I designed a code in python using the Reinforcement algorithm(PPO agent) and Graph neural network(GAT) to optimize and tune the two stage operational amplifier circuit design variables for getting the desired performance metrics, in my circuit environment i had 8 transistors in the two stage operational amplifier circuit design, during the optimization process (where the neural network tuning the circuit design variables, i.e., device dimensions of each transistors) i need to keep all the transistor in the saturation region, but the tuning process (continuous action space) i never get any one of the set of tuned values are getting all my circuit transistors to be in saturation region, it may lost any one or pairs or many are fall into either triode region or sub-threshold region. but i need all my transistor to be in saturation. for this purpose i added separate head to maintain the saturation region of each transistor in the GNN and impose heavy penalty in the reward calculation if it violates the saturation region and added a loss function for the saturation with the actor loss. but i am not getting the expected all transistor to be in saturation. the range of tuning is a continuous action, and the action space is moderately large, and the circuit device dimensions are very sensitive. but i have a manual tuning method for each transistor device dimensions, for any transistor which was either in the triode or in sub-threshold to get back to the required saturation region. can i able to include the manual tuning process in to the existing computation of optimization, if i include the manual tuning process whether the learning process will learn the manual tuning by itself, because for each transistor the tuning ration differs based on its present region.

above is my existing scenario, i need to know, which of the following suggestion method is very suiable and very correct method for my existing senario, choose the correct and best one for my implementation.

1. Manual Tuning as a Post-Processing Step
One approach is to allow the RL agent to propose a set of values and then apply a manual tuning step to ensure all transistors stay in the saturation region. This can be done either as an
additional post-processing step or as an integrated part of each action.
# Post-Processing Approach:
- Action Proposal: Let the PPO agent propose a full set of transistor dimensions.
- Saturation Check & Manual Adjustment: After the proposal, check the saturation status of each transistor. If any transistor is out of the saturation region, apply manual adjustments to
bring it back within the desired region.
- Reward Calculation: Calculate the reward based on the adjusted transistor dimensions and the desired performance metrics.

2. Manual Tuning as an Integrated Part of the Action
Alternatively, you could integrate manual tuning within the action selection step itself:
- Action Proposal: Each action step proposed by the PPO agent gets adjusted by the manual tuning process to ensure that all transistors stay within the saturation region.
- Modified Action: Use these manually tuned values as the actual action taken in the environment.

3. Incorporating Manual Tuning Knowledge into the Learning Process
To help the PPO agent learn the manual tuning process, you can do the following:
# Data Augmentation:
- Create a Dataset: Generate a set of (state, action) pairs using the manual tuning process. This dataset can provide examples where transistors are correctly tuned to stay within the
saturation region.
- Pre-Training: Pre-train the neural network on this dataset before fine-tuning with actual RL training. This helps the agent learn the relationship between transistor dimensions and their
regions.
# Mixed Training:
- Hybrid Loss Function: Combine the RL loss with a supervised loss based on the manually tuned dataset. This can help enforce the learning of manual adjustment heuristics.
- Reward Shaping: Shape the reward function to not just penalize but also provide higher rewards for states where manual tuning adheres to the saturation constraints

4. Constrained Optimization
Since remaining in the saturation region is a hard constraint:
- Constrained Action Space: Constrain your action space so that only actions that keep transistors in the saturation region are allowed. Although complex, this can be done using
projection methods or constrained optimization techniques.
- Penalty Functions: Impose severe penalties for actions that move any transistor out of the saturation region, discouraging such actions strongly.


5. Introduce a Post-Processing Heuristic
Enhance the PPO-based optimization with a post-processing step that applies manual tuning to any transistors not in the saturation region. This can ensure that all transistors meet the saturation criteria before evaluating the reward.

6. Use a Hybrid Learning Approach
Implement a hybrid learning system where the PPO agent learns from both the RL-based actions and manual tuning interventions. This can be achieved using imitation learning or constrained reinforcement learning.
# Imitation Learning
Initially train the model by incorporating manual tuning within the exploration phase, allowing the agent to learn corrective measures.

7. Dynamic Adjustment During Training
Periodic manual intervention to correct the action taken by the PPO agent. This can help the agent learn the correct adjustments over time.

8. Adjust Reward Function
You can also fine-tune the reward function to provide more nuanced feedback based on how far out of saturation the transistors are. Not just a flat penalty but a graded penalty.

9. Constrained Reinforcement Learning (CRL)
Using CRL methods like Constrained Policy Optimization (CPO) ensures the computed policies satisfy the required constraints.