A method to optimize AB using policy gradient reinforcement learning

AB testing is a technology widely used in online experiments. Its main purpose is to compare two or more versions of a page or application to determine which version achieves better business goals. These goals can be click-through rates, conversion rates, etc. In contrast, reinforcement learning is a machine learning method that uses trial-and-error learning to optimize decision-making strategies. Policy gradient reinforcement learning is a special reinforcement learning method that aims to maximize cumulative rewards by learning optimal policies. Both have different applications in optimizing business goals.

In AB testing, we treat different page versions as different actions, and business goals can be regarded as important indicators of reward signals. In order to achieve maximized business goals, we need to design a strategy that can select appropriate page versions and give corresponding reward signals based on business goals. In this regard, policy gradient reinforcement learning methods can be applied to learn optimal policies. Through continuous iteration and optimization, we can improve the performance of page versions to achieve optimal business goals.

The basic idea of ​​policy gradient reinforcement learning is to maximize the expected cumulative reward by updating the gradient of the policy parameters. In AB testing, we can define the strategy parameters as the probability of selection for each page version. To achieve this, we can use the softmax function to convert the selection probabilities for each page version into a probability distribution. The softmax function is defined as follows: softmax(x) = exp(x) / sum(exp(x)) Among them, x represents the selection probability of each page version. By feeding the selection probabilities into the softmax function, we can obtain a normalized probability distribution that determines the selection probability for each page version. In this way, we can improve the effect of AB testing by calculating the gradient and updating the policy parameters to increase the probability of selecting a page version with more potential. The core idea of ​​policy gradient reinforcement learning is to update the parameters based on the gradient, so that the policy

\pi(a|s;\theta)=\frac{e^{h(s,a ;\theta)}}{\sum_{a'}e^{h(s,a';\theta)}}

Among them,\pi(a|s;\ theta) represents the probability of choosing action a in state s, h(s,a;\theta) is the parameterized function of state s and action a, and \theta is the strategy parameter.

In policy gradient reinforcement learning, we need to maximize the expected cumulative reward, that is:

J(\theta)=\mathbb{ E}_{\tau\sim\pi_{\theta}}[\sum_{t=0}^{T-1}r_t]

Among them, \tau means a complete AB testing process, T represents the number of time steps of the test, r_t represents the reward obtained at time step t. We can use the gradient ascent method to update the policy parameters. The update equation is:

\theta_{t 1}=\theta_t \alpha\sum_{t=0}^{T-1 }\nabla_{\theta}\log\pi(a_t|s_t;\theta)r_t

where, \alpha is the learning rate, \nabla_{\theta}\log\pi (a_t|s_t;\theta) is the policy gradient. The meaning of this update equation is that by adjusting the policy parameters along the direction of the policy gradient, the probability of selecting a high-business target page version can be increased, thereby maximizing the expected cumulative reward.

In practical applications, policy gradient reinforcement learning needs to consider some issues, such as how to choose state representation, how to choose reward functions, etc. In AB testing, status representation can include user attributes, page display method, page content, etc. Reward functions can be set based on business goals, such as click-through rate, conversion rate, etc. At the same time, in order to avoid negative effects in actual applications, we should conduct simulations before AB testing, and we should limit the strategy to ensure that our strategy is safe and stable.

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