diff --git a/Machine_Learning_Algorithms/Proximal Policy Optimization (PPO)Algorithm /Program.c b/Machine_Learning_Algorithms/Proximal Policy Optimization (PPO)Algorithm /Program.c new file mode 100644 index 00000000..be24f25e --- /dev/null +++ b/Machine_Learning_Algorithms/Proximal Policy Optimization (PPO)Algorithm /Program.c @@ -0,0 +1,81 @@ +#include +#include +#include + +#define TRAJECTORY_LENGTH 100 +#define NUM_TRAJECTORIES 10 +#define CLIP_EPSILON 0.2 +#define LEARNING_RATE 0.001 +#define GAMMA 0.99 +#define LAMBDA 0.95 + +// Placeholder functions for the neural network +double policy(double state) { + // Simple placeholder function for policy + return state * 0.1; +} + +double value_function(double state) { + // Simple placeholder function for value function + return state * 0.5; +} + +// Calculate advantage function using Generalized Advantage Estimation (GAE) +double calculate_advantage(double rewards[], double values[], int t) { + double advantage = 0.0; + double discount = 1.0; + for (int k = t; k < TRAJECTORY_LENGTH; ++k) { + advantage += discount * (rewards[k] + GAMMA * values[k + 1] - values[k]); + discount *= GAMMA * LAMBDA; + } + return advantage; +} + +// Policy update with clipping +double clipped_objective(double ratio, double advantage) { + double clip_value = fmax(1 - CLIP_EPSILON, fmin(1 + CLIP_EPSILON, ratio)); + return fmin(ratio * advantage, clip_value * advantage); +} + +// Main PPO loop +void PPO() { + double states[TRAJECTORY_LENGTH]; + double actions[TRAJECTORY_LENGTH]; + double rewards[TRAJECTORY_LENGTH]; + double values[TRAJECTORY_LENGTH]; + double advantages[TRAJECTORY_LENGTH]; + double returns[TRAJECTORY_LENGTH]; + + for (int episode = 0; episode < NUM_TRAJECTORIES; ++episode) { + // Simulate data collection + for (int t = 0; t < TRAJECTORY_LENGTH; ++t) { + states[t] = (double)t; // Placeholder state + actions[t] = policy(states[t]); // Take action according to policy + rewards[t] = -fabs(actions[t]); // Placeholder reward function + values[t] = value_function(states[t]); + } + + // Calculate returns and advantages + for (int t = 0; t < TRAJECTORY_LENGTH; ++t) { + returns[t] = rewards[t] + GAMMA * values[t + 1]; + advantages[t] = calculate_advantage(rewards, values, t); + } + + // Update policy using clipped objective + for (int t = 0; t < TRAJECTORY_LENGTH; ++t) { + double old_policy = policy(states[t]); + double ratio = policy(states[t]) / old_policy; // Placeholder policy ratio + double objective = clipped_objective(ratio, advantages[t]); + + // Simple gradient update (mock update, as no neural network here) + // In practice, we would use neural network gradients + double policy_update = LEARNING_RATE * objective; + printf("Policy updated for state %f with value %f\n", states[t], policy_update); + } + } +} + +int main() { + PPO(); + return 0; +} diff --git a/Machine_Learning_Algorithms/Proximal Policy Optimization (PPO)Algorithm /README.md b/Machine_Learning_Algorithms/Proximal Policy Optimization (PPO)Algorithm /README.md new file mode 100644 index 00000000..38b321df --- /dev/null +++ b/Machine_Learning_Algorithms/Proximal Policy Optimization (PPO)Algorithm /README.md @@ -0,0 +1,97 @@ +# Proximal Policy Optimization (PPO) Algorithm in Machine Learning + +--- + +## Description + +Proximal Policy Optimization (PPO) is an advanced reinforcement learning (RL) algorithm designed to help agents learn optimal policies in complex environments. Developed by OpenAI, PPO strikes a balance between complexity and performance, making it popular for applications in areas such as game playing, robotics, and autonomous control systems. PPO is a policy-gradient method that improves the stability and efficiency of training by using clipped objectives, allowing it to find near-optimal policies while preventing overly large updates that can destabilize learning. + +--- + +## Key Features + +1. **Policy Optimization with Clipping**: PPO restricts large policy updates by applying a clipping mechanism to the objective function, ensuring stable learning without drastic changes that could harm the performance. +2. **Surrogate Objective Function**: PPO optimizes a surrogate objective that includes a penalty for large deviations from the old policy, reducing the risk of unstable updates. +3. **On-Policy Learning**: PPO is primarily an on-policy algorithm, meaning it learns from data generated by the current