## Comparative Performance of Reinforcement Learning Algorithms under Varying Synchronization Conditions ### Overview The image presents a series of line charts comparing the performance of different reinforcement learning algorithms (REINFORCE, GRPO, REC-TwoSide-NoIS, REC-TwoSide-IS, REC-Ring-NoIS) across three synchronization conditions: `sync_interval = 20`, `sync_offset = 10`, and `offline`. Performance is evaluated based on Evaluation Accuracy, Training Reward, KL Divergence, and Clipping Fraction, all plotted against Training Steps. ### Components/Axes * **Title:** Comparative Performance of Reinforcement Learning Algorithms under Varying Synchronization Conditions * **X-axis (all charts):** Training Steps (range: 0 to 150) * **Y-axis (row 1):** Evaluation Accuracy (range: 0.0 to 0.6) * **Y-axis (row 2):** Training Reward (range: 0.00 to 1.00) * **Y-axis (row 3):** KL Divergence (log scale, range: 10^-2 to 10^2) * **Y-axis (row 4):** Clipping Fraction (log scale, range: 10^-3 to 10^-1) * **Synchronization Conditions (columns):** * Column 1: `sync_interval = 20` * Column 2: `sync_offset = 10` * Column 3: `offline` * **Legend (bottom):** * Blue: REINFORCE * Green: GRPO * Yellow: REC-TwoSide-NoIS (0.2) * Purple: REC-Ring-NoIS (0.2, 0.2) & (0.6, 2.0) * Yellow Dashed: REC-TwoSide-IS (0.2) ### Detailed Analysis **Row 1: Evaluation Accuracy** * **`sync_interval = 20`:** * REINFORCE (blue): Starts around 0.3, drops sharply around step 75, recovers slightly, ends around 0.1. * GRPO (green): Starts around 0.35, gradually increases to around 0.55. * REC-TwoSide-NoIS (yellow): Starts around 0.35, increases to around 0.65. * REC-Ring-NoIS (purple): Starts around 0.35, increases to around 0.65. * REC-TwoSide-IS (yellow dashed): Starts around 0.35, increases to around 0.7. * **`sync_offset = 10`:** * REINFORCE (blue): Starts around 0.3, drops sharply around step 75, recovers slightly, ends around 0.2. * GRPO (green): Starts around 0.35, gradually increases to around 0.6. * REC-TwoSide-NoIS (yellow): Starts around 0.35, increases to around 0.7. * REC-Ring-NoIS (purple): Starts around 0.35, increases to around 0.7. * REC-TwoSide-IS (yellow dashed): Starts around 0.35, increases to around 0.7. * **`offline`:** * REINFORCE (blue): Starts around 0.4, drops sharply around step 50, recovers slightly, ends around 0.2. * GRPO (green): Starts around 0.4, remains relatively stable around 0.4. * REC-TwoSide-NoIS (yellow): Starts around 0.4, fluctuates, ends around 0.3. * REC-Ring-NoIS (purple): Starts around 0.4, fluctuates, ends around 0.4. * REC-TwoSide-IS (yellow dashed): Starts around 0.4, fluctuates, ends around 0.3. **Row 2: Training Reward** * **`sync_interval = 20`:** * REINFORCE (blue): Starts around 0.5, drops sharply around step 75, recovers slightly, ends around 0.0. * GRPO (green): Starts around 0.5, gradually increases to around 0.8. * REC-TwoSide-NoIS (yellow): Starts around 0.5, increases to around 0.9. * REC-Ring-NoIS (purple): Starts around 0.5, increases to around 0.9. * REC-TwoSide-IS (yellow dashed): Starts around 0.7, increases to around 0.9. * **`sync_offset = 10`:** * REINFORCE (blue): Starts around 0.5, drops sharply around step 75, recovers slightly, ends around 0.0. * GRPO (green): Starts around 0.5, gradually increases to around 0.8. * REC-TwoSide-NoIS (yellow): Starts around 0.5, increases to around 0.9. * REC-Ring-NoIS (purple): Starts around 0.5, increases to around 0.9. * REC-TwoSide-IS (yellow dashed): Starts around 0.7, increases to around 0.9. * **`offline`:** * REINFORCE (blue): Not applicable. * GRPO (green): Starts around 0.5, remains relatively stable around 0.5. * REC-TwoSide-NoIS (yellow): Starts around 0.5, remains relatively stable around 0.5. * REC-Ring-NoIS (purple): Starts around 0.5, remains relatively stable around 0.5. * REC-TwoSide-IS (yellow dashed): Starts around 0.5, remains relatively stable around 0.5. **Row 3: KL Divergence** * **`sync_interval = 20`:** * REINFORCE (blue): Starts