Behavior as a Cost Function: A Gradient Descent Perspective

Where Math ♾️ Meets Mind 🧠

Dear Friends,

This post details the mathematical comparison of the gradient descent approach with the uplifted behaviour model.

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Gradient descent is one of the fastest ways to reach the minimum of any objective function. Now, if we think of our daily life as an optimization problem, where the objective is to minimise errors in day-to-day activities, the question becomes:

… how do we track our progress?

A simple and effective method is to journal the key activities we want to improve. We start seeing patterns by regularly noting down what we do, how we feel about it, and where things could go better. This awareness helps us adjust our actions, just like how gradient descent adjusts parameters, moving us steadily toward a more efficient and fulfilling daily routine.

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So γ can be a willingness to adjust our behaviour model, and df/ dx can be a correction over time based on daily notes & reflections.

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• The Goal :

  • Gradient Descent (GD): Aims to find the parameters that minimize a "cost" or "loss" function (e.g., the error in a prediction). The lowest point represents the optimal solution.

  • Behavioural Model (BM): An individual often seeks to reach a desired state – maximising satisfaction, minimising discomfort/anxiety, achieving a goal, or mastering a skill. This desired state is analogous to the minimum point that Gradient Descent seeks.

• The Current State :

  • GD: Starts with an initial set of parameter values, which likely yield a high cost (far from optimal).

  • BM: An individual starts with their current behaviour pattern or skill level, which may be suboptimal for achieving their desired state.

• Feedback & Direction :

  • GD: Calculates the gradient - the direction of the steepest increase in the cost function. It then moves in the opposite direction (steepest descent) to reduce the cost.

  • BM: An individual receives feedback from their environment or internal state (e.g., success/failure, reward/punishment, satisfaction/discomfort). This feedback acts like the gradient, signalling whether the current behaviour is moving them closer to (+) or further from (-) their desired state, and indicating the most effective direction for change.

• Adjustment Size :

  • GD: Uses a learning rate to determine the size of the step taken in the direction of the negative gradient. Too large a step can overshoot the minimum; too small a step makes progress very slow.

  • BM: This corresponds to how much an individual adjusts their behaviour in response to feedback. Some might make large, quick changes (high learning rate), risking instability or overcorrection. Others might make small, incremental changes (low learning rate), leading to slower learning but potentially more stability.

• Iterative Process :

  • GD: Reaches the minimum through repeated iterations – calculate gradient, take a step, repeat.

  • BM: Behavioural change is rarely instantaneous. It involves an iterative process of trying a behaviour, observing the outcome (feedback), adjusting, and trying again (practice, experience).

• Getting Stuck :

  • GD: Can get stuck in a local minimum – a point that looks like the minimum in its immediate vicinity, but isn't the true global minimum.

  • BM: Individuals can get stuck in behavioural patterns or "comfort zones" that are "good enough" but aren't the most effective or fulfilling behaviour possible (the global minimum). Moving out of this rut might initially involve more discomfort or effort (moving "uphill" temporarily), making it hard to break free.

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A Note of Thanks 💗

First and foremost, thank you for taking the time to read this post. Your comments and likes matter the most. It gives me the Confidence 💡and has genuinely strengthened my confidence and mindset.

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