Double DQN vs Dueling DQN

#deep q-networks #double dqn #dueling dqn #q-learning #reinforcement learning #deep learning #neural networks #machine learning #python #optimization algorithms

1. Core Concepts of Q-Learning

Core Concepts of Q-Learning

Markov Decision Processes (MDPs)

Q-Learning operates within the framework of Markov Decision Processes (MDPs), which formalize sequential decision-making problems. An MDP is defined by the tuple (S, A, P, R, γ), where:

S is the state space,
A is the action space,
P(s'|s, a) is the transition probability function,
R(s, a, s') is the reward function,
γ ∈ [0, 1] is the discount factor.

The Markov property implies that future states depend only on the current state and action, not the history.

$$ P(s_{t+1} | s_t, a_t) = P(s_{t+1} | s_t, a_t, s_{t-1}, a_{t-1}, ...) $$

Q-Function and Bellman Equation

The Q-function Q(s, a) represents the expected cumulative reward when taking action a in state s and following the optimal policy thereafter. It satisfies the Bellman optimality equation:

$$ Q^*(s, a) = \mathbb{E}_{s'} \left[ R(s, a, s') + \gamma \max_{a'} Q^*(s', a') \right] $$

This recursive relationship forms the basis of Q-Learning, where the agent iteratively updates its Q-value estimates using temporal difference (TD) learning.

Temporal Difference Learning

Q-Learning is a model-free, off-policy TD algorithm. The update rule for the Q-value at each time step is:

$$ Q(s_t, a_t) \leftarrow Q(s_t, a_t) + \alpha \left[ r_{t+1} + \gamma \max_{a} Q(s_{t+1}, a) - Q(s_t, a_t) \right] $$

where α is the learning rate. The term in brackets is the TD error, representing the difference between the current Q-value estimate and the target value.

Exploration vs Exploitation

Balancing exploration and exploitation is critical in Q-Learning. Common strategies include:

ε-greedy: Select random actions with probability ε, otherwise choose the action with highest Q-value.
Boltzmann exploration: Select actions probabilistically based on a softmax distribution of Q-values.
Optimistic initialization: Initialize Q-values to encourage early exploration.

The choice of exploration strategy significantly impacts convergence properties.

Function Approximation

For large state spaces, Q-values are typically approximated using parameterized functions Q(s, a; θ), where θ are learnable parameters. Deep Q-Networks (DQNs) use neural networks for this approximation, enabling generalization across states. The loss function for training is:

$$ L(\theta) = \mathbb{E}_{(s,a,r,s')} \left[ \left( r + \gamma \max_{a'} Q(s', a'; \theta^-) - Q(s, a; \theta) \right)^2 \right] $$

where θ^- are the parameters of a target network, periodically updated to stabilize training.

Convergence Guarantees

Under the following conditions, Q-Learning with table-lookup representation converges to the optimal Q-function:

All state-action pairs are visited infinitely often,
The learning rate satisfies the Robbins-Monro conditions: ∑α = ∞ and ∑α² < ∞,
The MDP is finite and fully observable.

These conditions are relaxed in deep reinforcement learning, where convergence is not guaranteed but empirical success is common.

1.2 Deep Q-Networks: Architecture and Training

Core Architecture

The Deep Q-Network (DQN) extends traditional Q-learning by replacing the tabular Q-value representation with a deep neural network. The network approximates the action-value function Q(s, a; θ), where θ represents the trainable parameters. The input layer processes the state s, followed by multiple fully connected hidden layers with ReLU activations, culminating in an output layer with nodes corresponding to possible actions.

$$ Q(s, a; θ) ≈ Q^*(s, a) $$

Key architectural innovations in DQN include:

Frame stacking: The network takes a sequence of preprocessed frames (typically 4) as input to capture temporal dependencies.
Dimensionality reduction: Convolutional layers are often used for image-based states to extract spatial features before the fully connected layers.
Dueling variant: Later architectures split the network into separate value and advantage streams, which we'll explore in subsequent sections.

Training Algorithm

The DQN training process combines Q-learning with experience replay and target networks. The loss function for a minibatch of transitions (s, a, r, s') is:

$$ L(θ) = \mathbb{E}_{(s,a,r,s')∼D}\left[\left(r + γ \max_{a'} Q(s', a'; θ^-) - Q(s, a; θ)\right)^2\right] $$

Where θ^- represents the parameters of the target network, which are periodically synchronized with the online network. The training proceeds through these key steps:

Store transitions (s, a, r, s') in replay buffer D
Sample random minibatches from D to break temporal correlations
Compute target values using the target network
Update online network parameters via gradient descent on the loss
Periodically update target network parameters: θ^- ← θ

Stabilization Techniques

Several critical innovations enable stable training of deep RL agents:

Experience Replay

The replay buffer stores transitions (s, a, r, s', done), allowing the agent to learn from past experiences multiple times. This:

Breaks temporal correlations between consecutive samples
Enables more efficient data usage
Allows prioritized replay based on TD-error magnitude

Target Networks

A separate target network with parameters θ^- provides stable Q-value targets during training. The target network is updated either:

Periodically: Full replacement every C steps
Soft updates: Polyak averaging: θ^- ← τθ + (1-τ)θ^-

$$ θ^- ← τθ + (1-τ)θ^- \quad \text{where} \quad τ ≪ 1 $$

Hyperparameter Considerations

Critical hyperparameters that affect DQN performance include:

Parameter	Typical Value	Effect
Replay buffer size	10⁵ - 10⁶	Larger buffers increase diversity but may slow learning
Minibatch size	32 - 512	Larger batches stabilize gradients but increase memory
Discount factor (γ)	0.99 - 0.999	Higher values emphasize long-term rewards
Target update (τ or C)	τ=0.001 or C=10⁴	More frequent updates reduce stability

Practical Implementation Challenges

Real-world DQN implementations must address:

Partial observability: Frame stacking helps but may require LSTM layers for long-term dependencies
Reward scaling: Normalization or clipping is often necessary across different environments
Exploration: ε-greedy with linear decay is common, but more sophisticated methods like NoisyNets can be beneficial
Overestimation bias: Addressed in Double DQN by decoupling action selection and evaluation

Deep Q-Networks: Architecture and Training – Double DQN vs Dueling DQN – Tutorial Diagram

Diagram Description: The diagram would show the architecture of a DQN with frame stacking, convolutional layers, and fully connected layers, including the separation into value and advantage streams in the dueling variant.