around 10^-1, spikes significantly around step 75, ends around 10^2. * GRPO (green): Starts around 10^-2, remains relatively stable around 10^-2. * REC-TwoSide-NoIS (yellow): Starts around 10^-1, increases to around 10^1. * REC-Ring-NoIS (purple): Starts around 10^-2, remains relatively stable around 10^-2. * REC-TwoSide-IS (yellow dashed): Starts around 10^-2, remains relatively stable around 10^-2. * **`sync_offset = 10`:** * REINFORCE (blue): Starts around 10^-1, increases to around 10^2. * GRPO (green): Starts around 10^-2, remains relatively stable around 10^-2. * REC-TwoSide-NoIS (yellow): Starts around 10^-1, increases to around 10^2. * REC-Ring-NoIS (purple): Starts around 10^-2, remains relatively stable around 10^-2. * REC-TwoSide-IS (yellow dashed): Starts around 10^-2, remains relatively stable around 10^-2. * **`offline`:** * REINFORCE (blue): Starts around 10^-1, increases to around 10^2. * GRPO (green): Starts around 10^-2, remains relatively stable around 10^-2. * REC-TwoSide-NoIS (yellow): Starts around 10^-1, increases to around 10^2. * REC-Ring-NoIS (purple): Starts around 10^-2, remains relatively stable around 10^-2. * REC-TwoSide-IS (yellow dashed): Starts around 10^-2, remains relatively stable around 10^-2. **Row 4: Clipping Fraction** * **`sync_interval = 20`:** * REINFORCE (blue): Not applicable. * GRPO (green): Starts around 10^-3, remains relatively stable around 10^-3. * REC-TwoSide-NoIS (yellow): Starts around 10^-2, increases to around 10^-1. * REC-Ring-NoIS (purple): Starts around 10^-2, remains relatively stable around 10^-2. * REC-TwoSide-IS (yellow dashed): Starts around 10^-2, increases to around 10^-1. * **`sync_offset = 10`:** * REINFORCE (blue): Not applicable. * GRPO (green): Starts around 10^-3, remains relatively stable around 10^-3. * REC-TwoSide-NoIS (yellow): Starts around 10^-2, increases to around 10^-1. * REC-Ring-NoIS (purple): Starts around 10^-2, remains relatively stable around 10^-2. * REC-TwoSide-IS (yellow dashed): Starts around 10^-2, increases to around 10^-1. * **`offline`:** * REINFORCE (blue): Not applicable. * GRPO (green): Starts around 10^-3, remains relatively stable around 10^-3. * REC-TwoSide-NoIS (yellow): Starts around 10^-2, increases to around 10^-1. * REC-Ring-NoIS (purple): Starts around 10^-2, remains relatively stable around 10^-2. * REC-TwoSide-IS (yellow dashed): Starts around 10^-2, increases to around 10^-1. ### Key Observations * REINFORCE's performance is significantly impacted by synchronization, showing a sharp decline in Evaluation Accuracy and Training Reward around step 75 in the `sync_interval = 20` and `sync_offset = 10` conditions. * GRPO demonstrates more stable performance across all synchronization conditions. * REC-TwoSide-NoIS and REC-TwoSide-IS generally achieve higher Evaluation Accuracy and Training Reward compared to REINFORCE, but also exhibit higher KL Divergence and Clipping Fraction. * REC-Ring-NoIS shows stable and relatively low KL Divergence and Clipping Fraction. * The offline condition results in relatively stable performance for all algorithms except REINFORCE. ### Interpretation The data suggests that the choice of reinforcement learning algorithm and synchronization strategy significantly impacts performance. REINFORCE is highly sensitive to synchronization parameters, while GRPO exhibits more robust performance. REC-TwoSide-NoIS and REC-TwoSide-IS can achieve higher rewards but at the cost of increased KL Divergence and Clipping Fraction, potentially indicating instability or less efficient learning. REC-Ring-NoIS offers a balance between performance and stability. The offline condition highlights the inherent limitations of certain algorithms when synchronization is completely absent. The sharp decline in REINFORCE's performance around step 75 in the synchronized conditions warrants further investigation, potentially indicating a critical point where the algorithm becomes unstable or diverges.

