Reinforcement learning policy gradient algorithm

The policy gradient algorithm is an important reinforcement learning algorithm. Its core idea is to search for the best strategy by directly optimizing the policy function. Compared with the method of indirectly optimizing the value function, the policy gradient algorithm has better convergence and stability, and can handle continuous action space problems, so it is widely used. The advantage of this algorithm is that it can directly learn the policy parameters without the need for an estimated value function. This enables the policy gradient algorithm to cope with the complex problems of high-dimensional state space and continuous action space. In addition, the policy gradient algorithm can also approximate the gradient through sampling, thereby improving computational efficiency. In short, the policy gradient algorithm is a powerful and flexible method. In the policy gradient algorithm, we need to define a policy function\pi(a|s), which gives The probability of taking action a in state s. Our goal is to optimize this policy function so that it produces the maximum expected reward in the sense of long-term cumulative reward. Specifically, we need to maximize the expected return J(\theta) of the policy function:

J(\theta)=\mathbb{E}_{\tau\sim p_\ theta(\tau)}[R(\tau)]

Among them, \theta is the parameter of the strategy function, \tau represents a trajectory, and p_\theta(\tau) is the strategy The function generates the probability distribution of trajectory \tau, and R(\tau) is the return of trajectory \tau.

In order to maximize the expected return J(\theta), we need to optimize the policy function and use the gradient ascent algorithm. Specifically, we need to calculate the gradient of the policy function\nabla_\theta J(\theta), and then update the parameters of the policy function\theta according to the direction of the gradient. The gradient of the policy function can be calculated using importance sampling and logarithmic gradient techniques.

\nabla_\theta J(\theta)=\mathbb{E}_{\tau\sim p_\theta(\tau)}[\sum_{t=0}^ {T-1}\nabla_\theta\log\pi(a_t|s_t)R(\tau)]

Where, T is the length of the trajectory, \log\pi(a_t |s_t) is the logarithm of the policy function, which represents the logarithm of the probability of taking action a_t in state s_t, and R(\tau) is the reward of the trajectory.

The policy gradient algorithm can use different optimization methods to update the parameters of the policy function. Among them, gradient-based optimization method is a commonly used method. Specifically, we can use the stochastic gradient ascent algorithm (SGA) to update the parameters of the policy function, the formula is as follows:

\theta_{t 1}=\theta_t \alpha\nabla_\ theta\hat{J}(\theta_t)

where \alpha is the learning rate, \hat{J}(\theta_t) is the expectation estimated using the average return of a batch of trajectories Return J(\theta_t). In practical applications, we can use neural networks to represent the policy function, then use the backpropagation algorithm to calculate the gradient of the policy function, and use the optimizer to update the parameters of the policy function.

The policy gradient algorithm has many variants, such as the baseline policy gradient algorithm, Actor-Critic algorithm, TRPO algorithm and PPO algorithm, etc. These algorithms all use different techniques to improve the performance and stability of the policy gradient algorithm. For example, the baseline policy gradient algorithm reduces variance by introducing a baseline function, the Actor-Critic algorithm improves efficiency by introducing a value function, the TRPO algorithm ensures convergence by limiting the update amplitude of the policy function, and the PPO algorithm uses techniques such as shearing and cropping To balance the update of the policy function and ensure stability.

The policy gradient algorithm is widely used in practice and has been successfully used in many fields, such as robot control, game playing, natural language processing, etc. It has many advantages, such as the ability to handle continuous action space problems, better convergence and stability, etc. However, the policy gradient algorithm also has some problems, such as slow convergence and vulnerability to local optimal solutions. Therefore, future research needs to further improve the policy gradient algorithm to improve its performance and application range.

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