1.3 Challenges in Vanilla DQN

Vanilla Deep Q-Networks (DQN) introduced a breakthrough in reinforcement learning by combining Q-learning with deep neural networks. However, several fundamental challenges limit its performance, particularly in complex environments. These issues stem from the inherent properties of the Q-learning update rule and the interaction between the neural network and the reinforcement learning process.

Overestimation Bias

The Q-learning update rule in vanilla DQN uses the maximum estimated Q-value for the next state to compute the target value:

$$ y = r + \gamma \max_{a'} Q(s', a'; \theta^-) $$

This maximization step introduces a positive bias because the same Q-network selects and evaluates actions. Errors in Q-value estimates are systematically amplified, leading to overoptimistic value estimates. Thrun and Schwartz (1993) first proved this overestimation bias theoretically, and later work by van Hasselt et al. (2015) quantified its impact in deep reinforcement learning settings.

High Variance in Updates

The temporal difference (TD) targets in DQN exhibit high variance because:

Single transitions are used for updates rather than averaged estimates
The bootstrapping process propagates and amplifies estimation errors
The max operator in the target computation increases sensitivity to outliers

This variance makes learning unstable, particularly in environments with sparse rewards or long time horizons. The problem compounds as the network's initial random weights produce noisy Q-values that affect subsequent updates.

Slow Credit Assignment

Vanilla DQN struggles with temporal credit assignment in several scenarios:

Delayed rewards: The single-step update makes it difficult to associate actions with rewards that occur many steps later
Action sequences: The lack of explicit planning for action sequences requires the network to implicitly learn these relationships through many samples
State aliasing: Perceptually similar states with different optimal actions confuse the network's representation

These issues manifest as poor sample efficiency and the need for extensive experience replay to learn effective policies.

Catastrophic Forgetting

Even with experience replay, vanilla DQN suffers from catastrophic forgetting when:

The distribution of states in the replay buffer shifts significantly
The network overwrites previously learned Q-values when learning new ones
Important but rare transitions are overwritten in the replay buffer

This becomes particularly problematic in non-stationary environments or when the exploration strategy changes substantially during training.

Representational Limitations

The standard DQN architecture makes several implicit assumptions that limit its flexibility:

Monolithic Q-values: The network outputs a single Q-value per action without decomposing state value and action advantages
Fixed architecture: The same network structure is used regardless of the environment's specific requirements
State-action coupling: Changes to the action space require complete retraining of the network

These architectural constraints make vanilla DQN less adaptable to environments where different parts of the state space require different representational capacities or where the action space changes dynamically.

2. Overestimation Bias in Q-Learning

2.1 Overestimation Bias in Q-Learning

Overestimation bias is a well-documented phenomenon in Q-learning, where the learned action-value function systematically overestimates the true expected returns. This occurs due to the maximization step in the Q-learning update rule:

$$ Q(s_t, a_t) \leftarrow Q(s_t, a_t) + \alpha \left[ r_{t+1} + \gamma \max_{a} Q(s_{t+1}, a) - Q(s_t, a_t) \right] $$

The bias arises because the same Q-values are used both to select and evaluate actions. When noisy estimates are present, the max operator tends to select overestimated values, propagating errors through the learning process. Thrun and Schwartz (1993) first proved that this leads to an upward bias in the value estimates, which can destabilize learning and yield suboptimal policies.

Mathematical Derivation of the Bias

Let the true Q-value be $ Q^*(s, a) $, and the estimated Q-value be $ Q(s, a) = Q^*(s, a) + \epsilon(s, a) $, where $ \epsilon(s, a) $ is a zero-mean random noise term. The expected overestimation error $ \mathbb{E}[\max_a Q(s, a) - \max_a Q^*(s, a)] $ can be derived as follows:

$$ \mathbb{E}[\max_a Q(s, a)] = \mathbb{E}[\max_a (Q^*(s, a) + \epsilon(s, a))] $$

For a discrete action space with $ |A| $ actions, if the noise terms $ \epsilon(s, a) $ are independent and identically distributed, the expected overestimation grows with the number of actions:

$$ \mathbb{E}[\max_a Q(s, a) - \max_a Q^*(s, a)] \propto \sqrt{\frac{2 \ln |A|}{\sigma^{-2}}} $$

Empirical Consequences

In practice, overestimation bias manifests as:

Suboptimal policy convergence: The agent may prefer actions with overestimated values, even if they yield lower actual returns.
Training instability: Large overestimations can cause divergent learning dynamics, especially in high-dimensional or noisy environments.
Delayed convergence: The bias introduces additional variance, requiring more samples to achieve accurate value estimates.

Double Q-Learning as a Solution

Double Q-learning (van Hasselt, 2010) decouples action selection from evaluation by maintaining two Q-functions, $ Q_1 $ and $ Q_2 $. The update rule alternates between them:

$$ Q_1(s_t, a_t) \leftarrow Q_1(s_t, a_t) + \alpha \left[ r_{t+1} + \gamma Q_2 \left( s_{t+1}, \arg\max_a Q_1(s_{t+1}, a) \right) - Q_1(s_t, a_t) \right] $$

This reduces bias because the maximizing action is chosen using $ Q_1 $, while its value is estimated using $ Q_2 $, breaking the positive feedback loop of overestimation.

Visualizing the Bias

In a simple gridworld environment, the overestimation error can be visualized by comparing standard Q-learning and Double Q-learning value estimates. Standard Q-learning typically shows higher value estimates across states, particularly in regions with sparse rewards, while Double Q-learning remains closer to the ground truth.

Overestimation Bias in Q-Learning – Double DQN vs Dueling DQN – Tutorial Diagram

Diagram Description: The diagram would show a side-by-side comparison of standard Q-learning and Double Q-learning value estimates across states in a gridworld environment, highlighting the overestimation bias.

2.2 Double Q-Learning and Its Extension to DQN

Traditional Q-learning suffers from overestimation bias due to the maximization step in the Bellman update. This bias arises because the same Q-network is used to select and evaluate actions, leading to upwardly skewed value estimates. Double Q-learning, introduced by van Hasselt (2010), mitigates this by decoupling action selection from evaluation.

Mathematical Formulation of Double Q-Learning

The standard Q-learning update is given by:

$$ Q(s_t, a_t) \leftarrow Q(s_t, a_t) + \alpha \left[ r_{t+1} + \gamma \max_{a} Q(s_{t+1}, a) - Q(s_t, a_t) \right] $$

Double Q-learning maintains two separate value functions, $ Q^A $ and $ Q^B $, and alternates between them for selection and evaluation:

$$ Q^A(s_t, a_t) \leftarrow Q^A(s_t, a_t) + \alpha \left[ r_{t+1} + \gamma Q^B \left( s_{t+1}, \underset{a}{\arg\max} Q^A(s_{t+1}, a) \right) - Q^A(s_t, a_t) \right] $$

This decoupling reduces overestimation by ensuring that the action selection and value estimation are performed using different networks.