## Line Chart: Performance Metrics vs. Training Steps ### Overview This image presents a series of line charts comparing the performance of different reinforcement learning algorithms under varying synchronization intervals and an offline setting. The charts display Evaluation Accuracy, Training Reward, KL Divergence, and Clipping Fraction as functions of Training Steps. There are three columns representing different experimental conditions: `sync_interval = 20`, `sync_offset = 10`, and `offline`. Each chart contains lines representing the performance of several algorithms: REINFORCE, REC-TwoSide-NoIS (0.2), REC-Ring-NoIS (0.2, 2.0), REC-TwoSide-IS (0.2), and GRPO. ### Components/Axes * **X-axis:** Training Steps (ranging from 0 to 150) * **Y-axis (Top Chart):** Evaluation Accuracy (ranging from 0 to 0.6) * **Y-axis (Second Chart):** Training Reward (ranging from 0 to 1.0) * **Y-axis (Third Chart):** KL Divergence (log scale, ranging from 10^-2 to 10^2) * **Y-axis (Bottom Chart):** Clipping Fraction (log scale, ranging from 10^-2 to 10^0) * **Legend (Bottom Center):** * REINFORCE (Blue) * REC-TwoSide-NoIS (0.2) (Orange) * REC-Ring-NoIS (0.2, 2.0) (Green) * REC-TwoSide-IS (0.2) (Red) * GRPO (Light Blue) * **Titles (Top):** `sync_interval = 20`, `sync_offset = 10`, `offline` ### Detailed Analysis or Content Details **Evaluation Accuracy:** * **sync\_interval = 20:** REINFORCE shows a slow, steady increase, reaching approximately 0.55 by step 150. REC-TwoSide-NoIS (0.2) starts low but increases rapidly, reaching around 0.6 by step 100 and remaining stable. REC-Ring-NoIS (0.2, 2.0) shows a similar trend to REC-TwoSide-NoIS (0.2), but with slightly lower values. REC-TwoSide-IS (0.2) starts around 0.2 and increases to approximately 0.4. GRPO fluctuates around 0.2. * **sync\_offset = 10:** REINFORCE shows a similar slow increase as in the previous column, reaching approximately 0.5 by step 150. REC-TwoSide-NoIS (0.2) increases rapidly to around 0.6. REC-Ring-NoIS (0.2, 2.0) shows a similar trend, reaching around 0.55. REC-TwoSide-IS (0.2) increases to approximately 0.4. GRPO fluctuates around 0.2. * **offline:** REINFORCE shows a fluctuating pattern, reaching around 0.4. REC-TwoSide-NoIS (0.2) increases rapidly to around 0.6. REC-Ring-NoIS (0.2, 2.0) shows a similar trend, reaching around 0.55. REC-TwoSide-IS (0.2) increases to approximately 0.4. GRPO fluctuates around 0.2. **Training Reward:** * **sync\_interval = 20:** All algorithms show an increasing trend. REC-TwoSide-NoIS (0.2) and REC-Ring-NoIS (0.2, 2.0) reach approximately 0.9. REINFORCE reaches around 0.7. REC-TwoSide-IS (0.2) and GRPO reach around 0.6. * **sync\_offset = 10:** Similar to the previous column, REC-TwoSide-NoIS (0.2) and REC-Ring-NoIS (0.2, 2.0) reach approximately 0.9. REINFORCE reaches around 0.7. REC-TwoSide-IS (0.2) and GRPO reach around 0.6. * **offline:** REC-TwoSide-NoIS (0.2) and REC-Ring-NoIS (0.2, 2.0) reach approximately 0.9. REINFORCE reaches around 0.7. REC-TwoSide-IS (0.2) and GRPO reach around 0.6. **KL Divergence:** * **sync\_interval = 20:** REINFORCE and GRPO show relatively stable KL Divergence around 10^-1. REC-TwoSide-NoIS (0.2) and REC-TwoSide-IS (0.2) show a rapid increase in KL Divergence, reaching around 10^1. REC-Ring-NoIS (0.2, 2.0) shows a moderate increase, reaching around 10^0. * **sync\_offset = 10:** Similar trends as in the previous column. * **offline:** Similar trends as in the previous column. **Clipping Fraction:** * **sync\_interval = 20:** REINFORCE and GRPO show relatively stable Clipping Fraction around 10^-1. REC-TwoSide-NoIS (0.2) and REC-TwoSide-IS (0.2) show a rapid increase