Merge pull request #1518 from alo7lika/TEST

Proximal Policy Optimization (PPO)Algorithm in Machine Learning

Machine_Learning_Algorithms/Proximal Policy Optimization (PPO)Algorithm /Program.c

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+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#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;
+}

Machine_Learning_Algorithms/Proximal Policy Optimization (PPO)Algorithm /README.md

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+# 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.