Extension to Deep Q-Networks (Double DQN)

Double DQN (van Hasselt et al., 2016) adapts this idea to deep reinforcement learning by using the online network for action selection and the target network for evaluation:

$$ y_t = r_{t+1} + \gamma Q_{\theta^-} \left( s_{t+1}, \underset{a}{\arg\max} Q_\theta(s_{t+1}, a) \right) $$

where $ Q_\theta $ is the online network and $ Q_{\theta^-} $ is the target network. This modification is computationally efficient since it reuses the existing target network architecture of DQN rather than training two separate networks.

Practical Implications and Performance

Empirical results demonstrate that Double DQN significantly reduces overestimation bias across various Atari 2600 games while maintaining the sample efficiency of DQN. The improvement is particularly notable in environments where:

The action space contains many similar-valued actions
The reward structure is sparse or delayed
The state space contains many aliased states

The algorithm's effectiveness stems from its ability to provide more accurate value estimates without additional computational overhead beyond standard DQN. This makes it particularly suitable for real-world applications where training data may be limited or expensive to acquire.

Implementation Considerations

When implementing Double DQN, several practical aspects require attention:

The target network update frequency should balance stability with responsiveness
The experience replay buffer size must be sufficiently large to decorrelate updates
Network architecture choices (e.g., dueling networks) can be combined with Double DQN for further improvements

# PyTorch implementation of Double DQN update
def compute_double_dqn_loss(self, batch):
    states, actions, rewards, next_states, dones = batch
    
    # Current Q values for chosen actions
    current_q = self.q_net(states).gather(1, actions)
    
    # Double DQN: argmax using online net, evaluation using target net
    next_actions = self.q_net(next_states).argmax(1, keepdim=True)
    next_q = self.target_net(next_states).gather(1, next_actions)
    
    # Target Q values
    target_q = rewards + (1 - dones) * self.gamma * next_q
    
    # Huber loss
    loss = F.smooth_l1_loss(current_q, target_q)
    return loss

2.3 Practical Implementation of Double DQN

The Double Deep Q-Network (Double DQN) algorithm addresses the overestimation bias inherent in traditional DQN by decoupling action selection from action evaluation. This section provides a step-by-step guide to implementing Double DQN, covering key components such as network architecture, loss computation, and training dynamics.

Network Architecture

Double DQN employs two neural networks: the online network (with parameters θ) and the target network (with parameters θ⁻). The online network is updated at every training step, while the target network is periodically synchronized with the online network to stabilize training. The architecture typically consists of:

Input layer: State dimensionality matches the environment's observation space.
Hidden layers: Two or three fully connected layers with ReLU activation.
Output layer: Linear activation with dimensionality equal to the action space.

Loss Function Derivation

The Double DQN loss function modifies the standard DQN update by using the online network to select actions while evaluating them using the target network. The target value y is computed as:

$$ y = r + \gamma Q(s', \argmax_{a'} Q(s', a'; \theta); \theta⁻) $$

where:

r is the immediate reward
γ is the discount factor
s' is the next state
θ and θ⁻ represent online and target network parameters respectively

The loss function for a minibatch of transitions (s, a, r, s') is then:

$$ L(\theta) = \mathbb{E}_{(s,a,r,s') \sim D} \left[ (y - Q(s,a;\theta))^2 \right] $$

Training Algorithm

The complete Double DQN training procedure involves these key steps:

Initialize online network Q with random weights θ
Initialize target network Q⁻ with weights θ⁻ = θ
Initialize replay buffer D with capacity N
For each episode:
- Observe initial state s
- For each timestep:
  1. Select action a using ε-greedy policy based on Q(s,·;θ)
  2. Execute a, observe r and s'
  3. Store transition (s,a,r,s') in D
  4. Sample random minibatch from D
  5. Compute target values using Double DQN update rule
  6. Perform gradient descent step on L(θ)
  7. Every C steps: θ⁻ ← θ

Hyperparameter Considerations

Key hyperparameters and their typical ranges:

Learning rate: 1e-4 to 1e-3 (Adam optimizer works well)
Discount factor (γ): 0.95 to 0.99
Target network update frequency (C): 1000 to 10000 steps
Replay buffer size: 1e5 to 1e6 transitions
Minibatch size: 32 to 128
ε-greedy: Start at 1.0, decay to 0.01 or 0.1 over training

Implementation in PyTorch

import torch
import torch.nn as nn
import torch.optim as optim
import numpy as np
from collections import deque
import random

class DQN(nn.Module):
    def __init__(self, state_dim, action_dim):
        super(DQN, self).__init__()
        self.fc1 = nn.Linear(state_dim, 64)
        self.fc2 = nn.Linear(64, 64)
        self.fc3 = nn.Linear(64, action_dim)
        
    def forward(self, x):
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        return self.fc3(x)

class DoubleDQNAgent:
    def __init__(self, state_dim, action_dim):
        self.online_net = DQN(state_dim, action_dim)
        self.target_net = DQN(state_dim, action_dim)
        self.target_net.load_state_dict(self.online_net.state_dict())
        self.optimizer = optim.Adam(self.online_net.parameters(), lr=1e-3)
        self.memory = deque(maxlen=100000)
        self.batch_size = 64
        self.gamma = 0.99
        self.epsilon = 1.0
        self.epsilon_min = 0.01
        self.epsilon_decay = 0.995
        self.update_freq = 1000
        self.steps = 0
        
    def act(self, state):
        if np.random.rand() <= self.epsilon:
            return np.random.randint(self.action_dim)
        state = torch.FloatTensor(state)
        q_values = self.online_net(state)
        return torch.argmax(q_values).item()
    
    def train(self):
        if len(self.memory) < self.batch_size:
            return
        
        batch = random.sample(self.memory, self.batch_size)
        states = torch.FloatTensor(np.array([t[0] for t in batch]))
        actions = torch.LongTensor(np.array([t[1] for t in batch]))
        rewards = torch.FloatTensor(np.array([t[2] for t in batch]))
        next_states = torch.FloatTensor(np.array([t[3] for t in batch]))
        dones = torch.FloatTensor(np.array([t[4] for t in batch]))
        
        # Double DQN update
        current_q = self.online_net(states).gather(1, actions.unsqueeze(1))
        next_actions = self.online_net(next_states).argmax(1)
        next_q = self.target_net(next_states).gather(1, next_actions.unsqueeze(1))
        target_q = rewards + (1 - dones) * self.gamma * next_q
        
        loss = nn.MSELoss()(current_q, target_q.detach())
        self.optimizer.zero_grad()
        loss.backward()
        self.optimizer.step()
        
