AI’s Butterfly Effect: Early Decisions Matter More Than You Think

Author(s): Rhea Mall

Originally published on Towards AI.

With insights from Polya’s Urn Model, learn how an initial random bias can have lasting effects on an AI system’s learning trajectory.

“I’ve found that luck is quite predictable. If you want more luck, take more chances. Be more active. Show up more often.”

This quote by motivational speaker Brian Tracy highlights the idea that effort creates opportunity, which in turn results in greater luck. However, people intuitively think of luck as an independent random event, in the way that we think about tossing a coin and having a 50–50 chance of landing on heads no matter what the outcome of the previous toss was. I find that life does not necessarily reflect this. Imagine a musician who gets a lucky first break. They will find it easier to attract new listeners and will grow their audience with less effort. If you land your first job at a prestigious company, future recruiters may see you as a top candidate which will make each future career move easier.

Even though we don’t intuitively think about luck having a memory, life is full of instances like this, where small advantages reinforce themselves over time. Random events are likely to build upon themselves and stack the odds in favor of those who work harder to capitalize on their edge (“success breeds success” or “the rich get richer”) and vice versa, and this idea is not just philosophical. When it comes to stochastic processes (which refer to collections of random variables that change over time), few models capture the property of self-reinforcement as elegantly as Polya’s Urn Model. This statistical experiment demonstrates how a few initial imbalances get magnified over time.

Polya’s Urn Model — A Simple Mathematical Demonstration of Random Initial Imbalances Influencing Future Choices

(If you don’t like math/probability, you can skip to the next section. But don’t worry — this section only has a little bit of math.😀)

The premise of this model is straightforward: imagine an urn filled with r red and b black balls. At every step, you draw a ball at random, observe its colour, and then return it to the urn along with c (>0) additional balls of the same color.

Let us demonstrate the very basic working of this model. Let Xn denote the outcome of the nth draw. We define,

So, we have:

Each subsequent draw is inherently dependent on the previous draw. Let us consider the simplest case of 1 black and 1 red ball, with c = 1 (i.e., we replace each ball with 1 additional ball of the same colour).

The probability of the second draw being black given each scenario will be:

So, if we picked a black ball in the first draw (50–50 chance), we are twice as likely to pick a black ball than a red ball in the second draw.

For the third draw to be black, we’ll have the following probabilities:

A visual representation is given below.

It’s obvious that in case that we, by random chance, drew black balls in the initial two draws, then the probability of drawing a black ball in the third draw will be thrice that of drawing a red ball (see urn 4 in the image above).

Clearly, this modest rule of replacing a ball with c additional balls creates a dynamic where the probability of drawing a particular color increases with every selection of that color. Thus, unlike many classic stochastic processes that have the memoryless property (a key characteristic of Markov chains), Polya’s process is inherently non-Markovian since it shows dependence on the entire history of events. A small initial imbalance that may have happened purely due to chance would make the dominant color more likely to be picked in the future, creating an even greater imbalance. This phenomenon, where an initial advantage snowballs over time, is often referred to as a preferential attachment process and is found in many real-world scenarios, like A/B testing or online recommendation systems.

Examples of Early Biases Snowballing into Dominant Trends in AI/ML Systems

When an agent identifies an option that performs well it naturally gravitates towards it, sometimes to the extent that early randomness can determine long-term trends and dominant behaviors/strategies. For example, in a movie recommender system that begins training with a small set of users, the system might randomly assign higher weight to certain user preferences due to biases in the data (such as a few highly active users watching a certain genre of movies). Over time, because the system gave more weight to that genre early on, it would start recommending it more frequently to new users, leading more users to watch movies in that genre. This would create a feedback loop: the more the system recommends it, the more users interact with that genre, and the more the system reinforces the pattern. As a result, the trajectory of recommendations would become skewed, despite the original dataset being small and relatively unbiased.

Another example demonstrating the impact of early random decisions can be seen in reinforcement learning for robotics. Suppose a robot is learning to navigate a room using reinforcement learning. In its early exploration phase, if it randomly stumbles upon an efficient path to its goal, it is more likely to reinforce that path and optimize around it. Conversely, if it initially explores a suboptimal route, it may take significantly longer to discover better alternatives, as its learned policy is biased by those early random choices. This phenomenon, known as path dependence, illustrates how initial actions can have lasting effects on an AI system’s learning trajectory.

Strategies for Managing these Early Reinforcement Effects

When designing algorithms, understanding the impact of early rewards is crucial so that we build algorithms that can either capitalize on or mitigate these reinforcement effects, depending on the desired outcome. To minimize the risks of path dependence and to create models that remain robust and adaptable, consider these three strategies:

1. Introduce Controlled Randomness: During the early training stages of AI models, implement exploration mechanisms like epsilon-greedy strategies or softmax sampling, which can prevent the system from prematurely converging on suboptimal patterns.
2. Periodically Reset Biases: Regularly reinitialize certain weights or introduce controlled noise to models during training to mitigate the long-term effects of early randomness.
3. Monitor and Adapt Feedback Loops: Continuously track model outputs and user interactions to identify when early random biases are causing skewed results. Introduce dynamic learning rates or retraining cycles that allow the model to adapt to more recent and relevant data, ensuring balanced outcomes over time.

The insights derived from Polya’s urn model not only deepens our understanding of the interplay between chance and choice, but also encourages a more thoughtful approach to managing data biases and long-term trends in complex systems. We must focus on regularly re-evaluating AI models, diversify training data to avoid biases stemming from a limited dataset, and foster a culture of critical thinking where users are encouraged to question AI outputs and suggest improvements.

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Published via Towards AI