Alphabeta MathImitation learning and DAgger
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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
Combinatorics
Linear Algebra
Machine Learning Algorithms
Measure Theory
- Measurable Functions and Simple Approximation
- Measures and Their Basic Properties
- Pointwise Extended-Real Function Products
- 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
Lemma
Follow-the-Leader regret for bounded strongly convex losses
Lemma
Finite-horizon MDP policy occupancy is a probability distribution
Definition
Finite-horizon imitation learning and expert-surrogate loss
Algorithm
Dataset Aggregation (DAgger)
Lemma
Expert mixing changes finite-horizon state occupancy by at most the mixing mass
Lemma
Expert-surrogate loss bounds finite-horizon task-cost increase
Theorem
DAgger no-regret reduction under strongly convex surrogate losses
Theorem
Finite-sample DAgger surrogate-loss guarantee
Sources
- Stéphane Ross, Geoffrey J. Gordon, and J. Andrew Bagnell, A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning
- Richard S. Sutton and Andrew G. Barto, Reinforcement Learning: An Introduction, 2nd ed.
- James A. Bagnell, Byron Boots, and Sanjiban Choudhury, Modern Adaptive Control and Reinforcement Learning, Chapter 6: An Invitation to Imitation
- Bardienus Duisterhof, Kimberly Truong, and Khush Agrawal, Algorithmic Foundations of Interactive Learning, Lecture 9: DAgger & Covariate Shift in IL, lecturer J. Andrew Bagnell