        # Update target network
        if self.steps % self.update_freq == 0:
            self.target_net.load_state_dict(self.online_net.state_dict())
            
        self.steps += 1
        self.epsilon = max(self.epsilon_min, self.epsilon * self.epsilon_decay)

Practical Considerations

When implementing Double DQN in real-world scenarios:

State normalization: Scale inputs to [-1, 1] or use batch normalization for stability
Gradient clipping: Clip gradients to prevent explosion (typical norm of 10)
Prioritized experience replay: Can significantly improve sample efficiency
Frame stacking: For visual inputs, stack multiple frames to capture temporal information
Hardware acceleration: Utilize GPUs for faster training, especially for large networks

Practical Implementation of Double DQN – Double DQN vs Dueling DQN – Tutorial Diagram

Diagram Description: The diagram would show the dual-network architecture of Double DQN with clear separation between online and target networks, their interactions during action selection/evaluation, and the flow of data through the system.

2.4 Performance Comparison with Vanilla DQN

Empirical Performance Metrics

Vanilla DQN, while foundational, suffers from well-documented limitations such as overestimation bias and inefficient credit assignment. Double DQN (DDQN) mitigates overestimation by decoupling action selection and evaluation, while Dueling DQN improves value function approximation by separating state-value and advantage streams. Empirical comparisons typically measure:

Sample efficiency: Convergence speed in terms of training episodes.
Final performance: Average reward over the last 100 episodes.
Stability: Variance in rewards during training.

Quantitative Results in Benchmark Environments

In the Atari 2600 benchmark (e.g., Pong, Breakout), DDQN reduces the overestimation error by 30–50% compared to Vanilla DQN, quantified by the metric:

$$ \text{Overestimation Error} = \mathbb{E}\left[\max_a Q(s,a) - Q^*(s,a)\right] $$

Dueling DQN, meanwhile, achieves 15–25% higher final scores by better generalizing across actions, as its architecture enforces:

$$ Q(s,a) = V(s) + \left(A(s,a) - \frac{1}{|\mathcal{A}|}\sum_{a'} A(s,a')\right) $$

Training Dynamics and Robustness

DDQN’s primary advantage is stability in sparse-reward environments, where Vanilla DQN often diverges due to overoptimistic Q-values. Dueling DQN excels in environments with large action spaces (e.g., Montezuma’s Revenge), as the advantage stream focuses learning on critical actions. The following trends are observed:

DDQN: 20–40% faster convergence in deterministic environments.
Dueling DQN: 10–30% higher robustness to stochastic transitions.

Computational Overhead

Both variants introduce minimal computational overhead. DDQN requires a second network for target Q-value estimation, increasing memory by ~50%. Dueling DQN’s two-stream architecture adds < 10% more parameters than Vanilla DQN, as the final layer combines:

$$ \text{Parameters}_{\text{Dueling}} = \text{Parameters}_{\text{Base}} + |\mathcal{A}| + 1 $$

Case Study: Atari Seaquest

In Seaquest, Vanilla DQN plateaus at ~1,500 points, while DDQN and Dueling DQN reach ~2,100 and ~2,400 points, respectively. The hybrid Dueling DDQN achieves ~2,700 points, demonstrating complementary benefits:

DDQN corrects overestimation during exploration.
Dueling DQN improves action selection in complex states (e.g., oxygen management).

3. Value and Advantage Functions in RL

3.1 Value and Advantage Functions in RL

Value functions and advantage functions form the backbone of many reinforcement learning algorithms, particularly in value-based methods like DQN and its variants. The state-value function $ V^{\pi}(s) $ estimates the expected cumulative reward when starting in state $ s $ and following policy $ \pi $:

$$ V^{\pi}(s) = \mathbb{E}_{\pi}\left[ \sum_{k=0}^{\infty} \gamma^k r_{t+k} \mid s_t = s \right] $$

Similarly, the action-value function $ Q^{\pi}(s, a) $ extends this notion by accounting for the expected return when taking action $ a $ in state $ s $ and subsequently following $ \pi $:

$$ Q^{\pi}(s, a) = \mathbb{E}_{\pi}\left[ \sum_{k=0}^{\infty} \gamma^k r_{t+k} \mid s_t = s, a_t = a \right] $$

The advantage function $ A^{\pi}(s, a) $ measures the relative benefit of taking action $ a $ over the policy's default behavior, defined as:

$$ A^{\pi}(s, a) = Q^{\pi}(s, a) - V^{\pi}(s) $$

Interpretation and Practical Utility

Advantage functions resolve a critical limitation of pure Q-learning: they decouple the estimation of state-dependent baseline values ($ V^{\pi}(s) $) from the action-specific advantages. This separation:

Reduces variance in gradient estimates during policy optimization.
Enables more efficient credit assignment by highlighting which actions outperform the policy's average behavior.
Facilitates better generalization across similar states in high-dimensional spaces.

Connection to Dueling DQN Architecture

The dueling network architecture explicitly leverages this decomposition by using separate streams to estimate $ V(s) $ and $ A(s,a) $, combining them via a special aggregator:

$$ Q(s,a) = V(s) + \left( A(s,a) - \frac{1}{|\mathcal{A}|} \sum_{a'} A(s,a') \right) $$

This forced identification (subtracting the mean advantage) maintains the theoretical consistency $ \mathbb{E}_{a \sim \pi}[A(s,a)] = 0 $ while improving optimization stability. The architecture's empirical success in Atari benchmarks demonstrates how advantage-aware learning can outperform monolithic Q-value estimation.

Mathematical Derivation of Advantage Policy Gradients

Consider the policy gradient theorem with advantage estimates. The gradient of the expected return $ J(\theta) $ becomes:

$$ \nabla_\theta J(\theta) = \mathbb{E}_{\pi_\theta} \left[ \nabla_\theta \log \pi_\theta(a|s) A^{\pi_\theta}(s,a) \right] $$

Substituting the Q-value decomposition:

$$ = \mathbb{E}_{\pi_\theta} \left[ \nabla_\theta \log \pi_\theta(a|s) \left( Q^{\pi_\theta}(s,a) - V^{\pi_\theta}(s) \right) \right] $$

The baseline $ V^{\pi_\theta}(s) $ leaves the expectation unchanged because:

$$ \mathbb{E}_{\pi_\theta} \left[ \nabla_\theta \log \pi_\theta(a|s) V^{\pi_\theta}(s) \right] = 0 $$

This zero-expectation property holds since $ V^{\pi_\theta}(s) $ doesn't depend on the action $ a $, and the expectation of the score function is zero. The derivation confirms why advantage-based methods achieve lower variance than pure Q-value gradients.

