Alphabeta MathOptimistic exploration and PAC-MDP sample complexity
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✓ 8 results · all verified · 0 also independently AI-judged
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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
- 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
- Rⁿ as a Normed Space; Vector-Valued Functions
- 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 discounted MDP with bounded real rewards
Theorem
Well-defined discounted values and optimal Bellman fixed points
Lemma
Concentration for adaptively sampled MDP observations
Definition
PAC-MDP sample complexity of exploration
Definition
Admissible upper heuristic for a discounted MDP
Lemma
Value stability under empirical model error
Definition
Known-state/action MDP with prescribed absorbing values
Algorithm
R-MAX with an admissible heuristic
Algorithm
Delayed Q-learning with an admissible heuristic
Theorem
Escape-event reduction for optimistic greedy learning
Lemma
Adaptive empirical-model accuracy for R-MAX
Lemma
Delayed Q-learning optimism and update-count bounds
Theorem
The zero-tolerance boundary of PAC-MDP exploration
Theorem
PAC-MDP sample complexity of R-MAX
Theorem
PAC-MDP sample complexity of Delayed Q-learning
Sources
- Alexander L. Strehl, Lihong Li, and Michael L. Littman, Reinforcement Learning in Finite MDPs: PAC Analysis
- Csaba Szepesvári, Algorithms for Reinforcement Learning
- Richard S. Sutton and Andrew G. Barto, Reinforcement Learning: An Introduction, 2nd ed.
- Alexander L. Strehl, Lihong Li, Eric Wiewiora, John Langford, and Michael L. Littman, PAC Model-Free Reinforcement Learning
- Strehl, Li, and Littman, Reinforcement Learning in Finite MDPs: PAC Analysis
- Strehl et al., PAC Model-Free Reinforcement Learning