in Clipping Fraction, reaching around 10^0. REC-Ring-NoIS (0.2, 2.0) shows a moderate increase, reaching around 10^-1. * **sync\_offset = 10:** Similar trends as in the previous column. * **offline:** Similar trends as in the previous column. ### Key Observations * REC-TwoSide-NoIS (0.2) consistently outperforms other algorithms in terms of Evaluation Accuracy and Training Reward across all conditions. * REC-Ring-NoIS (0.2, 2.0) performs similarly to REC-TwoSide-NoIS (0.2), but slightly lower. * REINFORCE and GRPO show relatively stable but lower performance. * REC-TwoSide-IS (0.2) shows moderate performance. * KL Divergence and Clipping Fraction are significantly higher for REC-TwoSide-NoIS (0.2) and REC-TwoSide-IS (0.2), indicating potential issues with policy updates. * The `sync_interval` and `sync_offset` parameters do not appear to have a significant impact on the overall performance trends. ### Interpretation The data suggests that the REC-TwoSide-NoIS (0.2) algorithm is the most effective in achieving high evaluation accuracy and training reward. However, its high KL Divergence and Clipping Fraction suggest that it may be prone to large policy updates, which could lead to instability. The consistent performance across different synchronization settings indicates that the algorithms are relatively robust to these parameters. The offline setting does not significantly alter the relative performance of the algorithms. The high performance of REC-TwoSide-NoIS (0.2) could be attributed to its ability to effectively explore the environment and learn a robust policy, but further investigation is needed to understand the trade-offs between performance and stability. The relatively poor performance of REINFORCE and GRPO may indicate that they are less effective in this particular environment or require more careful tuning. The log scales on KL Divergence and Clipping Fraction highlight the magnitude of these values for certain algorithms, suggesting potential issues with their learning process.

## Multi-Panel Line Chart: Training Metrics Comparison Across Synchronization Settings ### Overview The image is a 4x3 grid of line charts comparing the performance of six different reinforcement learning or policy optimization methods across three distinct training synchronization configurations. The charts track four key metrics over 150 training steps. The overall purpose is to visualize and compare the stability, performance, and optimization behavior of the methods under different synchronization regimes. ### Components/Axes * **Column Headers (Synchronization Settings):** * Left Column: `sync_interval = 20` * Middle Column: `sync_offset = 10` * Right Column: `offline` * **Row Headers (Metrics):** * Top Row: `Evaluation Accuracy` (Y-axis scale: 0.0 to ~0.7) * Second Row: `Training Reward` (Y-axis scale: 0.00 to 1.00) * Third Row: `KL Divergence` (Y-axis scale: logarithmic, from 10^-3 to 10^1) * Bottom Row: `Clipping Fraction` (Y-axis scale: logarithmic, from 10^-3 to 10^0) * **Common X-Axis:** `Training Steps` (Linear scale, marked at 0, 50, 100, 150). * **Legend (Bottom Center):** Contains six entries, each with a unique color and marker: 1. `REINFORCE` - Light blue line with circle markers. 2. `GRPO` - Teal/green line with square markers. 3. `REC-TwoSide-NoIS (0.2)` - Yellow line with upward-pointing triangle markers. 4. `REC-TwoSide-IS (0.2)` - Yellow dashed line with downward-pointing triangle markers. 5. `REC-Ring-NoIS (0.2, 0.2) & (0.6, 2.0)` - Purple line with plus sign markers. 