policy, which improves sample efficiency and stability. +4. **Trust Region-Free**: Unlike traditional Trust Region Policy Optimization (TRPO), PPO avoids complex constraints and uses simpler clipping methods for policy updates, making it computationally efficient. +5. **Entropy Bonus**: The algorithm incorporates an entropy bonus to encourage exploration, helping the agent avoid local optima. + +--- + +## Problem Definition + +In reinforcement learning, an agent aims to learn an optimal policy, \( \pi(a|s) \), that maximizes expected cumulative rewards over time. The main challenges in policy optimization include: + +1. **Stability**: Large updates to policies can lead to drastic performance drops. +2. **Sample Efficiency**: Efficient use of data is crucial, especially in complex environments with high-dimensional state and action spaces. +3. **Exploration vs. Exploitation**: The agent needs to balance exploring new actions with exploiting known, rewarding actions. + +PPO addresses these challenges by refining the policy-gradient update approach through a clipped objective function, which stabilizes learning by controlling the impact of each update. + +--- + +## Algorithm Review + +### Steps of the PPO Algorithm: + +1. **Initialize** the policy network \( \pi_{\theta} \) and the value network \( V_{\phi} \) with random weights \( \theta \) and \( \phi \). +2. **Generate Trajectories**: Using the current policy \( \pi_{\theta} \), generate multiple trajectories (i.e., sequences of states, actions, and rewards) by interacting with the environment. +3. **Compute Rewards-to-Go**: For each state in a trajectory, compute the cumulative rewards-to-go, also known as the return, to approximate the true value function. +4. **Compute Advantages**: Calculate the advantage function, which estimates how much better an action is than the average action in a given state. PPO often uses Generalized Advantage Estimation (GAE) for a more stable advantage computation. +5. **Update the Policy with Clipping**: Use the surrogate objective function with a clipping factor to update the policy. The objective is given by: + + \[ + L^{\text{CLIP}}(\theta) = \mathbb{E} \left[ \min \left( r_t(\theta) \hat{A}_t, \, \text{clip}\left( r_t(\theta), 1 - \epsilon, 1 + \epsilon \right) \hat{A}_t \right) \right] + \] + + where: + + - \( r_t(\theta) = \frac{\pi_{\theta}(a|s)}{\pi_{\theta_{\text{old}}}(a|s)} \): the probability ratio between the new policy and the old policy. + - \( \epsilon \): the clipping threshold. + - \( \hat{A}_t \): the advantage function, which estimates the relative benefit of taking action \( a \) in state \( s \) compared to the average action in that state. + +6. **Update the Value Network**: Minimize the difference between the estimated values \( V_{\phi}(s) \) and the computed returns for more accurate value predictions. +7. **Repeat**: Iterate steps 2-6 until convergence or a pre-defined number of episodes. + +--- + +## Time Complexity + +The time complexity of PPO mainly depends on: + +1. **Policy Network Forward Pass**: The forward pass complexity is given by: + + \[ + O(N \cdot T \cdot P) + \] + + where: + - \( N \): number of trajectories. + - \( T \): trajectory length. + - \( P \): complexity of the policy network. + +2. **Gradient Update**: PPO typically requires several updates per episode, leading to a training complexity of: + + \[ + O(E \cdot N \cdot T \cdot P) + \] + + where \( E \) is the number of episodes. + +Overall, PPO has lower time complexity than more constrained methods like TRPO but requires more samples than off-policy algorithms like DDPG. + +--- + +## Applications + +PPO is widely used in applications that benefit from robust policy optimization, including: + +1. **Robotics**: Control tasks for robotic arms and autonomous agents. +2. **Gaming**: Game AI that needs to learn complex behaviors in environments like chess, Go, and various video games. +3. **Autonomous Vehicles**: Path planning and decision-making systems in self-driving cars. + +--- + +## Conclusion + +Proximal Policy Optimization (PPO) is a powerful reinforcement learning algorithm designed to stabilize the policy-gradient update process. Its clipped objective function provides a balance between exploration and exploitation, which improves stability, data efficiency, and convergence speed in various reinforcement learning applications.