Value and Advantage Functions in RL – Double DQN vs Dueling DQN – Tutorial Diagram

Diagram Description: The diagram would show the decomposition of Q-values into state-value and advantage streams in Dueling DQN, illustrating how they combine via the aggregator.

3.2 Dueling Network Architecture

The dueling network architecture introduces a novel way to decompose the state-action value function Q(s, a) into two separate streams: the state value function V(s) and the advantage function A(s, a). This decomposition allows the network to learn which states are valuable without needing to evaluate the effect of each action in those states, leading to more efficient policy evaluation.

Mathematical Formulation

The dueling architecture computes Q(s, a) as:

$$ Q(s, a; \theta, \alpha, \beta) = V(s; \theta, \beta) + \left( A(s, a; \theta, \alpha) - \frac{1}{|\mathcal{A}|} \sum_{a'} A(s, a'; \theta, \alpha) \right) $$

Here, θ represents the shared parameters of the convolutional layers, while α and β are the parameters of the advantage and value streams, respectively. The subtraction of the mean advantage ensures identifiability and prevents the network from simply increasing both V(s) and A(s, a) without meaningful separation.

Architecture Design

The network splits into two streams after the final convolutional layer:

Value Stream: Estimates V(s), representing how good it is to be in a particular state regardless of the action.

Advantage Stream: Estimates A(s, a), representing how much better a specific action is compared to others in that state.

This separation allows the agent to efficiently learn state values while still maintaining the flexibility to evaluate actions. The architecture is particularly useful in environments where many actions have identical or negligible effects on the state value.

Practical Advantages

The dueling architecture provides several key benefits:

Improved Generalization: By separating state and action evaluations, the network can generalize better across similar states.

Robustness to Irrelevant Actions: In states where most actions yield similar returns, the advantage stream can focus on meaningful distinctions.

Faster Convergence: The value stream stabilizes learning by providing a baseline, reducing variance in updates.

Implementation Considerations

When implementing a dueling DQN, the following design choices are critical:

Aggregation Method: The mean subtraction in the advantage stream ensures stable training, but alternatives like max subtraction (A(s, a) - max_{a'} A(s, a')) have also been explored.

Shared Features: Early layers should be shared between streams to maintain computational efficiency.

Initialization: The final layers of both streams should be initialized carefully to avoid initial bias toward either component.

Empirical results show that dueling architectures often outperform standard DQNs, particularly in environments with large action spaces or where state values dominate action advantages.

Diagram Description: The diagram would physically show the network architecture split into value and advantage streams after the shared convolutional layers, illustrating the flow of data and the separation of functions.

3.3 Training and Optimization Techniques

Target Network Updates in Double DQN

Double DQN decouples action selection from value estimation by using two separate networks: the online network Q_θ and the target network Q_θ'. The target network is updated periodically by either:

Hard updates: Full parameter synchronization θ' ← θ every N steps

Soft updates: Exponential moving average: θ' ← τθ + (1-τ)θ' where τ ≪ 1

$$ y^{\text{DoubleDQN}} = r + \gamma Q_{\theta'}(s', \underset{a}{\text{argmax}} Q_\theta(s', a)) $$

This reduces overestimation bias by preventing the same network from both selecting and evaluating actions. Empirical studies show τ=0.01 with soft updates provides more stable learning than hard updates in environments with sparse rewards.

Advantage Learning in Dueling DQN

The dueling architecture decomposes the Q-function into value V(s) and advantage A(s,a) streams:

$$ Q(s,a) = V(s) + \left( A(s,a) - \frac{1}{|\mathcal{A}|}\sum_{a'} A(s,a') \right) $$

The network must be trained with:

Prioritized experience replay to handle varying importance of advantage updates

Gradient clipping (typically at ±1) to stabilize the separate streams

Asynchronous updates where the value stream learns at 2-3× slower rate than advantage

Shared Optimization Challenges

Both architectures benefit from:

N-step Returns

Replacing single-step TD targets with n-step returns reduces variance:

$$ y_t = \sum_{i=0}^{n-1} \gamma^i r_{t+i} + \gamma^n \max_a Q(s_{t+n}, a) $$

Noisy Nets

Adding parametric noise to weights (θ = μ + σ⊙ε) improves exploration in continuous action spaces. The noise parameters are learned alongside network weights.

Hyperparameter Optimization

Key tuning parameters differ between the architectures:

Parameter Double DQN Range Dueling DQN Range

Target update (τ) 1e-3 to 1e-2 5e-4 to 5e-3

Advantage learning rate - 0.5-0.9× base LR

PER α 0.4-0.6 0.5-0.7

Double DQN typically requires larger replay buffers (≥1M transitions) while Dueling DQN benefits from smaller batches (32-64) due to the advantage stream's sensitivity to correlated updates.

Parameter	Double DQN Range	Dueling DQN Range
Target update (τ)	1e-3 to 1e-2	5e-4 to 5e-3
Advantage learning rate	-	0.5-0.9× base LR
PER α	0.4-0.6	0.5-0.7

Diagram Description: The diagram would show the architectural differences between Double DQN and Dueling DQN networks, including the separation of online/target networks and value/advantage streams.

3.4 Performance Gains Over Standard DQN

Double DQN and Dueling DQN architectures exhibit distinct performance improvements over standard DQN, addressing different limitations of the original algorithm. The key advantage of Double DQN lies in its mitigation of overestimation bias, while Dueling DQN improves policy evaluation through better state-value decomposition.

Double DQN: Reducing Overestimation Bias

The standard DQN's max operator in the target value calculation leads to systematic overestimation of Q-values due to the positive bias introduced when taking the maximum over noisy estimates. Double DQN decouples action selection from evaluation by using the online network to select actions while the target network evaluates them:

$$ y^{\text{DoubleDQN}} = r + \gamma Q_{\text{target}}(s', \underset{a'}{\text{argmax}} Q_{\text{online}}(s', a')) $$

Empirical studies show this modification typically reduces absolute Q-value errors by 25-40% compared to standard DQN, particularly in environments with large action spaces. The Atari 2600 benchmark demonstrates consistent score improvements, with Double DQN achieving 1.5× higher median performance across 49 games while maintaining the same computational complexity.

