Linear programming: Building smarter AI agents from the fundamentals, part 3

The AI Fundamentalists

We continue with our series about building agentic AI systems from the ground up and for desired accuracy. In this episode, we explore linear programming and optimization methods that enable reliable decision-making within constraints.

Show notes:

• Linear programming allows us to solve problems with multiple constraints, like finding optimal flights that meet budget requirements
• The Lagrange multiplier method helps find optimal solutions within constraints by reformulating utility functions
• Combinatorial optimization handles discrete choices like selecting specific flights rather than continuous variables
• Dynamic programming techniques break complex problems into manageable subproblems to find solutions efficiently
• Mixed integer programming combines continuous variables (like budget) with discrete choices (like flights)
• Neurosymbolic approaches potentially offer conversational interfaces with the reliability of mathematical solvers
• Unlike pattern-matching LLMs, mathematical optimization guarantees solutions that respect user constraints

Make sure you check out Part 1: Mechanism design and Part 2: Utility functions. In the next episode, we'll pull all of the components from these three episodes to demonstrate a complete travel agent AI implementation with code examples and governance considerations.

What we're reading:

• Burn Book - Kara Swisher, March 2025
• Signal and the Noise - Nate Silver, 2012
• Leadership in Turbulent Times - Doris Kearns Goodwin

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1. Introduction and book discussions (00:00:00)

2. Recap: Utility functions and mechanism design (00:05:30)

3. Linear solvers versus loss optimizers (00:08:02)

4. Constraints and optimization problems (00:12:20)

5. Combinatorial and discrete optimization (00:17:30)

6. Mixed integer programming for agents (00:22:32)

7. Episode Wrap-up and Preview (00:29:00)