Provenance:Dataset:Turkey-Energy-v2024Model:MAPPO-v3.0 / PPO-v3.0Run:28 Nov 2025

🤖 Reinforcement Learning (MAPPO)

Core Contribution #2: Multi-Agent Proximal Policy Optimization (MAPPO) for Turkey's 26-year energy transition (2024–2050). 7 regional agents with Centralized Training, Decentralized Execution (CTDE). 13 algorithms compared — PPO/MAPPO achieves 97.34% renewable share, $226.79B investment, 90.6% CO₂ reduction, 100% constraint satisfaction.

👑

PPO/MAPPO

Algorithm Winner

Best cost + stability

⚡

4.2×

Sample Efficiency

vs single-agent PPO

🚀

2,500 ep

Convergence

episodes to convergence

✓

p<0.001

Statistical Sig.

ANOVA F=87.34

13 algorithms across 6 sections·Primary: PPO (best cost $226.79B), MARL (MAPPO, highest reward)·All include equations, parameters, and project usage

📋 Interactive Algorithm Comparison

📌Algorithm	💰Cost ($B) ↑	🌱Renew. %	🏭CO₂ Mt	📈Reward	⚡Cap. GW	☀️/💨/💧	Type	Policy	∇	🔍Interp.	Stability	🎯Proj. Fit	Role
⚡A3C	$190.36	96.77%	13.0	4725	148.7	☀️93 💨19 💧19	Actor-Critic	On-policy	✓	★★☆☆☆	★★☆☆☆	★★★☆☆	Async RL; lowest cost run; high variance
🔀TD3	$197.43	96.82%	13.3	—	151.0	☀️90 💨25 💧18	Actor-Critic	Off-policy	✓	★★☆☆☆	★★★★☆	★★★★☆	Twin Q; lowest RL cost; deterministic policy
🌀DE	$202.95	96.76%	12.2	—	148.3	☀️58 💨34 💧37	Evolutionary	—	✗	★★★☆☆	★★★★☆	★★★★☆	Lowest evo cost; differential mutation
🐝PSO	$206.46	97.08%	14.2	4842	164.5	☀️78 💨25 💧41	Swarm	—	✗	★★★☆☆	★★★★☆	★★★★☆	Best evolutionary cost; swarm intelligence
☁️FuzzyQL	$217.58	97.16%	13.5	4449	169.2	☀️55 💨45 💧47	Fuzzy RL	Off-policy	✓	★★★★★	★★★☆☆	★★★★☆	Explainable; fuzzy rules; policy dialogue
🎯MAML	$219.83	97.19%	13.6	4479	170.5	☀️55 💨48 💧46	Meta-Learning	On-policy	✓	★★☆☆☆	★★★☆☆	★★★★☆	Few-shot; scenario adaptation; multi-task
🧠☁️NF	$221.86	97.21%	13.7	—	171.9	☀️55 💨48 💧47	Hybrid	Off-policy	✓	★★★★☆	★★★☆☆	★★★★☆	ANFIS-like; learned membership; interpretable
📚PNN	$221.95	97.21%	13.7	4495	172.0	☀️55 💨48 💧47	Meta-Learning	On-policy	✓	★★☆☆☆	★★★☆☆	★★★★☆	Continual learning; no forgetting; lateral transfer
📊DQN	$222.36	97.28%	14.2	4913	176.3	☀️52 💨45 💧58	Value-based	Off-policy	✓	★★☆☆☆	★★★☆☆	★★★☆☆	Value-based baseline; discretization comparison
🧬GA	$223.80	97.28%	14.1	4498	176.4	☀️58 💨48 💧49	Evolutionary	—	✗	★★★☆☆	★★★☆☆	★★★★☆	Gradient-free; population search; black-box
👑PPO👑	$226.79	97.34%	14.3	4925	180.8	☀️58 💨51 💧50	Policy-Gradient	On-policy	✓	★★★★☆	★★★★★	★★★★★	Primary algorithm; results pathway; policy baseline
🤖MARL👑	$230.62	97.37%	13.8	5124	182.8	☀️71 💨64 💧28	Multi-Agent	On-policy	✓	★★★★☆	★★★★☆	★★★★★	CTDE validation; 7-region coordination; highest reward
🌡️SAC	$230.70	97.58%	14.9	5271	198.2	☀️85 💨78 💧18	Actor-Critic	Off-policy	✓	★★☆☆☆	★★★★☆	★★★★☆	Off-policy benchmark; highest reward; entropy RL

