Beyond the agent and the environment, one can identify four main sub-elements to a reinforcement learning system: a policy, a reward function, a value function, and, optionally, a model of the environment.
A policy defines the learning agent's way of behaving at a given time. Roughly speaking, a policy is a mapping from perceived states of the environment to actions to be taken when in those states. It corresponds to what in psychology would be called a set of stimulus-response rules or associations. In some cases the policy may be a simple function or lookup table, whereas in others it may involve extensive computation such as a search process. The policy is the core of a reinforcement learning agent in the sense that it alone is sufficient to determine behavior. In general, policies may be stochastic.
A reward function defines the goal in a reinforcement learning problem. Roughly speaking, it maps perceived states (or state-action pairs) of the environment to a single number, a reward, indicating the intrinsic desirability of the state. A reinforcement-learning agent's sole objective is to maximize the total reward it receives in the long run. The reward function defines what are the good and bad events for the agent. In a biological system, it would not be inappropriate to identify rewards with pleasure and pain. They are the immediate and defining features of the problem faced by the agent. As such, the reward function must necessarily be fixed. It may, however, be used as a basis for changing the policy. For example, if an action selected by the policy is followed by low reward then the policy may be changed to select some other action in that situation in the future. In general, reward functions may also be stochastic.
Whereas a reward function indicates what is good in an immediate sense, a value function specifies what is good in the long run. Roughly speaking, the value of a state is the total amount of reward an agent can expect to accumulate over the future starting from that state. Whereas rewards determine the immediate, intrinsic desirability of environmental states, values indicate the long-term desirability of states after taking into account the states that are likely to follow, and the rewards available in those states. For example, a state might always yield a low immediate reward, but still have a high value because it is regularly followed by other states that yield high rewards. Or the reverse could be true. To make a human analogy, rewards are like pleasure (if high) and pain (if low), whereas values correspond to a more refined and far-sighted judgment of how pleased or displeased we are that our environment is in a particular state. Expressed this way, we hope it is clear that value functions formalize a very basic and familiar idea.
Rewards are in a sense primary, whereas values, as predictions of rewards, are secondary. Without rewards there could be no values, and the only purpose of estimating values is to achieve more reward. Nevertheless, it is values with which we are most concerned when making and evaluating decisions. Action choices are made on the basis of value judgments. We seek actions that bring about states of highest value, not highest reward, because these actions obtain for us the greatest amount of reward over the long run. In decision-making and planning, the derived quantity called value is the one with which we are most concerned. Unfortunately, it is also much harder to determine values than it is to determine rewards. Rewards are basically given directly by the environment, but values must be estimated and re-estimated from the sequences of observations an agent makes over its entire lifetime. In fact, the most important component of almost all reinforcement learning algorithms is a method for efficiently estimating values. The importance and centrality of estimating values is perhaps the most important thing we have learned about reinforcement learning in the last two decades.
Although all the reinforcement learning methods we consider in this book are structured around estimating value functions, it is not strictly necessary to do this to solve reinforcement learning problems. For example, search methods such as genetic algorithms, genetic programming, simulated annealing, and other function optimization methods, have been used to solve reinforcement learning problems. These methods search directly in the space of policies without ever appealing to value functions. We call these evolutionary methods because their operation is analogous to how biological evolution produces organisms with skilled behavior even though they do not themselves learn during their individual lifetimes. If the space of policies is sufficiently small, or can be structured so that good policies are common or easy to find, then evolutionary methods are often effective. In addition, evolutionary methods have advantages on problems in which the learning agent cannot accurately sense the state of its environment.
Nevertheless, what we mean by reinforcement learning involves learning while interacting with the environment, which evolutionary methods do not do. It is our belief that methods able to take advantage of the details of individual behavioral interactions can be much more efficient than evolutionary methods in a great many cases. Evolutionary methods ignore much of the useful structure of the reinforcement learning problem: they do not use the fact that the policy they are searching for is a function from states to actions; they do not notice which states an individual passes through during its lifetime, or which actions it selects. In some cases this information can be misleading (e.g., when states are mis-perceived), but more often it should enable more efficient search. Although evolution and learning share many features and can naturally work together as they do in nature, we do not consider evolutionary methods by themselves to be especially well-suited to reinforcement learning problems. For simplicity, in this book when we use the term ``reinforcement learning" we do not include evolutionary methods.
The fourth and final element of some reinforcement learning systems is a model of the environment. This is something that mimics the behavior of the environment. For example, given a state and action, the model might predict the resultant next state and next reward. Models are used for planning, by which we mean any way of deciding on a course of action by considering possible future situations before they are actually experienced. The incorporation of models and planning into reinforcement learning systems is a relatively new development. Early reinforcement learning systems were explicitly trial-and-error learners; what they did was viewed as almost the opposite of planning. Nevertheless, it gradually became clear that reinforcement learning methods are closely related to dynamic programming methods, which do use models, and that they in turn are closely related to state-space planning methods. In Chapter 9 we explore reinforcement learning systems that simultaneously learn by trial and error, learn a model of the environment, and use the model for planning. Modern reinforcement learning spans the spectrum from low-level, trial-and-error learning to high-level, deliberative planning.