * **Y-axis:** "Accuracy" ranging from 0.42 to 0.56, with markers at 0.42, 0.44, 0.46, 0.48, 0.50, 0.52, 0.54, and 0.56. * **Legend:** Located in the bottom-right corner, identifying the three data series: * PPO (λ=0.95) – Blue line with circle markers. * PPO (λ=1.0) – Blue line with square markers. * GRPO – Green line with diamond markers. * **Gridlines:** Horizontal and vertical gridlines are present to aid in reading values. ### Detailed Analysis * **PPO (λ=0.95):** The blue line with circle markers starts at approximately 0.44 at 0 steps. It shows a generally upward trend, with some fluctuations. * At 500 steps: ~0.49 * At 1000 steps: ~0.52 * At 1500 steps: ~0.53 * At 2000 steps: ~0.54 * At 2500 steps: ~0.54 * **PPO (λ=1.0):** The blue line with square markers starts at approximately 0.46 at 0 steps. It also exhibits an upward trend, but is generally lower than the PPO (λ=0.95) line. * At 500 steps: ~0.47 * At 1000 steps: ~0.48 * At 1500 steps: ~0.49 * At 2000 steps: ~0.50 * At 2500 steps: ~0.51 * **GRPO:** The green line with diamond markers starts at approximately 0.45 at 0 steps. It demonstrates the steepest upward trend, reaching the highest accuracy values. * At 500 steps: ~0.51 * At 1000 steps: ~0.54 * At 1500 steps: ~0.55 * At 2000 steps: ~0.54 * At 2500 steps: ~0.55 ### Key Observations * GRPO consistently outperforms both PPO configurations across all steps. * PPO with λ=0.95 generally achieves higher accuracy than PPO with λ=1.0. * All three algorithms show diminishing returns in accuracy as the number of steps increases, particularly after 1500 steps. * The GRPO algorithm shows a more rapid initial increase in accuracy compared to the PPO algorithms. ### Interpretation The data suggests that GRPO is the most effective algorithm for this task, achieving the highest accuracy levels. The parameter λ in PPO appears to influence performance, with a value of 0.95 yielding better results than 1.0. The diminishing returns observed in all algorithms indicate that further increasing the number of steps may not significantly improve accuracy. This could be due to the algorithms converging towards an optimal solution or reaching the limits of their learning capacity. The initial rapid increase in GRPO's accuracy suggests it may be more efficient at exploring the solution space or adapting to the task's requirements. The differences in performance between the algorithms could be attributed to variations in their underlying mechanisms for policy optimization and reward handling.

## Line Chart: Accuracy vs. Training Steps for Three Reinforcement Learning Algorithms ### Overview The image is a line chart comparing the performance of three reinforcement learning algorithms over the course of training. The chart plots "Accuracy" on the y-axis against "Steps" on the x-axis. All three algorithms show an upward trend in accuracy as training steps increase, but they start at different points and improve at different rates, with GRPO consistently achieving the highest accuracy. ### Components/Axes * **Chart Type:** Line chart with markers. * **X-Axis:** * **Label:** "Steps" * **Scale:** Linear, ranging from approximately 0 to 2500. * **Major Tick Marks:** 500, 1000, 1500, 2000, 2500. * **Y-Axis:** * **Label:** "Accuracy" * **Scale:** Linear, ranging from 0.42 to 0.56. * **Major Tick Marks:** 0.42, 0.44, 0.46, 0.48, 0.50, 0.52, 0.54, 0.56. * **Legend:** Located in the bottom-right corner of the plot area. It contains three entries: 1. **PPO (λ=0.95):** Represented by a dark blue line with circular markers. 2. **PPO (λ=1.0):** Represented by a light blue line with square markers. 3. **GRPO:** Represented by a green line with diamond markers. * **Grid:** A light gray grid is present, aligned with the major tick marks on both axes. ### Detailed Analysis **Trend Verification & Data Point Extraction (Approximate Values):** 1. **PPO (λ=0.95) - Dark Blue Line with Circles:** * **Visual Trend:** Shows a steady, moderate upward slope throughout the training steps. It is the lowest-performing line for the entire duration. * **Data Points (Steps, Accuracy):** * (~200, ~0.423) * (~400, ~0.450) * (~600, ~0.463) * (~800, ~0.469) * (~1000, ~0.478) * (~1200, ~0.483) * (~1400, ~0.491) * (~1600, ~0.489) * (~1800, ~0.495) * (~2000, ~0.502) * (~2200, ~0.498) * (~2400, ~0.501) 2. **PPO (λ=1.0) - Light Blue Line with Squares:** * **Visual Trend:** Shows a strong upward slope initially, which begins to plateau after approximately 1600 steps. It consistently performs better than PPO (λ=0.95) but worse than GRPO after the initial steps. * **Data Points (Steps, Accuracy):** * (~200, ~0.442) * (~400, ~0.465) * (~600, ~0.491) * (~800, ~0.500) * (~1000, ~0.512) * (~1200, ~0.516) * (~1400, ~0.528) * (~1600, ~0.536) * (~1800, ~0.537) * (~2000, ~0.535) * (~2200, ~0.546) * (~2400, ~0.536) 3. **GRPO - Green Line with Diamonds:** * **Visual Trend:** Shows the steepest initial upward slope and maintains the highest accuracy throughout. It exhibits a slight dip around 2000 steps before recovering and reaching its peak at the final measured step. * **Data Points (Steps, Accuracy):** * (~200, ~0.442) * (~400, ~0.497) * (~600, ~0.512) * (~800, ~0.516) * (~1000, ~0.530) * (~1200, ~0.530) * (~1400, ~0.531) * (~1600, ~0.543) * (~1800, ~0.541) * (~2000, ~0.539) * (~2200, ~0.548) * (~2400, ~0.554) ### Key Observations 1. **Performance Hierarchy:** A clear and consistent hierarchy is established after the first ~400 steps: GRPO > PPO (λ=1.0) > PPO (λ=0.95). 