Protocol
Optimization from Objectives to Updates
Choose an optimizer for a constrained least-squares toy problem. Compare it with the analytic solution and defend the stopping tolerance and work budget.
45–75 active hours60–90 min sessionsIntermediate
Mastery contract
Core protocol · Standard 1.0 · Choose an optimizer for a constrained least-squares toy problem. Compare it with the analytic solution and defend the stopping tolerance and work budget.
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Reasoning — not yet passed
The quadratic and KKT derivations state feasibility, convexity and differentiability assumptions.
Reliable implementation — not yet passed
Solvers reach a known quadratic optimum within declared tolerances and detect divergence rather than hiding it.
Reproducible experiment — not yet passed
Compare gradient descent and the selected alternative from matched initial conditions; retain objective/residual curves, tolerances and work counts for every step-size setting.
Defense and handoff — not yet passed
Construct and execute a nonconvex counterexample with different initializations, using its outcomes to delimit the convex convergence guarantee.
All four criteria must pass. Activity completion does not satisfy them.
An independent reviewer reruns your work and varies something you did not rehearse: a fresh input, a different working directory, or a declared edge case.
Pilot decisions are provisional, not external credentials. For an appeal or sensitive artifact, contact your designated pilot operator with the submission ID. Export your assessment history.
What you will do
6 total
Derive gradient descent for a quadratic and KKT conditions for a constrained two-variable problem; identify when sufficient optimality conditions apply.
Implement fixed-step descent, backtracking line search and minibatch descent in NumPy with objective and gradient-norm logging.
Compare 3 step sizes on the same well-conditioned and ill-conditioned quadratics; hold initial points fixed and report objective evaluations as well as iterations.
Debug an update with the wrong sign and a stochastic stopping rule that mistakes noise for convergence.
Write a 500–900 word technical report linking the reasoning, code, measurements, and limitations; include the project decision below.
Assess all 4 mastery criteria against saved artifacts, request an independent review, and repeat each failed criterion on a fresh example.
Essentials
A reading session alone never satisfies a mastery criterion.
Store source references, assumptions, and artifact paths beside every result.
Keep an untouched check case that differs from the worked example.
Record all attempts, including failures and results that contradict your prediction.
Use the stated comparison conditions; document every deviation before drawing a conclusion.
Protocol guardrails
Do
- +State the expected result before running the comparison.
- +Keep one minimal reproducible failing case when debugging.
- +Record environment versions and the exact command used.
- +Compare explanations with saved intermediate values.
- +Ask a reviewer to challenge the weakest assumption.
Don't
- ×Do not copy a worked solution and present it as an independent implementation.
- ×Do not tune against held-out evaluation outcomes.
- ×Do not report only the best seed or discard inconvenient runs.
- ×Do not equate elapsed hours or a completed run with a passed assessment.
- ×Do not conceal reduced-scale experiments behind claims about the original full-scale result.
Protocol authorship
Written by NuthinButta as instructional design. The teaching sources are the official references linked in each milestone; the exercises, workload and pass thresholds are ours, not their authors'.