# Outline ##### Key Idea to Explore > There is a relationship between search, exploration, constraints, objective functions, environment and a search space. I want to try and unify these things under a single mental model. I want to create nice images that make this nice to read. These images should solidify the concept in readers minds. #### Key Ideas to Explore * What are the main ways in which spaces are searched? How are they similar? How are they different? * What structure does a space provide you? How can you exploit it? * Have an objective function? Then you may be able to use gradients or hessians. Other times randomness could be useful. * Search vs Exploration * Gradients and direction * Trajectories in design space without gradients * Evolution vs Deep Learning vs Reinforcement Learning ### Goals * Communicate good *abstractions* of evolution, gradient descent, and RL and how they search/explore spaces ## Structure * Intro * Set the stage for the problem. * We have spaces (share some varieties, maybe add some visuals). * There are many different ways to navigate/traverse/journey (what is a term that encompasses these - see [here](https://chat.openai.com/c/7e09a249-2ba9-4eb9-a64e-f6e0f33ea378)) these spaces. * We can ask: what are the root essences (abstractions) to exploring these spaces? * Given these abstractions, what are the distinctions between these * Other ideas for a name "A Mathematics Inspired Space Odyssey" * Evolution: Expansion in Constrained Spaces * Evolution * Why Greatness Can't be Planned * [Revising the Evolutionary Computation Abstraction: Minimal Criteria Novelty Search](http://eplex.cs.ucf.edu/papers/lehman_gecco10a.pdf) * Gradient Descent / Gradient Based Methods (hill climbing, continuous space) * Graph Search (discrete) * RL * Randomness / Monte Carlo * ([estimate properties of spaces via law of large numbers and statistical approach](https://chat.openai.com/c/7e09a249-2ba9-4eb9-a64e-f6e0f33ea378)) * As you write about these approaches, really work on distilling the *essence* of what they each do. And try to come up with *connections* between different fields. Process: * Start with evolution and gradient based methods because you know those the best Today: * 500 words + structure ### Links to [Natural Selection is a Constraint](Natural%20Selection%20is%20a%20Constraint.md) [Environment, Agent and Constraints](Environment,%20Agent%20and%20Constraints.md) ### Resources [Searching vs Exploring](https://chat.openai.com/c/7e09a249-2ba9-4eb9-a64e-f6e0f33ea378)