The insurance industry is dynamic and competitive, with risks constantly changing and markets constantly fluctuating. The ability to accurately price insurance is especially important for retail businesses. Traditional actuarial methods, while robust, often struggle to adapt quickly to changing conditions and customer behavior.
Reinforcement learning (RL) and contextual multi-armed bandits (CMAB) are cutting-edge AI and machine learning techniques that can help insurance companies gain a competitive advantage. Here we discuss these techniques and explore how they can reshape policy pricing and customer segmentation to improve profitability and sales volumes. This is not intended as a technical specification of the CMAB algorithm, but only a conceptual overview to inspire further research.
Reinforcement learning
RL is a type of machine learning where an agent learns to make decisions as it interacts with the environment. It learns through trial and error and receives feedback in the form of rewards (Figure 1).
RL has a wide range of use cases across various industries, including insurance. For example, online platforms use RL to create personalized recommendations for users based on their past interactions and preferences. In the finance industry, RL can be applied to optimize trading strategies in financial markets, such as stock trading and portfolio management. In the healthcare industry, it is used to create personalized treatment plans based on patients' medical history, symptoms, and responses to previous treatments.
Insurers can use RL to dynamically adjust prices in response to changing market conditions, customer behavior, and competitor behavior. Over time, agents learn how to optimize pricing strategies to maximize profits or other objectives, adapting to new information and changing conditions.
The process begins with an agent (the part of the algorithm that decides what action to take) observing the current state of the environment, such as customer behavior and market conditions. The agent acts based on these observations. For example, the algorithm might lower prices to increase sales volume for customers in a certain demographic segment who tend to be price sensitive. Conversely, if demand is high and customers are willing to pay more, the algorithm might increase prices to maximize revenue.
The agent receives feedback in the form of rewards. For example, if it increases its prices during a spike period and still gets significant conversions, it receives a larger or positive reward. On the other hand, if it sets its prices too high and loses customers, it receives a smaller or negative reward. Over time, the agent learns which pricing strategies lead to the best rewards (profits) in different situations.
Famous examples of reinforcement learning include AlphaGo and AlphaZero, developed by Google's AI division DeepMind: the former famously defeated the world champion Go player, and the latter surpassed human performance at a range of board games by learning through self-play and reinforcement learning techniques.
Contextual multi-armed robbery
In RL and decision theory, a multi-armed bandit problem is a scenario where you need to make an optimal choice between different options, each with a different probability distribution of success. Imagine a slot machine with k levers instead of one lever (arm). You pull a lever each time you want to perform an action. The reward is the payoff you get from choosing a particular lever. Your goal is to maximize your winnings by focusing on the most profitable lever.
In CMAB, additional context or information is presented next to each action. Imagine a slot machine with a display that changes color as the action value changes. This information helps you make a more informed decision. The goal of maximizing cumulative rewards over time remains the same — deciding which lever to choose to get the highest reward.
CMAB is particularly useful in repetitive decision-making tasks that involve multiple distinct actions (k). A numerical reward is given after each decision made by the agent. The objective is to optimize the expected overall reward over a defined time window, such as decisions or time steps over a day or across a period of time.
Each of the k actions leads to a reward based on the use case, for example depending on the number of clicks or profits for the user. These actions are selected by the agent at each timestep within a given time window or episode.
Based on the rewards and actions, we can obtain a value function. An episode represents a complete sequence of actions and outcomes. The values reflect the expected rewards of actions and are dynamically updated based on experience. They are then used to guide the agent's decision-making process. In CMAB, the goal is to learn a policy that finds the optimal action for each situation.
The problem would be easy to solve if we knew the exact value of each action: the algorithm should always choose the action with the highest value. However, we might not know the value associated with each action, although we can compute an estimate. The lack of a clear best action leads to one of the fundamental concepts of RL: the explore-exploit trade-off.
In explore-exploit, at each time step, there is at least one action that maximizes value by leveraging current value-action knowledge. On the other hand, if the current action is not optimal, new actions may need to be tested. These are the explored values. Typically, multi-armed bandit algorithms use a near-greedy (or epsilon-greedy) algorithm to select an action. Greedy action selection leverages current knowledge to select the action with the highest estimated reward value.
An alternative to greedy selection is to choose seemingly non-optimal random actions with probability epsilon, independent of the action value estimates. These actions allow the algorithm to explore all possible actions, which may lead to value-action convergence and an optimal solution in the long run.
Contextual bandits are halfway between the k-arm bandit problem or basic learning algorithm and the full RL challenge. Like full RL, it requires learning a policy. However, in the k-arm bandit problem, each action only affects the immediate reward. If actions could affect not only the immediate reward but also the subsequent state, it would become full RL.
As you iterate through an episode, you get multiple rewards for each context or state. There are many ways to get these rewards. The easiest way to calculate the reward is to find its average value. You can then convert it to an incremental calculation of the average value for computational purposes. This allows you to solve problems with stationary rewards (fixed probabilities).
If the reward probability varies, you need to move to a non-stationary problem. For example, you might want to give more reward to more recent data points. In other words, you can calculate a weighted average of the rewards. Otherwise, you can introduce priorities into the action selection and use techniques such as the bandit gradient algorithm.
Once the value function is ready, i.e., it has converged after many iterations over multiple episodes, we select the action or arm that brings the highest reward at each time step.