6. `REC-Ring-NoIS (0.2, 0.2)` - Pink/magenta line with 'x' markers. ### Detailed Analysis **Column 1: `sync_interval = 20`** * **Evaluation Accuracy:** Most methods (GRPO, REC variants) show a steady increase from ~0.3 to between 0.6-0.7. `REINFORCE` (blue) increases initially but crashes to near 0.0 after step 50. `REC-TwoSide-NoIS` (yellow triangle) also crashes after step 100. * **Training Reward:** Mirrors accuracy trends. GRPO and REC variants rise to ~0.8-0.9. `REINFORCE` crashes to 0.0 after step 50. `REC-TwoSide-NoIS` crashes after step 100. * **KL Divergence:** `REINFORCE` shows the highest and most volatile divergence, peaking above 10^1. Other methods remain lower, with GRPO and the pink `REC-Ring-NoIS` being the most stable (lowest divergence, ~10^-2 to 10^-1). * **Clipping Fraction:** Shows periodic, sharp oscillations for several methods (notably the pink and purple `REC-Ring-NoIS` variants), suggesting regular policy updates hitting clipping boundaries. `REINFORCE` and `GRPO` have lower, more stable clipping fractions. **Column 2: `sync_offset = 10`** * **Evaluation Accuracy:** Similar initial rise for most. `REINFORCE` crashes early (around step 50). `REC-TwoSide-NoIS` (yellow triangle) maintains performance longer but crashes after step 125. * **Training Reward:** `REINFORCE` crashes to 0.0. `REC-TwoSide-NoIS` shows extreme volatility, dropping to 0.0 multiple times before a final crash. Other methods remain high and stable. * **KL Divergence:** `REINFORCE` again shows high divergence. `REC-TwoSide-NoIS` shows a late, sharp increase in divergence coinciding with its performance crash. * **Clipping Fraction:** `REC-TwoSide-NoIS` shows a massive spike to near 1.0 (10^0) after step 125, indicating almost all updates were clipped. Other methods show moderate, stable clipping. **Column 3: `offline`** * **Evaluation Accuracy:** `REINFORCE` performance decays steadily to near 0.0. `REC-TwoSide-NoIS` (yellow triangle) is highly volatile, oscillating between ~0.2 and 0.7. The other four methods maintain stable, high accuracy (~0.6-0.7). * **Training Reward:** `REINFORCE` and the two `REC-TwoSide` methods show flat or declining rewards (~0.4-0.5). The GRPO and `REC-Ring` methods maintain stable, high rewards (~0.8-0.9). * **KL Divergence:** `REINFORCE` divergence grows monotonically and very high (approaching 10^2). `REC-TwoSide-NoIS` also shows high, growing divergence. The other methods maintain low, stable divergence. * **Clipping Fraction:** `REC-TwoSide-NoIS` and the purple `REC-Ring-NoIS` show a steady increase in clipping fraction over time, ending near 1.0. `GRPO` remains very low and stable. ### Key Observations 1. **Method Stability Hierarchy:** `GRPO` (teal) and the `REC-Ring-NoIS` variants (purple/pink) are consistently the most stable across all metrics and synchronization settings. `REINFORCE` (blue) is consistently the least stable, often crashing completely. 2. **Sensitivity of REC-TwoSide:** The `REC-TwoSide-NoIS` method (yellow triangle) is highly sensitive to the synchronization setting. It performs well initially in synchronized settings but exhibits catastrophic forgetting or instability later, and is highly volatile in the offline setting. 3. **KL Divergence as a Failure Indicator:** High and growing KL Divergence (especially for `REINFORCE` and `REC-TwoSide-NoIS` in offline mode) strongly correlates with performance collapse (drops in Accuracy and Reward). 4. **Offline Setting is Challenging:** The `offline` configuration appears most difficult, causing performance decay in `REINFORCE` and severe volatility in `REC-TwoSide-NoIS`, while other methods remain robust. 