What is a multi-armed bandit? Full explanation

A multi-armed bandit is a more complex version of A/B testing that applies an exploration-exploitation approach. It uses machine learning algorithms that allocate resources to maximize specific metrics.

Businesses use multi-armed bandit testing to improve their products, create engaging campaigns, and deliver a superior customer experience. They help save time and money by focusing on what customers love, ultimately driving growth.

Multi-armed bandit example

Let’s say you want to find the most effective version of an online advertisement. You have multiple ad variations and want to see which yields the highest click-through rate (CTR) or conversion rate.

Instead of dividing the audience evenly (as in traditional A/B testing) and risking showing an inferior ad to your audience, a multi-armed bandit approach allocates traffic to variations based on real-time performance data.

Here’s a closer look at how that works:

• Exploration: The algorithm explores by randomly selecting different ad variations and showing them to part of the audience. The exploration phase enables the algorithm to gather data on each performance.
• Exploitation: As the algorithm collects data, it exploits by favoring ads with better performance. It directs more traffic to ads with higher CTR or conversion rates—the company’s desired outcome.

What is a contextual bandit?

In a contextual bandit setting, the algorithm has extra information (like user demographics or browsing history) about each option.

Instead of mindlessly selecting options, it uses this added data to make smarter decisions. Our online ad scenario might consider user location or time of day.

Here’s how they function:

• Observing the context: The algorithm gets information about the current situation or user.
• Selecting an action: It picks an action from the available choices using this information.
• Observing rewards: After taking the action, the algorithm gets a specific reward signal for that action.

Learning and adapting: The algorithm uses the context, chosen action, and received rewards to improve its understanding. With time, it learns which actions work best in different situations, aiming for the highest rewards.

Imagine you’re in a casino with several slot machines. You want to win as much money as possible but don’t know which arm gives you the best chance of winning.

You would instead have to figure it out by trying different machines over time and learning which arms are more likely to land the prize.

The challenge is balancing testing new machines to learn more about them and sticking with what you currently know to cash in on the rewards—this is the multi-armed bandit problem.

This is especially important in a business setting with limited resources like time, money, and user attention. Here, you can’t afford to keep trying new options (machines) until you win big.

In statistics and probability, we frame the problem like this:

• Multiple options (arms): You have several choices or actions, represented as arms.
• Unknown reward distributions: Each choice has a hidden probability of giving a reward, which you don’t know initially.
• Exploration vs. exploitation: You face a dilemma between trying new options (exploration) to understand their rewards or sticking with the best option (exploitation) based on the information gathered so far.
• Objective: You aim to determine the best action (the one with the highest chance of giving a reward) and maximize your total rewards over time.

Researchers have created various algorithms (including Epsilon-Greedy, Upper Confidence Bound (UCB), or Thompson Sampling) to address the multi-armed bandit dilemma. They help businesses make intelligent decisions, optimizing their strategies for maximum benefit.

You’ll likely encounter A/B testing and multi-armed bandits when planning your experimentation workflow.

Both methods optimize decision-making in various scenarios, but they have different approaches and applications.

Let’s compare the two so you have a better idea of which to pick.

A/B testing

• Fixed allocation: The audience is split into equal groups (A, B, C, etc.), with each group seeing a different product or content variant. The allocation to each group stays fixed throughout the experiment.
• Statistical significance: A/B testing uses a set sample size and duration. Statistical methods are then used to see if there’s a significant difference in performance metrics (like conversion rates) between variants.
• Exploitation over exploration: A/B testing mainly concentrates on finding the best-performing option based on predetermined criteria. It doesn’t emphasize exploring new options, instead exploiting the known variants.
• Suitable for stable environments: A/B testing works well in stable situations where user preferences or other factors aren’t expected to change rapidly during the experiment.

Multi-armed bandits

• Dynamic allocation: Traffic is allocated in real-time based on how well each option performs. Successful options get more traffic while underperforming ones receive less.
• Continuous optimization: Multi-armed bandits constantly adjust resource allocation, enabling ongoing exploration and exploitation. This means they adapt in real time.
• Balanced exploration and exploitation: These systems balance exploring new options to gather data and exploiting known working options by allocating more traffic to them.

Suitable for dynamic environments: Multi-armed bandits are suitable for changing situations where conditions can shift. They are adaptive and respond effectively to dynamic changes.

Multi-armed bandits empower businesses to make data-driven, adaptive, and personalized decisions.

They offer several advantages to support sustainable growth, including:

• Dynamic personalization: Multi-armed bandits show the best-performing option in real-time. This personalized approach improves user experience by adapting to what users will likely engage with the most.
• Revenue-based optimization: Businesses can make more money by focusing their resources on the most profitable options, optimizing for maximum revenue.
• Flexibility and automation: They automatically adjust and adapt to changes in user behavior and market conditions, unlike static methods like A/B testing. This flexibility is vital in fast-changing environments where strategies must evolve continuously.
• Real-time data control: Businesses have real-time control over their data, making it easier to reach data-driven decisions. They analyze changing performance metrics and make quick adjustments for better outcomes.
• Ease of implementation: They need little IT intervention, even for complex experiments. This enables businesses to run intricate optimization projects smoothly without major delays or technical challenges.

Integrating multi-armed bandits with Amplitude generates a powerful optimization framework.

Use Amplitude to monitor your experiment and analyze the performance of different variations, applying the platform’s powerful analytics tools to track key metrics.

Robust reporting and visualization features enable you to compare those metrics across variations. You can assess how well your different website designs, ad creatives, product features, or any other optimized elements perform.

You can then refine your changes based on the insights gained from Amplitude’s analysis, ensuring you’re always delivering the best possible option to your customers.

Amplitude simplifies experimentation's complexities and provides actionable insights derived from real-time data.

By embracing its capabilities alongside multi-armed bandits, you can make smarter, data-backed decisions, increasing revenue, higher customer satisfaction, and a competitive edge in the market.

Shape a future of endless business possibilities. Sign up for Amplitude today.