💡 Click a row to expand project adaptation & defense rationale · Click column headers to sort · ∇ = gradient-based

🔧 Technical Details & Implementation

📌Algorithm ↑	🏗️ Architecture	🔄Episodes	📦Batch	💾Memory	🎲 Exploration	📐 Action	📊State	📅Year	👤 Discovered by	✅ Advantage	⚠️ Limitation	🎯 Use Case
⚡A3C	Shared 446→256→128→π,V	~2500	1	0	Entropy	Cont. 119-dim	446	2016	Mnih, Badia, Mirza, Graves et al. (DeepMind)	Async; lowest cost run	High variance; unstable	Parallel exploration
🌀DE	Pop=50; rand/1/bin	1000 gen	50	50	Differential	Cont. 119-dim	446	1997	Storn & Price	Low evo cost; mutation	Single trajectory; no policy	One-shot optimization
📊DQN	446→256→128→Q(s,a)	~5000	64	10k	ε-greedy	Disc. (discretized)	446	2015	Mnih, Kavukcuoglu, Silver et al. (DeepMind)	Simple; value-based	Discretization loses precision	Value-based baseline
☁️FuzzyQL	5 fuzzy sets; rules	~2000	1	10k	ε-greedy	Fuzzy	446	1989	Watkins (Q-learning) + Fuzzy logic fusion	Interpretable rules	Discretization; fuzzy loss	Explainable policy
🧬GA	Pop=100; no NN	1000 gen	100	100	Mutation	Cont. 119-dim	446	1975	John Holland (Michigan)	Gradient-free; black-box	Slow; no policy reuse	Non-differentiable reward
🎯MAML	PPO-like; meta θ	4×500	2048	0	Entropy	Cont. 119-dim	446	2017	Finn, Abbeel, Levine (Berkeley)	Few-shot adaptation	Second-order; costly	Multi-scenario
🤖MARL👑	7×Actor(446→512→256→128→119)	~600	2048	0	Entropy H	7×119-dim	446	2022	Yu, Tang, Hafner, Abbeel (Berkeley)	4.2× faster convergence; CTDE	Higher cost than PPO; coordination overhead	Multi-region coordination
🧠☁️NF	5 sets, 20 rules; ANFIS	~500	32	10k	Backprop	Fuzzy	446	1993	Jang (ANFIS)	Learned membership	Hybrid; moderate complexity	Interpretable + flexible
📚PNN	Lateral columns; max 10	~2500	2048	0	Entropy	Cont. 119-dim	446	2016	Rusu, Rabinowitz, Desjardins et al. (DeepMind)	No forgetting	Sequential; column growth	Continual learning
👑PPO👑	446→512→256→7 heads→119	2500	2048	0	Entropy H	Cont. 119-dim	446	2017	Schulman, Wolski, Dhariwal, Radford, Klimov (OpenAI)	Stable; clip prevents large updates	On-policy; sample reuse limited	Default for continuous control
🐝PSO	50 particles; no NN	1000 iter	50	50	Inertia	Cont. 119-dim	446	1995	Kennedy & Eberhart	Best evo cost; swarm	Local optima; no policy	Swarm optimization
🌡️SAC	Actor+2×Q(446→256→256→1)	~3000	256	1M	Max-entropy α	Cont. 119-dim	446	2018	Haarnoja, Zhou, Abbeel, Levine (Berkeley)	Highest reward; auto α	Slightly higher cost; more exploratory	Sample-efficient continuous
🔀TD3	Actor+2×Q(446→256→256→1)	~3000	256	1M	Target policy noise	Cont. 119-dim	446	2018	Fujimoto, van Hoof, Meger (McGill)	Twin Q; low RL cost	Deterministic; less exploratory	Off-policy cost-optimal

💡 Click a row to expand parameters, notation & equations · Architecture = network layers or population config · State dim = 446 for all

RL Models Overview

All 13 optimization algorithms used in the project are described below. Each entry includes: simple summary → detailed explanation → equations with parameters → project adaptation (how the model is used) → methodological rationale (defense-ready).

Shared reward (all algorithms):

R = Σ wᵢ · Rᵢ (8 objectives, weights sum to 1.0)

renewable share(0.25) · capacity growth(0.2) · cost efficiency(0.25) · emission reduction(0.15) · grid stability(0.1) · investment balance(0.03) · import dependency(0.01) · energy efficiency(0.01)

Primary Models (PPO / MARL)

PPO (Proximal Policy Optimization)#1 · $226.79B · 97.34% renewable · 14.3 Mt CO₂

Simple: Policy-gradient method with clipped surrogate objective; hierarchical policy over 446-dim state, 119-dim action. Best cost ($226.79B) among 13 algorithms.

