Alphabeta MathModel-based planning, Dyna, and model exploitation
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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✓ 9 results · all verified · 8 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 1 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
Abstract Algebra
- Binary Operations, Monoids, Groups and Subgroups
- Cosets, Index and Lagrange's Theorem
- Divisibility, Euclidean Domains, Principal Ideal Domains and Unique Factorisation
- Ideals, Quotient Rings and the Isomorphism Theorems for Rings
- Normal Subgroups and Quotient Groups
- Polynomial Rings, the Division Algorithm and Roots
- Rings, Subrings, Integral Domains and Fields
- Simple Field Extensions and the Construction of the Complex Numbers
Bayesian Computational Statistics
Linear Algebra
Machine Learning Algorithms
Measure Theory
- Measurable Functions and Simple Approximation
- Measures and Their Basic Properties
- Outer Measure and the Caratheodory Extension Theorem
- Product Measures and the Fubini Tonelli Theorems
- Sigma Algebras and Borel Sets
- Signed and Complex Measures Hahn and Jordan
- The Lebesgue Integral and the Convergence Theorems
- The Lᵖ Spaces Holder Minkowski and Riesz Fischer
- The Radon Nikodym Theorem and Lebesgue Decomposition
Probability
Real Analysis
- Absolute and Conditional Convergence; Rearrangement; Products
- Construction of the Real Numbers via Cauchy Sequences
- Construction of the Real Numbers via Dedekind Cuts
- Continuity, IVT, EVT, and Uniform Continuity
- Countability and Uncountability
- Foundations of the Real Numbers for Analysis
- Limits of Real Functions
- limsup, liminf, and Subsequential Limits
- Monotone Functions, Discontinuities, and Continuity Sets
- Monotone Sequences, Bolzano-Weierstrass, and Cauchy Completeness
- Power Series and Real-Analytic Functions
- Properties of the Integral and the Working FTC
- Roots, Rational Powers, and Classical Inequalities
- Sequences and Limits
- Sequences and Series of Functions; Uniform Convergence
- Series: Convergence and the Nonnegative Tests
- Suprema and Infima
- The Derivative and the Mean Value Theorems
- The Exponential Function
- The Logarithm and General Powers
- The Riemann Integral: Definition and Integrability
- Topology of ℝ
Set Theory
2 · Logical flowchart
3 · Items
Definition
Finite learned transition and reward models
Definition
Finite stochastic shortest-path problems
Definition
Finite-horizon return under a Markov policy
Algorithm
Trial-based real-time dynamic programming
Lemma
One-step total-variation propagation under a fixed policy
Theorem
Finite positive-cost stochastic shortest-path value
Remark
Ensemble disagreement is not calibrated uncertainty by definition
Algorithm
Tabular Dyna-Q with a deterministic last-observation model
Algorithm
Finite-horizon model-predictive control
Theorem
Finite-horizon simulation bound for one fixed policy
Lemma
Asynchronous value iteration for finite positive-cost shortest paths
Theorem
RTDP convergence on recurrently backed states
Counterexample
RTDP need not visit every state reachable under an optimal policy
Definition
Model exploitation under support shift
Sources
- Richard S. Sutton and Andrew G. Barto, Reinforcement Learning: An Introduction, second-edition-in-progress
- Sergey Levine, Aviral Kumar, George Tucker, and Justin Fu, Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems
- Andrew G. Barto, Steven J. Bradtke, and Satinder P. Singh, Learning to Act Using Real-Time Dynamic Programming
- Barto, Bradtke and Singh, Learning to Act Using Real-Time Dynamic Programming, Appendix A recurrent-set argument, corrected to exclude the false all-optimal-reachable conclusion