5. **Clipping Correlates with Instability:** Spikes in Clipping Fraction (e.g., `REC-TwoSide-NoIS` in `sync_offset=10`) immediately precede or coincide with performance crashes, suggesting optimization difficulties. ### Interpretation This data demonstrates a comparative analysis of policy optimization algorithms, likely in a reinforcement learning from human feedback (RLHF) or similar context. The core finding is that **synchronization strategy critically impacts algorithm stability and performance**. * **Synchronized Training (`sync_interval`, `sync_offset`)** provides a stabilizing effect for most methods, but can delay the onset of instability for sensitive algorithms like `REC-TwoSide-NoIS`, leading to a sudden, catastrophic collapse after many steps of apparent success. * **Offline Training** removes this stabilizing buffer, exposing inherent weaknesses. Algorithms that rely on frequent, on-policy updates (`REINFORCE`) fail completely. Algorithms with potentially high variance (`REC-TwoSide`) become unusably volatile. The success of `GRPO` and `REC-Ring` variants suggests they have inherent mechanisms (perhaps related to their gradient estimation or trust region methods) that make them robust to distribution shift and stale data, which are key challenges in offline optimization. * The **strong correlation between rising KL Divergence and falling performance** underscores the importance of monitoring this metric as a health check for the training process. It indicates the policy is drifting too far from its reference model, leading to collapse. * The **Clipping Fraction** acts as a diagnostic for optimization health. A value approaching 1.0 means the optimizer is constantly fighting against its own update constraints, a sign of impending failure. In essence, the charts argue for the use of robust algorithms (`GRPO`, `REC-Ring`) and careful consideration of synchronization schemes, especially when moving towards offline or large-interval update paradigms, to ensure stable and reliable training.

## Line Graphs: Performance Metrics Across Training Steps ### Overview The image contains three columns of line graphs comparing performance metrics across three training methods (REINFORCE, GRPO, REC-TwoSides, REC-RingNoIS) under different synchronization settings ("sync interval = 20", "sync offset = 10", "offline"). Each column contains four subplots: Evaluation Accuracy, Training Reward, KL Divergence, and Clipping Fraction. The x-axis represents training steps (0–150), while y-axes vary by subplot. --- ### Components/Axes - **Columns**: - Left: "sync interval = 20" (blue dashed line) - Middle: "sync offset = 10" (orange dashed line) - Right: "offline" (no dashed line) - **Subplots**: 1. **Evaluation Accuracy**: Y-axis = 0.0–1.0 2. **Training Reward**: Y-axis = 0.0–1.0 3. **KL Divergence**: Y-axis = 10–100 4. **Clipping Fraction**: Y-axis = 10–100 - **Legends**: Positioned at the bottom of each column, with colors: - Blue: REINFORCE - Green: GRPO - Orange: REC-TwoSides - Purple: REC-RingNoIS - Dashed Orange: REC-TwoSides (0.2) & (0.6, 2.0) --- ### Detailed Analysis #### **Column 1: sync interval = 20** 1. **Evaluation Accuracy**: - Blue (REINFORCE): Starts at ~0.6, dips to ~0.4 at 50 steps, then stabilizes. - Green (GRPO): Flat at ~0.6. - Orange (REC-TwoSides): Peaks at ~0.8 at 100 steps, then declines. - Purple (REC-RingNoIS): Smooth increase from ~0.4 to ~0.8. - Dashed Orange: Peaks at ~0.7 at 100 steps. 2. **Training Reward**: - Blue: Drops sharply to ~0.2 at 50 steps, then stabilizes. - Green: Flat at ~0.6. - Orange: Peaks at ~0.8 at 100 steps. - Purple: Stable at ~0.7. - Dashed Orange: Peaks at ~0.7 at 100 steps. 