2. **Convergence Behavior:** PPO (λ=1.0) appears to converge or plateau after ~1600 steps, hovering around 0.535-0.537 accuracy. GRPO shows no clear plateau and is still trending upward at 2400 steps. 3. **Initial Conditions:** All three algorithms start at a similar accuracy level (~0.42-0.44) at step ~200. 4. **Stability:** The GRPO line shows more volatility (e.g., the dip at 2000 steps) compared to the smoother curves of the two PPO variants. 5. **Lambda Impact:** For the PPO algorithm, a higher lambda value (1.0 vs. 0.95) correlates with significantly better performance throughout training. ### Interpretation This chart demonstrates a comparative study of algorithmic efficiency in a reinforcement learning context. The data suggests that the **GRPO algorithm is more sample-efficient and achieves a higher final accuracy** than the PPO algorithm under the tested conditions. Its steeper learning curve indicates it extracts more performance per training step, especially in the early to mid-stages (200-1000 steps). The comparison between the two PPO lines highlights the **critical impact of the hyperparameter λ (lambda)**. Setting λ=1.0 leads to markedly better performance than λ=0.95, suggesting that for this specific task, a higher value for this parameter (which likely controls the trade-off between bias and variance in the advantage estimation) is beneficial. The plateauing of PPO (λ=1.0) could indicate it has reached its performance limit for the given model architecture or data, while GRPO's continued ascent suggests it may have further potential with more training steps. The slight volatility in the GRPO line might reflect a more aggressive or exploratory update rule, which pays off in higher ultimate performance but introduces minor instability. Overall, the chart provides strong visual evidence for the superiority of GRPO and the importance of hyperparameter tuning for PPO in this specific experimental setup.

## Line Chart: Accuracy vs. Steps for Different Optimization Methods ### Overview The chart compares the accuracy of three optimization methods (PPO with λ=0.95, PPO with λ=1.0, and GRPO) across 2500 training steps. Accuracy is measured on a scale from 0.42 to 0.56, with distinct line styles and colors for each method. ### Components/Axes - **X-axis (Steps)**: Ranges from 0 to 2500, marked at intervals of 500. - **Y-axis (Accuracy)**: Ranges from 0.42 to 0.56, marked at intervals of 0.02. - **Legend**: Located in the bottom-right corner, with three entries: - **Blue circles**: PPO (λ=0.95) - **Blue squares**: PPO (λ=1.0) - **Green diamonds**: GRPO ### Detailed Analysis 1. **PPO (λ=0.95)** (Blue circles): - Starts at **0.422** at 0 steps. - Gradually increases to **0.502** at 2000 steps. - Slight dip to **0.500** at 2500 steps. - Trend: Slow, steady growth with minor fluctuations. 2. **PPO (λ=1.0)** (Blue squares): - Starts at **0.440** at 0 steps. - Sharp rise to **0.535** at 2000 steps. - Slight decline to **0.537** at 2500 steps. - Trend: Rapid improvement followed by stabilization. 3. **GRPO** (Green diamonds): - Starts at **0.442** at 0 steps. - Consistent upward trajectory to **0.555** at 2500 steps. - Trend: Steady, uninterrupted growth. ### Key Observations - **GRPO** consistently outperforms both PPO variants, achieving the highest accuracy (0.555) by 2500 steps. - **PPO (λ=1.0)** surpasses **PPO (λ=0.95)** in both speed and final accuracy. - **PPO (λ=0.95)** exhibits the slowest growth and lowest final accuracy (0.500). - All methods show diminishing returns after ~1500 steps, but GRPO maintains momentum. ### Interpretation The data suggests that **GRPO** is the most effective optimization method for this task, demonstrating superior scalability and final performance. The two PPO variants highlight the impact of the λ parameter: a higher λ (1.0) improves both convergence speed and final accuracy compared to λ=0.95. The slight dip in PPO (λ=0.95) at 2500 steps may indicate overfitting or sensitivity to hyperparameter tuning. GRPO’s uninterrupted growth implies robustness to training dynamics, making it the optimal choice for long-term optimization.