GRL Tutorial Paper: Publication Sections¶
Format: Paper-ready sections for the GRL tutorial paper
Audience: Academic readers, peer reviewers
Goal: Polished, rigorous sections ready for publication
Overview¶
This directory contains paper-ready sections of the GRL tutorial paper. Each document represents a complete, publishable section with:
- Clear mathematical exposition
- Rigorous notation
- Complete algorithms
- Proper citations
Paper Structure¶
Front Matter¶
| Section | Title | Status |
|---|---|---|
| Abstract | GRL Tutorial Paper Abstract | ⏳ Planned |
| Introduction | Motivation and Overview | ⏳ Planned |
Main Sections¶
| Section | Title | Description | Status |
|---|---|---|---|
| II | Preliminaries | Background and notation | ⏳ Planned |
| III | Reinforcement Field | Functional field in RKHS | ⏳ Planned |
| IV | Policy Inference | Particle-based algorithms | ⏳ Planned |
| V | Theoretical Analysis | Properties and interpretation | ⏳ Planned |
| VI | Implementation | Practical considerations | ⏳ Planned |
| VII | Experiments | Empirical validation | ⏳ Planned |
| VIII | Discussion | Connections and extensions | ⏳ Planned |
Supplementary Material¶
| Section | Title | Description | Status |
|---|---|---|---|
| S1 | Energy-Based Interpretation | Connection to EBMs | ⏳ Planned |
| S2 | Gradient Flow | Deterministic limits | ⏳ Planned |
| S3 | Convergence Analysis | Theoretical guarantees | ⏳ Planned |
Section IV: Policy Inference (Key Section)¶
This is the core algorithmic section, containing:
IV-A: Particle-Based Belief Update¶
Algorithm 1: MemoryUpdate
- Belief-state transition operator
- Kernel-based association
- Particle management
IV-B: Reinforcement Propagation¶
Algorithm 2: RF-SARSA
- Two-layer architecture
- Primitive TD learning
- Field-based generalization
IV-C: Soft State Transitions¶
- Emergent uncertainty
- Distributed successor representation
- Kernel-induced smoothness
IV-D: POMDP Interpretation¶
- Belief-based control
- Particle ensemble as belief state
- Inference vs. optimization
Writing Standards¶
Mathematical Rigor¶
- All claims precisely stated
- Notation consistent throughout
- Proofs provided or cited
Algorithm Presentation¶
- Complete pseudocode
- Line-by-line explanation
- Complexity analysis
Clarity¶
- One concept per paragraph
- Examples for abstract ideas
- Clear section transitions
Notation Reference¶
| Symbol | Meaning |
|---|---|
| \(\mathcal{S}\) | State space |
| \(\Theta\) | Action parameter space |
| \(z = (s, \theta)\) | Augmented state-action point |
| \(k: \mathcal{Z} \times \mathcal{Z} \to \mathbb{R}\) | Kernel function |
| \(\mathcal{H}_k\) | RKHS induced by \(k\) |
| \(Q^+: \mathcal{Z} \to \mathbb{R}\) | Reinforcement field |
| \(E(z) = -Q^+(z)\) | Energy function |
| \(\Omega = \{(z_i, w_i)\}\) | Particle memory |
| \(\delta_t\) | TD error at time \(t\) |
Last Updated: January 11, 2026