# Reinforcement Learning¶

In the previous sections, we have introduced data-based learning, where we are given a dataset $$\{\mathbf{x}_i\}$$ for training. Depending on whether we are given labels $$y_i$$ with each data point, we have further divided our learning task as either being supervised or unsupervised, respectively. The aim of machine learning is then to classify unseen data (supervised), or extract useful information from the data and generate new data resembling the data in the given dataset (unsupervised). However, the concept of learning as commonly understood certainly encompasses other forms of learning that are not falling into these data-driven categories.

An example for a form of learning not obviously covered by supervised or unsupervised learning is learning how to walk: in particular, a child that learns how to walk does not first collect data on all possible ways of successfully walking to extract rules on how to walk best. Rather, the child performs an action, sees what happens, and then adjusts their actions accordingly. This kind of learning thus happens best ‘on-the-fly’, in other words while performing the attempted task. Reinforcement learning formalizes this different kind of learning and introduces suitable (computational) methods.

As we will explain in the following, the framework of reinforcement learning considers an agent, that interacts with an environment through actions, which, on the one hand, changes the state of the agent and on the other hand, leads to a reward. Whereas we tried to minimize a loss function in the previous sections, the main goal of reinforcement learning is to maximize this reward by learning an appropriate policy. One way of reformulating this task is to find a value function, which associates to each state (or state-action pair) a value, or expected total reward. Note that, importantly, to perform our learning task we do not require knowledge, a model, of the environment. All that is needed is feedback to our actions in the form of a reward signal and a new state. We stress again that we study in the following methods that learn at each time step. One could also devise methods, where an agent tries a policy many times and judges only the final outcome.

The framework of reinforcement learning is very powerful and versatile. Examples include:

• We can train a robot to perform a task, such as using an arm to collect samples. The state of the agent is the position of the robot arm, the actions move the arm, and the agent receives a reward for each sample collected.

• We can use reinforcement learning to optimize experiments, such as chemical reactions. In this case, the state contains the experimental conditions, such as temperature, solvent composition, or pH and the actions are all possible ways of changing these state variables. The reward is a function of the yield, the purity, or the cost. Note that reinforcement learning can be used at several levels of this process: While one agent might be trained to target the experimental conditions directly, another agent could be trained to reach the target temperature by adjusting the current running through a heating element.

• We can train an agent to play a game, with the state being the current state of the game and a reward is received once for winning. The most famous example for such an agent is Google’s AlphaGo, which outperforms humans in the game of Go. A possible way of applying reinforcement learning in the sciences is to phrase a problem as a game. An example, where such rephrasing was successfully applied, is error correction for (topological) quantum computers.

• In the following, we will use a toy example to illustrate the concepts introduced: We want to train an agent to help us with the plants in our lab: in particular, the state of the agent is the water level. The agent can turn on and off a growth lamp and it can send us a message if we need to show up to water the plants. Obviously, we would like to optimize the growth of the plants and not have them die.

As a full discussion of reinforcement learning goes well beyond the scope of this lecture, we will focus in the following on the main ideas and terminology with no claim of completeness.