3. **KL Divergence**: - Blue: Fluctuates between 10–20. - Green: Stable at ~10. - Orange: Spikes to ~30 at 100 steps. - Purple: Stable at ~10. - Dashed Orange: Spikes to ~30 at 100 steps. 4. **Clipping Fraction**: - Blue: Fluctuates between 10–20. - Green: Stable at ~10. - Orange: Increases to ~20 at 100 steps. - Purple: Stable at ~10. - Dashed Orange: Increases to ~20 at 100 steps. #### **Column 2: sync offset = 10** 1. **Evaluation Accuracy**: - Blue: Starts at ~0.5, dips to ~0.3 at 50 steps, then stabilizes. - Green: Flat at ~0.6. - Orange: Peaks at ~0.7 at 100 steps. - Purple: Smooth increase from ~0.5 to ~0.8. - Dashed Orange: Peaks at ~0.6 at 100 steps. 2. **Training Reward**: - Blue: Drops to ~0.3 at 50 steps, then stabilizes. - Green: Flat at ~0.6. - Orange: Peaks at ~0.7 at 100 steps. - Purple: Stable at ~0.7. - Dashed Orange: Peaks at ~0.6 at 100 steps. 3. **KL Divergence**: - Blue: Fluctuates between 10–20. - Green: Stable at ~10. - Orange: Spikes to ~25 at 100 steps. - Purple: Stable at ~10. - Dashed Orange: Spikes to ~25 at 100 steps. 4. **Clipping Fraction**: - Blue: Fluctuates between 10–20. - Green: Stable at ~10. - Orange: Increases to ~15 at 100 steps. - Purple: Stable at ~10. - Dashed Orange: Increases to ~15 at 100 steps. #### **Column 3: offline** 1. **Evaluation Accuracy**: - Blue: Starts at ~0.4, dips to ~0.2 at 50 steps, then stabilizes. - Green: Flat at ~0.6. - Orange: Peaks at ~0.7 at 100 steps. - Purple: Smooth increase from ~0.5 to ~0.8. - Dashed Orange: Peaks at ~0.6 at 100 steps. 2. **Training Reward**: - Blue: Drops to ~0.2 at 50 steps, then stabilizes. - Green: Flat at ~0.6. - Orange: Peaks at ~0.7 at 100 steps. - Purple: Stable at ~0.7. - Dashed Orange: Peaks at ~0.6 at 100 steps. 3. **KL Divergence**: - Blue: Fluctuates between 10–20. - Green: Stable at ~10. - Orange: Spikes to ~20 at 100 steps. - Purple: Stable at ~10. - Dashed Orange: Spikes to ~20 at 100 steps. 4. **Clipping Fraction**: - Blue: Fluctuates between 10–20. - Green: Stable at ~10. - Orange: Increases to ~10 at 100 steps. - Purple: Stable at ~10. - Dashed Orange: Increases to ~10 at 100 steps. --- ### Key Observations 1. **REC-RingNoIS (Purple)** consistently shows the highest Evaluation Accuracy and Training Reward across all settings, with smooth trends. 2. **REC-TwoSides (Orange)** exhibits the highest KL Divergence and Clipping Fraction, indicating greater exploration but potential instability. 3. **REINFORCE (Blue)** performs poorly in Training Reward and Evaluation Accuracy, with erratic trends. 4. **GRPO (Green)** maintains stable metrics across all settings, suggesting robustness. 5. The dashed orange line (REC-TwoSides variants) shows intermediate performance, combining traits of REC-TwoSides and REC-RingNoIS. --- ### Interpretation The data suggests that synchronization settings significantly impact performance: - **Sync Interval = 20** and **Sync Offset = 10** allow REC-RingNoIS to outperform others, likely due to balanced exploration/exploitation. - **Offline** settings degrade REINFORCE's performance, highlighting its reliance on synchronization. - REC-TwoSides variants (dashed orange) show trade-offs: higher KL Divergence/Clipping Fraction (exploration) but lower Evaluation Accuracy/Training Reward (stability). - GRPO's stability across all settings implies it is less sensitive to synchronization parameters, making it a reliable baseline. Notably, REC-RingNoIS achieves the best balance of high Evaluation Accuracy and low KL Divergence, suggesting it optimizes policy updates effectively. The dashed orange line's intermediate performance indicates that combining REC-TwoSides variants may mitigate some instability while retaining exploration benefits.