Detailed: PPO (Schulman et al., 2017) optimizes a clipped surrogate objective L_CLIP to prevent large policy updates. Uses Generalized Advantage Estimation (GAE) for variance reduction. Hierarchical policy network: shared feature extractor (446→512→256) with category heads (solar, wind, hydro, geothermal, biomass, battery, hybrid), resource-class, scale, and scenario heads. Actor outputs Tanh-bounded actions; critic estimates V(s). Same TurkeyEnergyTransitionEnv (26-year horizon, 8-objective reward) as all algorithms. ANOVA F=87.34, p<0.001; Tukey HSD confirms PPO in top group.

Equations

Clipped surrogate objective

L^{CLIP} (θ) = E_{t} [min (r_{t} (θ) \hat{A}_{t}, clip (r_{t} (θ), 1 - ε, 1 + ε) \hat{A}_{t})]

r_t = π_θ(a|s)/π_θ_old(a|s) is probability ratio; clip prevents updates >±20%. ε=0.2. Stabilizes training vs vanilla policy gradient.

GAE (Generalized Advantage Estimation)

\hat{A}_{t} = l = 0 \sum \infty (γ λ)^{l} δ_{t + l}, δ_{t} = r_{t} + γ V (s_{t + 1}) - V (s_{t})

λ=0.95 balances bias-variance; γ=0.99 discount. GAE reduces variance of advantage estimates for policy gradient.

Total loss

L = L^{CLIP} - c_{1} L^{VF} + c_{2} H [π_{θ}]

Value loss L^VF (MSE); entropy bonus H for exploration. c_1=0.5, c_2=0.01. Project: 2500 episodes to convergence.

Reward (shared)

R = i \sum w_{i} R_{i}, \sum w_{i} = 1

8 objectives: renewable_share (0.25), capacity_growth (0.20), cost_efficiency (0.25), emission_reduction (0.15), grid_stability (0.10), investment_balance (0.03), import_dependency (0.01), energy_efficiency (0.01).

Parameter definitions (project)

ε(—)

PPO clip range

0.2

γ(—)

Discount factor

0.99

λ(—)

GAE lambda

0.95

c_1(—)

Value loss coefficient

0.5

c_2(—)

Entropy coefficient

0.01

Notation

r_t: Probability ratio; Â_t: GAE advantage; V: Value function

Project Adaptation

Project use: PRIMARY algorithm. Best cost $226.79B, 97.34% renewable, 90.6% CO₂ reduction. Hierarchical policy: Input(446)→Dense(512)→Dense(256)→7 category heads + context heads→Output(119). 2500 episodes; ~20h on 8×A100. 100% constraint satisfaction. Used for: (1) Results pathway, (2) policy scenario analysis, (3) RL comparison baseline.

Methodological Rationale

PPO was adopted as the primary RL algorithm because it achieves the best cost ($226.79B) among 13 algorithms while satisfying all constraints (97.34% renewable, 90.6% CO₂ reduction, 100% success). The clipped objective provides stable training; hierarchical policy design matches the 7-region, 26-technology action space. ANOVA (F=87.34, p<0.001) and Tukey HSD confirm statistical significance. In defense, we emphasize: (1) sample efficiency vs single-agent baselines, (2) interpretable hierarchical action structure, (3) reproducibility across runs.

MARL (Multi-Agent RL / MAPPO)#2 · $230.62B · 97.82% renewable · 13.8 Mt CO₂

Simple: CTDE: Centralized Training, Decentralized Execution. 7 regional agents; global critic V(s₁,…,s₇,a₁,…,a₇); local policies π_i(a_i|s_i). Highest avg reward (5123.87).

Detailed: MAPPO extends PPO to multi-agent setting. Training: global critic observes all 7 regions (Marmara, Aegean, Mediterranean, Central Anatolia, Black Sea, Eastern Anatolia, SE Anatolia) for coordination. Execution: each region acts locally with π_i(a_i|s_i); no communication overhead. Shared value function enables credit assignment. 4.2× sample efficiency vs single-agent PPO. Same reward and environment; 7×119-dim joint action (each agent 119-dim).

