How do you design the reward function and the discount factor for the actor-critic algorithms?
Actor-critic algorithms are a popular class of reinforcement learning methods that combine the advantages of value-based and policy-based approaches. They use two neural networks: an actor that learns the optimal policy by taking actions, and a critic that evaluates the value of the current state and provides feedback to the actor. In this article, you will learn how to design the reward function and the discount factor for the actor-critic algorithms, and what are some of the trade-offs involved.
The reward function is the most important component of any reinforcement learning problem, as it defines the goal and the feedback for the agent. The reward function should be aligned with the desired behavior and outcomes, and should be informative, sparse, and consistent. For actor-critic algorithms, the reward function should also be differentiable, as it is used to update the actor network through gradient ascent. Some common examples of reward functions are binary rewards, linear rewards, exponential rewards, and shaped rewards.
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Advantage Actor-Critic (A2C) algorithms combine a policy gradient and a learned value function. A2C algorithms have two components, learned jointly: (1) an Actor, which learns a parametrized policy, and (2) a Critic, which learns a value function to evaluate state-action pairs. The Critic provides a reinforcing signal to the actor. A learned reinforcing signal is more informative than general RL rewards (e.g., it can transform a sparse reward where the agent only receives 1 upon success into a dense reinforcing signal). An Advantage Function underlies the policy gradient function learned by the Actor and measures the extent to which an action is better or worse than the policy's average action in a particular state.
The discount factor is a hyperparameter that controls how much the agent values future rewards over immediate ones. It is usually denoted by gamma, and ranges from 0 to 1. A low gamma means the agent is short-sighted and only cares about the current reward, while a high gamma means the agent is far-sighted and considers the long-term consequences of its actions. For actor-critic algorithms, the discount factor affects the critic network, as it is used to calculate the expected return or the advantage function. Choosing the right discount factor depends on the characteristics of the problem, such as the horizon, the variance, and the stability.
The advantage function is a key concept in actor-critic algorithms, as it measures how much better or worse an action is compared to the average action in a given state. It is defined as the difference between the action value and the state value, or the difference between the actual return and the expected return. The advantage function is used to update the actor network, as it provides a more accurate and less noisy gradient signal than the raw reward. There are different ways to estimate the advantage function, such as using Monte Carlo methods, temporal difference methods, or generalized advantage estimation.
The policy gradient is the core algorithm for updating the actor network in actor-critic methods. It is based on the idea of maximizing the expected return by following the current policy. The policy gradient is computed by multiplying the advantage function by the log-probability of the action taken by the actor. The policy gradient is then used to perform gradient ascent on the actor network parameters, which improves the policy by increasing the probability of good actions and decreasing the probability of bad actions. The policy gradient can be improved by using various techniques, such as entropy regularization, baseline subtraction, or actor-critic methods.
The value function approximation is the technique for updating the critic network in actor-critic methods. It is based on the idea of minimizing the error between the predicted value and the target value for a given state or state-action pair. The value function approximation can be done by using either a state value function or an action value function, depending on the type of actor-critic algorithm. The state value function estimates the expected return from a given state, while the action value function estimates the expected return from a given state-action pair. The value function approximation can be done by using either a bootstrapping method or a Monte Carlo method, depending on the type of critic network.
Actor-critic algorithms have many variants, each with its own advantages and disadvantages. A2C, or Advantage Actor-Critic, uses a single actor network and multiple critic networks to parallelize the learning process and reduce the variance. A3C, or Asynchronous Advantage Actor-Critic, takes it a step further with multiple asynchronous agents sharing a global network. DDPG, or Deep Deterministic Policy Gradient, handles continuous action spaces and learns from off-policy data. TD3, or Twin Delayed Deep Deterministic Policy Gradient, improves DDPG by using two critic networks to reduce overestimation bias. Finally, SAC, or Soft Actor-Critic, uses an entropy regularization term to encourage exploration and a reparameterization trick to simplify the policy gradient calculation.
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