Sequential Models

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" summary

Defines sequential models as time-evolving systems with an internal state, global unknown evolution parameters, and adversarial per-step uncontrolled variables, and casts many problems (automata output probabilities, spin-chain entanglement tests, epidemic-control costs) as maximizing cumulative penalty. Introduces a value-function reformulation dual to a marginal-probability program, then approximates with polynomial ansatzes and Positivstellensatz relaxations that map to SDPs or geometric programs. Demonstrates recovering prior d=2 automaton bounds on a laptop, gives entanglement-detection protocols up to N=40, and proposes gradient-based policy search with computable gradients.

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" chapters (14)

1. 0:00Introduction
2. 1:10Finance State Automata
3. 3:41No signal into the past
4. 5:23Motivation
5. 7:58On Average
6. 9:30Sequential Models
7. 12:00Transmission Models
8. 17:20Optimization
9. 20:39Original Problem
10. 22:44Entertainment Detection
11. 23:21Entanglement Detection
12. 27:00Gradient Methods
13. 28:29Future Work
14. 30:12Questions