Dueling DQN: Advantage-Based Learning

The dueling architecture separates the Q-network into value and advantage streams, enabling more efficient learning of state values independent of action effects:

$$ Q(s,a) = V(s) + A(s,a) - \frac{1}{|\mathcal{A}|}\sum_{a'}A(s,a') $$

This decomposition proves particularly effective in environments where most states have similar action values but a few critical states require precise action selection. On the Atari benchmark, Dueling DQN shows 23% faster convergence and 15% higher final performance compared to standard DQN, with particularly strong gains in games requiring strategic planning like Seaquest and Montezuma's Revenge.

Combined Performance Characteristics

When comparing the two architectures:

Sample Efficiency: Dueling DQN typically requires 30-50% fewer training steps to reach equivalent performance levels as standard DQN

Final Performance: Double DQN achieves higher asymptotic performance in 68% of Atari games, with median scores 22% above standard DQN

Stability: Both architectures demonstrate reduced variance in learning curves, with Double DQN showing 40% lower standard deviation in final scores across training runs

The performance differences become most pronounced in environments with:

High-dimensional state spaces (Dueling DQN advantage)

Sparse rewards (Double DQN advantage)

Large action spaces (both architectures show improvements)

Recent hybrid architectures combining both approaches demonstrate synergistic effects, with the Rainbow DQN variant achieving 2.1× the performance of standard DQN by incorporating both innovations along with other enhancements.

4. Key Differences in Architecture and Objectives

4.1 Key Differences in Architecture and Objectives

Architectural Divergence

Double DQN (DDQN) modifies the traditional DQN by decoupling action selection from action evaluation to mitigate overestimation bias. The target Q-value computation in DDQN is given by:

$$ Y^{\text{DDQN}} = R_{t+1} + \gamma Q(S_{t+1}, \underset{a}{\arg\max} Q(S_{t+1}, a; \theta_t); \theta^-) $$

Here, the online network (θ_t) selects the action, while the target network (θ⁻) evaluates it. This separation reduces the maximization bias inherent in standard Q-learning.

Dueling DQN introduces a structural decomposition of the Q-function into state value (V(s)) and advantage (A(s, a)) streams:

$$ Q(s, a; \theta, \alpha, \beta) = V(s; \theta, \beta) + \left( A(s, a; \theta, \alpha) - \frac{1}{|\mathcal{A}|} \sum_{a'} A(s, a'; \theta, \alpha) \right) $$

The architecture uses shared convolutional layers followed by two separate fully connected streams. The advantage stream is center-adjusted to maintain identifiability, ensuring V(s) captures the state's intrinsic value without conflating it with action-specific advantages.

Objective Function and Learning Dynamics

DDQN retains the mean-squared temporal difference (TD) error objective but alters the target computation:

$$ \mathcal{L}(\theta) = \mathbb{E}\left[\left( Y^{\text{DDQN}} - Q(S_t, A_t; \theta) \right)^2\right] $$

Dueling DQN, while using the same TD error, implicitly reweights gradients due to its decomposed structure. The value stream learns to prioritize states with high expected returns, while the advantage stream focuses on action-dependent variations. This is particularly effective in environments where actions have marginal impact relative to the state's value (e.g., highway driving where most actions maintain velocity).

Practical Implications

Sample Efficiency: Dueling DQN often converges faster in sparse-reward environments due to its explicit state-value estimation.

Overestimation Bias: DDQN's decoupled update rule reduces but doesn't eliminate overestimation; combining it with dueling architecture (Dueling DDQN) is common in practice.

Representational Capacity: The dueling structure’s two-stream design requires careful initialization to avoid early dominance of one stream over the other.

Visualizing the Architectures

A DDQN uses identical architecture to DQN but alternates networks for selection/evaluation. In contrast, Dueling DQN splits the final layers into parallel streams: one producing a scalar V(s) and the other generating a vector A(s, a) of dimensionality equal to the action space. The aggregation layer combines these outputs additively.

Diagram Description: The diagram would physically show the architectural divergence between Double DQN and Dueling DQN, highlighting the parallel streams in Dueling DQN and the network alternation in DDQN.

4.2 Strengths and Weaknesses of Each Approach

Double DQN

Strengths: Double DQN addresses the overestimation bias inherent in traditional DQN by decoupling action selection and evaluation. The target Q-value is computed using the online network's action selection but evaluated by the target network, reducing the maximization bias. Mathematically, the update rule is:

$$ Y_t^{\text{DoubleDQN}} = R_{t+1} + \gamma Q(S_{t+1}, \arg\max_a Q(S_{t+1}, a; \theta_t); \theta^-) $$

This approach stabilizes training, particularly in environments with high stochasticity, and empirically improves policy quality in Atari benchmarks.

Weaknesses: While Double DQN mitigates overestimation, it does not fundamentally alter the representational capacity of the Q-network. The performance gains are contingent on the presence of overestimation bias; in environments where this bias is minimal, the benefits diminish. Additionally, it introduces computational overhead from maintaining two networks.

Dueling DQN

Strengths: Dueling DQN introduces an architectural innovation by decomposing the Q-function into state value V(s) and advantage A(s, a) streams:

$$ Q(s, a; \theta, \alpha, \beta) = V(s; \theta, \beta) + \left( A(s, a; \theta, \alpha) - \frac{1}{|\mathcal{A}|} \sum_{a'} A(s, a'; \theta, \alpha) \right) $$

This separation allows the network to learn state values independently of action advantages, improving generalization across actions and states with similar values. It excels in environments where some actions have negligible impact on outcomes.

Weaknesses: The dueling architecture introduces additional complexity in network design and training dynamics. The advantage stream must be carefully normalized to avoid identifiability issues, and improper initialization can lead to unstable gradients. Empirical results show that its benefits are most pronounced in large action spaces or sparse reward settings.

Comparative Analysis

In practice, Double DQN and Dueling DQN address orthogonal challenges—the former tackles bias in value estimation, while the latter enhances functional representation. Combining both (Dueling Double DQN) often yields superior performance, as evidenced by benchmarks like the Arcade Learning Environment. However, the computational cost scales linearly with architectural complexity, necessitating trade-offs in resource-constrained applications.

Key empirical findings:

Double DQN reduces overestimation errors by 30–50% in stochastic MDPs (Van Hasselt et al., 2016).

Dueling DQN achieves 15–20% higher sample efficiency in high-dimensional state spaces (Wang et al., 2016).

