In the field of machine learning, gradient descent is a powerful optimization algorithm used to minimize the loss function and improve model accuracy.

But what if we could apply this concept to our lives to maximize satisfaction?

Imagine having a set of actions and a set of goals or outcomes. By treating outcomes as a function of actions, we can use gradient descent to minimize the loss between our goals and desired outcomes.

Let’s explore how this might work and whether it can truly enhance our life satisfaction. Probably not but it’s an interesting experiment!

Understanding Gradient Descent

Gradientdescent Graph GIFfrom Gradientdescent GIFs

Gradient Descent Animation

Gradient descent is an iterative optimization algorithm used to find the minimum of a function. It works by taking steps proportional to the negative of the gradient (or approximate gradient) of the function at the current point. In simpler terms, it adjusts parameters incrementally to reduce the error or loss.

The formula for gradient descent is:

where:

Theta represents the parameters (actions in our case).
Alpha is the learning rate, determining the step size.
Nabla J is the gradient of the loss function with respect to Theta.

Applying Gradient Descent to Life Satisfaction

In the quest for a fulfilling life, we often seek ways to align our actions with our goals. By borrowing concepts from machine learning, specifically gradient descent, we can create a structured approach to optimize our daily decisions and habits.

The Framework

Define Actions and Goals:

Actions: Daily habits, career choices, relationships, hobbies.
Goals/Outcomes: Happiness, financial stability, health, personal growth.

Loss Function:

The loss function measures the difference between desired outcomes and actual outcomes. For life satisfaction, this could be the gap between your current state and your goals.

Iterative Improvement:

Just like in machine learning, you start with an initial set of actions and iteratively adjust them to minimize the loss function. This involves evaluating the impact of each action on your goals and making incremental changes.

Experiment: Simulating Life Satisfaction Optimization

Let’s conduct a simple experiment to illustrate this concept using Python.

Objective: To simulate how gradient descent can be used to optimize life satisfaction by minimizing the loss between goals and outcomes.

Python Code

The code to execute our gradient descent model is below.

import numpy as np

# Defining our goals and outcomes as decimal variables
actions = np.array([0.5, 0.5, 0.5]) # Initial actions
goals = np.array([1.0, 1.0, 1.0]) # Desired outcomes

# Define the loss function
def loss_function(actions, goals):
  return np.sum((actions – goals) ** 2)

# Define the gradient of the loss function
def gradient(actions, goals):
  return 2 * (actions – goals)

# Function to perform gradient descent and plot the loss over iterations
def gradient_descent_plot(learning_rate=0.05):
    actions = actions_initial.copy()
    num_iterations = 100
    loss_history = []
    
    for i in range(num_iterations):
        grad = gradient(actions, goals)
        actions = actions - learning_rate * grad
        loss = loss_function(actions, goals)
        loss_history.append(loss)

# Plotting the loss over iterations
plt.figure(figsize=(10, 6))
plt.plot(range(1, num_iterations + 1), loss_history, marker='o')
plt.title('Loss Progression Over Iterations')
plt.xlabel('Iteration')
plt.ylabel('Loss')
plt.grid(True)
plt.show()
print(f"Final Loss: {loss_history[-1]:.4f}")
print(f"Optimized Actions: {actions}")

# Create an interactive widget for the learning rate
interact(gradient_descent_plot, learning_rate=FloatSlider(min=0.01, max=1.0, step=0.01, value=0.1, description='Learning Rate'));

Does it Work?

As you can see from graph below, the loss between our actions and outcomes starts relatively but rapidly decreases and converges to 0 in around 10 iterations of the algorithm.
Now, before you start thinking that we’ve unlocked the secret to living your best life through some fancy algorithm, let’s come back to planet Earth for a second. Real life isn’t exactly a playground for such theoretical fantasies. Here are a few delightful realities to chew on:

The Randomness of Life

While actions in our experiment can be adjusted linearly to close the gap on our desired outcomes, real life is not always so predictable. Life can easily throw us unexpected challenges that significantly alter our path.

For example, taking a promising new job might seem like a positive step, but it could lead to unexpected stress levels and negatively impact your overall happiness.

As a result, a more realistic model might add randomness to the adjustment of actions and their real impact. Actions can be altered by certain amounts depending on the level of randomness at a given time step.

Dynamic Environment and Influences

Our experiment assumes perfect information for adjusting actions, which is not realistic. In real life, feedback is often sporadic and can come from various sources, such as colleagues, friends, and family.

Additionally, altering actions in isolation is not practical. Our daily interactions and evolving perspectives continuously influence our actions and their outcomes. For instance, advice from a friend might change how you approach your career, adding another layer of complexity to the optimization task.

Multiple Objectives

The experiment models outcomes as finite, but in reality, people have a diverse range of goals they value. For instance, someone could simultaneously aim for career success, personal happiness, and physical health. This illustrated by the artwork above .

Assessing how to quantify such outcomes meaningfully and accurately would be a significant challenge. Incorporating these multiple objectives into the experiment would require a more sophisticated model that can handle complex, multi-faceted goals and the trade-offs between them

Final Thoughts?

Using gradient descent to maximize life satisfaction is an intriguing` concept that highlights the importance of iterative improvement and adaptability. It is an approach that is normally used in the context of systems but there are no rules stating the principles cannot be used for own self-development.

While the mathematical model provides a useful framework, real-life application requires flexibility and awareness of the complexities involved. This simple experiment stands to understand the fundamentals of this approach to decision optimisation. More nuanced models might incorporate stochastic processes, increased numbers of variables, and more.

An interesting experiment would be to add an LLM to the mix to test the approach of iterative feedback-feeding to adapt actions and see if it does minimise loss from a target outcome.

Using Gradient Descent to Maximize Satisfaction in Your Life

Understanding Gradient Descent