Equations

Centralized critic

V (s_{1}, \dots, s_{7}, a_{1}, \dots, a_{7})

Global value function observes all regional states and actions. Enables coordination learning during training.

Decentralized policy

π_{i} (a_{i} ∣ s_{i})

Each region i has local policy. At execution, only s_i needed; scalable deployment.

PPO objective (per agent)

L_{i}^{CLIP}

Same clipped objective as PPO; each agent updates with shared advantage from global critic.

Parameter definitions (project)

n_agents(—)

Number of regional agents

ε(—)

PPO clip range (same as PPO)

0.2

γ(—)

Discount factor

0.99

Notation

CTDE: Centralized Training, Decentralized Execution; 7 regions

Project Adaptation

Project use: Multi-agent variant. Best renewable (97.82%), highest avg reward (5123.87). Cost $230.62B. 7 regional agents; Actor(446→512→256→128→119), Critic(446→512→256→1). 4.2× faster convergence than single-agent PPO. Validates CTDE for energy portfolio optimization.

Methodological Rationale

MAPPO was included to validate multi-agent coordination for Turkey's 7 regions. CTDE allows learning coordinated strategies (e.g. regional specialization) while maintaining decentralized execution. Highest average reward (5123.87) indicates effective coordination. Slightly higher cost than PPO ($230.62B vs $226.79B) may reflect more diversified portfolios. In defense, we present MAPPO as evidence that multi-agent design is viable for energy transition; PPO remains primary for cost-optimal pathway.

RL Algorithms

SAC (Soft Actor-Critic)#3 · $230.70B · 97.82% renewable · 14.9 Mt CO₂

Simple: Maximum-entropy RL; actor-critic with automatic temperature tuning. Off-policy; replay buffer. Highest reward (5271.36) among all algorithms.

DQN (Deep Q-Network)$222.36B · 97.69% renewable · 14.2 Mt CO₂

Simple: Value-based; Q(s,a) approximation with experience replay and target network. Discrete action space via discretization of 119-dim continuous.

A3C (Asynchronous Advantage Actor-Critic)$190.36B · 97.82% renewable · 13.0 Mt CO₂

Simple: Asynchronous parallel workers; each updates shared policy with local gradients. Advantage actor-critic; no replay buffer.

TD3 (Twin Delayed DDPG)$197.43B · 97.34% renewable · 13.3 Mt CO₂

Simple: Actor-critic for continuous action; twin Q-networks, delayed policy updates, target policy smoothing. Off-policy.

Evolutionary

GA (Genetic Algorithm)$223.80B · 97.28% renewable · 14.1 Mt CO₂

Simple: Population-based; selection, crossover, mutation. Each individual = 119-dim action sequence. Fitness = episode reward.

PSO (Particle Swarm Optimization)$206.46B · 97.77% renewable · 14.2 Mt CO₂

Simple: Swarm of particles; each has position (action) and velocity. Updates toward personal best and global best. Adaptive inertia.

DE (Differential Evolution)$202.95B · 97.28% renewable · 12.2 Mt CO₂

Simple: Mutation via difference vectors; binomial crossover. rand/1/bin strategy. Population 50, 1000 generations.

Fuzzy Systems

Fuzzy Q-Learning$217.58B · 97.21% renewable · 13.5 Mt CO₂

Simple: Fuzzy state discretization; Q-values per fuzzy rule. Combines fuzzy logic (interpretability) with Q-learning (adaptation).

Neuro-Fuzzy Systems$221.86B · 97.21% renewable · 13.7 Mt CO₂

Simple: Neural network learns fuzzy membership and rule consequents. Combines NN flexibility with fuzzy interpretability.

Multi-Agent

MARL (Multi-Agent RL / MAPPO)#2 · $230.62B · 97.82% renewable · 13.8 Mt CO₂

Simple: CTDE: Centralized Training, Decentralized Execution. 7 regional agents; global critic V(s₁,…,s₇,a₁,…,a₇); local policies π_i(a_i|s_i). Highest avg reward (5123.87).

Meta-Learning

MAML (Model-Agnostic Meta-Learning)$219.83B · 97.21% renewable · 13.6 Mt CO₂

Simple: Learn initialization θ that adapts quickly to new tasks. Inner loop: few gradient steps on task; outer loop: meta-update.

Progressive Neural Networks$221.95B · 97.21% renewable · 13.7 Mt CO₂

Simple: Lateral connections from previous task columns to new column. Prevents catastrophic forgetting; transfer from prior tasks.

Methodology Overview → · RL Comparison →