prediction, learning, and games
این کتاب و مرجع برای محققین و دانش آموزان یادگیری ماشین، نظریه بازی ها، آمار و تئوری احتمالات طراحی شده است و به آنها ایدهها و راه کارهایی جامعی در مورد ترتیب یا دنباله یهای خاص پیش بینی میدهد. برخلاف راهکارهای استاندارد آماری برای پیش بینی یا پیشگویی حالات بخصوص دنبالهها یا ترتیب ها، این روش هیچ گونه فرضهای احتمالی بر روی مکانیزمهای تولید داده ایجاد نمیکند . با اینحال، این الگوریتمهای پیش بینی به گونه ای ساختار یافته میشوند که برای تمامی دنبالههای احتمالی کاربرد دارند، در کنار داشتن بهترین بازدهی در پیشگویی .
Introduction
Prediction
Learning
Games
A Gentle Start
A Note to the Reader
Prediction with Expert Advice
Weighted Average Prediction
An Optimal Bound
Bounds That Hold Uniformly over Time
An Improvement for Small Losses
Forecasters Using the Gradient of the Loss
Scaled Losses and Signed Games
The Multilinear Forecaster
The Exponential Forecaster for Signed Games
Simulatable Experts
Minimax Regret
Discounted Regret
Bibliographic Remarks
Exercises
Tight Bounds for Specific Losses
Introduction
Follow the Best Expert
Exp-concave Loss Functions
The Greedy Forecaster
The Aggregating Forecaster
Mixability for Certain Losses
General Lower Bounds
Bibliographic Remarks
Exercises
Randomized Prediction
Introduction
Weighted Average Forecasters
Follow the Perturbed Leader
Internal Regret
Calibration
Generalized Regret
Calibration with Checking Rules
Bibliographic Remarks
Exercises
Efficient Forecasters for Large Classes of Experts
Introduction
Tracking the Best Expert
Tree Experts
The Shortest Path Problem
Tracking the Best of Many Actions
Bibliographic Remarks
Exercises
Prediction with Limited Feedback
Introduction
Label Efficient Prediction
Lower Bounds
Partial Monitoring
A General Forecaster for Partial Monitoring
Hannan Consistency and Partial Monitoring
Multi-armed Bandit Problems
An Improved Bandit Strategy
Lower Bounds for the Bandit Problem
How to Select the Best Action
Bibliographic Remarks
Exercises
Prediction and Playing Games
Games and Equilibria
Minimax Theorems
Repeated Two-Player Zero-Sum Games
Correlated Equilibrium and Internal Regret
Unknown Games: Game-Theoretic Bandits
Calibration and Correlated Equilibrium
Blackwell’s Approachability Theorem
Potential-based Approachability
Convergence to Nash Equilibria
Convergence in Unknown Games
Playing Against Opponents That React
Bibliographic Remarks
Exercises
Absolute Loss
Simulatable Experts
Optimal Algorithm for Simulatable Experts
Static Experts
A Simple Example
Bounds for Classes of Static Experts
Bounds for General Classes
Bibliographic Remarks
Exercises
Logarithmic Loss
Sequential Probability Assignment
Mixture Forecasters
Gambling and Data Compression
The Minimax Optimal Forecaster
Examples
The Laplace Mixture
A Refined Mixture Forecaster
Lower Bounds for Most Sequences
Prediction with Side Information
A General Upper Bound
Further Examples
Bibliographic Remarks
Exercises
Sequential Investment
Portfolio Selection
The Minimax Wealth Ratio
Prediction and Investment
Universal Portfolios
The EG Investment Strategy
Investment with Side Information
Bibliographic Remarks
Exercises
Linear Pattern Recognition
Prediction with Side Information
Bregman Divergences
Potential-Based Gradient Descent
The Transfer Function
Forecasters Using Bregman Projections
Time-Varying Potentials
The Elliptic Potential
A Nonlinear Forecaster
Lower Bounds
Mixture Forecasters
Bibliographic Remarks
Exercises
Linear Classification
The Zero–One Loss
The Hinge Loss
Maximum Margin Classifiers
Label Efficient Classifiers
Kernel-Based Classifiers
Bibliographic Remarks
Exercises