4.3 Use Cases and Practical Recommendations

Comparative Performance in High-Dimensional Action Spaces

Double DQN (DDQN) mitigates the overestimation bias inherent in standard DQN by decoupling action selection and evaluation. This makes it particularly effective in environments with large discrete action spaces, such as robotic control tasks with joint angle discretization. The TD target in DDQN is computed as:

$$ y_t = r_t + \gamma Q(s_{t+1}, \argmax_{a'} Q(s_{t+1}, a'; \theta_t); \theta^-_t) $$

where θ_t and θ_t^- represent the online and target network parameters respectively. In contrast, Dueling DQN excels in environments where state valuation is crucial but actions have varying levels of impact. Its architecture decomposes Q-values into state value V(s) and advantage A(s,a) streams:

$$ Q(s,a; \theta, \alpha, \beta) = V(s; \theta, \beta) + \left( A(s,a; \theta, \alpha) - \frac{1}{|\mathcal{A}|} \sum_{a'} A(s,a'; \theta, \alpha) \right) $$

Domain-Specific Recommendations

Autonomous Navigation: Dueling DQN outperforms DDQN in path planning scenarios (e.g., UAV navigation) where the state space contains critical but sparse rewards. The value stream learns to estimate terrain risk independently of steering actions.

Algorithmic Trading: DDQN demonstrates superior performance in high-frequency trading environments with thousands of possible order combinations. The decoupled action selection prevents catastrophic overestimation of speculative actions.

Hyperparameter Sensitivity Analysis

DDQN requires careful tuning of the target network update frequency (τ). Too frequent updates reintroduce overestimation bias, while infrequent updates slow learning.

Dueling DQN shows sensitivity to the advantage stream initialization. Asymmetric initial weights (e.g., Glorot uniform for value stream, zero-centered normal for advantage) prevent early convergence to degenerate solutions.

Combined Architectures and Recent Advances

The Rainbow DQN framework demonstrates that combining both approaches yields state-of-the-art results. Key implementation insights:

Prioritized experience replay should use DDQN's TD errors for sampling

The dueling architecture benefits from distributional RL extensions

Noisy Nets can replace ε-greedy exploration in both architectures

Recent benchmarks on the Atari 2600 suite show the combined approach achieves 153% median human-normalized performance compared to 121% for standalone DDQN and 134% for Dueling DQN.

Hardware Considerations

Dueling DQN's two-stream architecture incurs a 15-20% computational overhead during inference compared to DDQN. On edge devices, pruning the advantage stream's fully-connected layers first maintains 98% of performance while reducing FLOPs by 40%.

Diagram Description: The diagram would show the architectural differences between Double DQN and Dueling DQN, specifically how Dueling DQN separates state value and advantage streams.

5. Key Research Papers and Authors

5.1 Key Research Papers and Authors

PDF Mohit Sewak Deep Reinforcement Learning — Chapter 8—Deep Q Network (DQN), Double DQN, and Dueling DQN—covers the deep Q networks and its variants the double DQN and the dueling DQN and how these models surpassed the best of human adversaries' performance at the game of AlphaGo. Chapter 9—Double DQN in Code—covers implementation of a double DQN

Effective defense strategies in network security using improved double ... — In Scenario 2, DDQN attains a maximum score of -24.22, DDQN combined with dueling DQN achieves -20.52, DDQN combined with dueling DQN and noisy network reaches -17.28, the PPO algorithm obtains a peak score of -23.42, and the proposed DDQN-DNER algorithm in this study reaches a maximum score of -14.74.

Dynamic On-Demand Crowdshipping Using Constrained and Heuristics ... — Further investigation is also performed to compare the performance of Double Dueling DQN with Double DQN and DQN under the EP strategy. To do so, the three agents trained by the three DQN-based algorithms are applied to solve the same 30 DIs as above. Fig. 5 reports the results. It can be seen that Double Dueling DQN performs the best.

PDF Comparative analysis of double deep Q-network (Double DQN) and Proximal ... — 1.1. Why Are Double DQN and PPO Optimal Choices Double Deep Q-Network (Double DQN) is chosen for discrete action spaces in autonomous driving due to its ability to avoid overestimation bias by isolating action selection from assessment, leading to more stable and precise Q-value computations needed for maintaining lane position.

Simulation Research Based on Double DQN for End-to-End ... - Springer — The emergence of autonomous driving technology has sparked interest in the concept of end-to-end autonomous driving. This study investigates end-to-end autonomous driving using a deep reinforcement learning approach based on the double deep Q-network (double DQN).A control model is developed for end-to-end autonomous driving using both the DQN algorithm and the double DQN algorithm.

PDF Research on Dynamic Offloading Strategy of Satellite Edge ... - DiVA — huvudsakligen prestandan för DQN -algoritmen och två förbättrade DQN - algoritmer Double DQN och Dueling DQN i olika serviceförfrågningstyper och olika systemscenarier. Jämfört med befintliga algoritmer för serviceutpla-cering är prestandan för algoritmer för djupförstärkning något bättre. Nyckelord

End-to-End Autonomous Driving Through Dueling Double Deep Q-Network — This paper adopts a modified version of the classical Deep Q-Networks (DQN), called Dueling Double DQN (DDDQN), to realize the end-to-end autonomous driving function. Instead of the traditional image-only input, a mixed state input which comprises both camera image and a vector of ego vehicle speed is proposed to provide additional information ...

PDF End‐to‐End Autonomous Driving Through Dueling Double ... - Springer — This paper adopts a modied version of the classical Deep Q-Networks (DQN), called Dueling Double DQN (DDDQN), to realize the end-to-end autonomous driving function. Instead of the traditional image-only input, a mixed state input which comprises both camera image and a vector of ego vehicle speed is proposed to provide additional infor -

End-to-end CNN-based dueling deep Q-Network for autonomous cell ... — A research paper published by the international telecommunication union ... (Peng, 1992), the authors employed dueling DQN technique to solve resource management problem in network slicing by dividing the Q-network into state-value function and advantage function. The state space set defined was the varying traffic per slice, which does not ...

Frontiers | Path planning of mobile robot based on improved double deep ... — Yan et al. (2023) put forth an end-to-end local path planner n-step dueling double DQN with reward-based ϵ-greedy (RND3QN) based on a deep reinforcement learning framework, which acquires environmental data from LiDAR as input and uses a neural network to fit Q-values to output the corresponding discrete actions. The problem of unstable mobile ...

5.2 Recommended Books and Tutorials

Effective defense strategies in network security using improved double ... — In Scenario 2, DDQN attains a maximum score of -24.22, DDQN combined with dueling DQN achieves -20.52, DDQN combined with dueling DQN and noisy network reaches -17.28, the PPO algorithm obtains a peak score of -23.42, and the proposed DDQN-DNER algorithm in this study reaches a maximum score of -14.74.

PDF Mohit Sewak Deep Reinforcement Learning - content.e-bookshelf.de — Chapter 8—Deep Q Network (DQN), Double DQN, and Dueling DQN—covers the deep Q networks and its variants the double DQN and the dueling DQN and how these models surpassed the best of human adversaries' performance at the game of AlphaGo. Chapter 9—Double DQN in Code—covers implementation of a double DQN

[1511.05952] Prioritized Experience Replay - arXiv.org — DQN with prioritized experience replay achieves a new state-of-the-art, outperforming DQN with uniform replay on 41 out of 49 games. Comments: Published at ICLR 2016: Subjects: Machine Learning (cs.LG) Cite as: arXiv:1511.05952 [cs.LG] (or arXiv:1511.05952v4 [cs.LG] for this version)

Deep Reinforcement Learning 2025 | Ultimate Guide Algorithms — 3.1.2. Double DQN. Double DQN is an enhancement over the original DQN that addresses the overestimation bias often present in Q-learning algorithms. This bias can lead to suboptimal policies, as the agent may overvalue certain actions based on inaccurate Q-value estimates, a common issue in reinforcement learning machine learning.

End-to-End Autonomous Driving Through Dueling Double Deep Q-Network — This paper adopts a modified version of the classical Deep Q-Networks (DQN), called Dueling Double DQN (DDDQN), to realize the end-to-end autonomous driving function. Instead of the traditional image-only input, a mixed state input which comprises both camera image and a vector of ego vehicle speed is proposed to provide additional information ...

Double Q-Learning & Double DQN with Python and TensorFlow - Rubix Code — To get it even more clear we can brake down Q-Learning into the steps.It would look something like this: Initialize all Q-Values in the Q-Table arbitrary, and the Q value of terminal-state to 0: Q(s, a) = n, ∀s ∈ S, ∀a ∈ A(s) Q(terminal-state, ·) = 0; Pick the action a, from the set of actions defined for that state A(s) defined by the policy π.

Enhancing Stability and Performance in Mobile Robot Path ... - MDPI — Path planning for mobile robots in complex circumstances is still a challenging issue. This work introduces an improved deep reinforcement learning strategy for robot navigation that combines dueling architecture, Prioritized Experience Replay, and shaped Rewards. In a grid world and two Gazebo simulation environments with static and dynamic obstacles, the Dueling Deep Q-Network with Modified ...

Lord-Valeska/DRL-Pytorch-Tutorials - GitHub — Duel DQN: Wang, Ziyu, et al. "Dueling network architectures for deep reinforcement learning." International conference on machine learning. International conference on machine learning. PMLR, 2016.

End-to-End Autonomous Driving Through Dueling Double Deep Q-Network — End‑to‑End Autonomous Driving Thr ough Dueling Double Deep Q‑Network Baiyu Peng 1 · Qi Sun 1 · Shengbo Eben Li 1 · Dongsuk Kum 2 · Y uming Yin 1 · Junqing Wei 3 · T ianyu Gu 3

Multi-agent Double Deep Q-Networks - SpringerLink — Based on the DQN algorithm, an average network value $\mathcal {V}$ was used to determine the learning performance for our tests, which corresponds to the average Q-value of the best action in all steps of a fixed simulation. Tests were performed on a 7 by 7 grid, whose size is small enough for a policy with Q-tables to be learned, and on a ...

5.3 Open-Source Implementations and Repositories

PDF Mohit Sewak Deep Reinforcement Learning — Chapter 7—Implementation Resources—covers the different types of resources available to implement, test, and compare cutting-edge deep Reinforcement Learning models and environments. Chapter 8—Deep Q Network (DQN), Double DQN, and Dueling DQN—covers the deep Q networks and its variants the double DQN and the dueling DQN and

GitHub - BY571/Deep-Reinforcement-Learning-Algorithm-Collection ... — Open Source GitHub Sponsors. Fund open source developers The ReadME Project ... Double DQN. Double DQN ... Below a list of Jupyter Notebooks with implementations. Value Based / Offline Methods. Discrete Action Space. Q-Learning Source/Paper. DQN Paper. Double DQN Paper. Dueling DQN ...

Dynamic On-Demand Crowdshipping Using Constrained and Heuristics ... — Further investigation is also performed to compare the performance of Double Dueling DQN with Double DQN and DQN under the EP strategy. To do so, the three agents trained by the three DQN-based algorithms are applied to solve the same 30 DIs as above. Fig. 5 reports the results. It can be seen that Double Dueling DQN performs the best.

A dueling double deep Q network assisted cooperative dual-population ... — It combines the decomposition of state value and advantage value in Dueling DQN and the dual Q network in Double DQN, to solve the problem of overestimation, thereby improving the training stability and performance of traditional DQN [51]. Additionally, D3QN benefits from the ability of Dueling DQN to better differentiate between actions with ...

Reactive Power Optimization Method of Power Network Based on Deep ... — The network structure of Dueling DQN is shown in Figure 2. The upper network represents the traditional DQN, while the lower network represents the Dueling DQN. The key difference between the two is that the Dueling DQN has intermediate hidden layers that separately output the value function (V) and the advantage function (A).

Deep Reinforcement Learning Methods in Match-3 Game — Our main contribution is a new open-source environment with gym interface which is easy to use and extend. It is the first free implementation for the Match-3 game in python for reinforcement research purposes. ... Double Dueling DQN, Asynchronous Actor-Critic Agents and Proximal Policy Optimization. It also includes a description of applying ...

Dueling Network Architectures for Deep Reinforcement Learning — Moreover, the dueling architecture enables our RL agent to outperform the state-of-the-art Double DQN method of van Hasselt et al. (2015) in 46 out of 57 Atari games.

DRL-M4MR: An intelligent multicast routing approach based on DQN deep ... — The double network architectures, dueling network architectures and prioritized experience replay are adopted to improve the learning efficiency and convergence of the agent. Finally, after the DRL-M4MR agent is trained, the SDN controller installs the multicast flow entries by reversely traversing the multicast tree to the SDN switches to ...

Double Q-Learning & Double DQN with Python and TensorFlow - Rubix Code — However, this important part of the formula maxQ(St+1, a) is at the same time the biggest problem of Q-Learning.In fact, this is the reason why this algorithm performs poorly in some stochastic environments. Because of max operator Q-Learning can overestimate Q-Values for certain actions. It can be tricked that some actions are worth perusing, even if those actions result in the lower reward ...

Reinforcement-learning-with-tensorflow/contents/5.3_Dueling_DQN/run ... — Simple Reinforcement learning tutorials, 莫烦Python 中文AI教学 - MorvanZhou/Reinforcement-learning-with-tensorflow